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<p><a class="glightbox" href="../assets/covers/chapter_searching.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Searching" class="cover-image" src="../assets/covers/chapter_searching.jpg" /></a></p> <p><a class="glightbox" href="../assets/covers/chapter_searching.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Searching" class="cover-image" src="../assets/covers/chapter_searching.jpg" /></a></p>
<div class="admonition abstract"> <div class="admonition abstract">
<p class="admonition-title">Abstract</p> <p class="admonition-title">Abstract</p>
<p>Searching is an unknown adventure, where we may need to traverse every corner of a mysterious space, or perhaps quickly pinpoint our target.</p> <p>Searching is an adventure into the unknown; where we may need to traverse every corner of a mysterious space, or perhaps we’ll quickly locate our target.</p>
<p>In this journey of discovery, each exploration may yield an unexpected answer.</p> <p>On this journey of discovery, each exploration may end up with an unexpected answer.</p>
</div> </div>
<h2 id="chapter-contents">Chapter contents<a class="headerlink" href="#chapter-contents" title="Permanent link">&para;</a></h2> <h2 id="chapter-contents">Chapter contents<a class="headerlink" href="#chapter-contents" title="Permanent link">&para;</a></h2>
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<h1 id="106-summary">10.6 &nbsp; Summary<a class="headerlink" href="#106-summary" title="Permanent link">&para;</a></h1> <h1 id="106-summary">10.6 &nbsp; Summary<a class="headerlink" href="#106-summary" title="Permanent link">&para;</a></h1>
<ul> <ul>
<li>Binary search depends on the order of data and performs the search by iteratively halving the search interval. It requires the input data to be sorted and is only applicable to arrays or array-based data structures.</li> <li>Binary search depends on the order of data and performs the search by iteratively halving the search interval. It requires the input data to be sorted and is only applicable to arrays or array-based data structures.</li>
<li>Brute force search locates data by traversing the data structure. Linear search is suitable for arrays and linked lists, while breadth-first search and depth-first search are suitable for graphs and trees. These algorithms are highly versatile, requiring no preprocessing of data, but have a higher time complexity of <span class="arithmatex">\(O(n)\)</span>.</li> <li>Brute force search may be required to locate an entry in an unordered dataset. Different search algorithms can be applied based on the data structure: Linear search is suitable for arrays and linked lists, while breadth-first search (BFS) and depth-first search (DFS) are suitable for graphs and trees. These algorithms are highly versatile, requiring no preprocessing of data, but they have a higher time complexity of <span class="arithmatex">\(O(n)\)</span>.</li>
<li>Hash search, tree search, and binary search are efficient searching methods, capable of quickly locating target elements in specific data structures. These algorithms are highly efficient, with time complexities reaching <span class="arithmatex">\(O(\log n)\)</span> or even <span class="arithmatex">\(O(1)\)</span>, but they usually require additional data structures.</li> <li>Hash search, tree search, and binary search are efficient search methods that can quickly locate target elements within specific data structures. These algorithms are highly efficient, with time complexities reaching <span class="arithmatex">\(O(\log n)\)</span> or even <span class="arithmatex">\(O(1)\)</span>, but they usually require extra space to accommodate additional data structures.</li>
<li>In practice, we need to analyze factors such as data volume, search performance requirements, data query and update frequencies, etc., to choose the appropriate search method.</li> <li>In practice, we need to analyze factors such as data volume, search performance requirements, data query and update frequencies, etc., to choose an appropriate search method.</li>
<li>Linear search is suitable for small or frequently updated data; binary search is suitable for large, sorted data; hash search is suitable for scenarios requiring high query efficiency without the need for range queries; tree search is appropriate for large dynamic data that needs to maintain order and support range queries.</li> <li>Linear search is ideal for small or frequently updated (volatile) data. Binary search works well for large and sorted data. Hash search is suitable for data that requires high query efficiency and does not need range queries. Tree search is best suited for large dynamic data that require maintaining order and need to support range queries.</li>
<li>Replacing linear search with hash search is a common strategy to optimize runtime, reducing the time complexity from <span class="arithmatex">\(O(n)\)</span> to <span class="arithmatex">\(O(1)\)</span>.</li> <li>Replacing linear search with hash search is a common strategy to optimize runtime performance, reducing the time complexity from <span class="arithmatex">\(O(n)\)</span> to <span class="arithmatex">\(O(1)\)</span>.</li>
</ul> </ul>
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<h1 id="71-binary-tree">7.1 &nbsp; Binary tree<a class="headerlink" href="#71-binary-tree" title="Permanent link">&para;</a></h1> <h1 id="71-binary-tree">7.1 &nbsp; Binary tree<a class="headerlink" href="#71-binary-tree" title="Permanent link">&para;</a></h1>
<p>A <u>binary tree</u> is a non-linear data structure that represents the hierarchical relationship between ancestors and descendants, embodying the divide-and-conquer logic of "splitting into two". Similar to a linked list, the basic unit of a binary tree is a node, each containing a value, a reference to the left child node, and a reference to the right child node.</p> <p>A <u>binary tree</u> is a non-linear data structure that represents the hierarchical relationship between ancestors and descendants and embodies the divide-and-conquer logic of "splitting into two". Similar to a linked list, the basic unit of a binary tree is a node, and each node contains a value, a reference to its left child node, and a reference to its right child node.</p>
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<p>Each node has two references (pointers), pointing to the <u>left-child node</u> and <u>right-child node</u>, respectively. This node is called the <u>parent node</u> of these two child nodes. When given a node of a binary tree, we call the tree formed by this node's left child and all nodes under it the <u>left subtree</u> of this node. Similarly, the <u>right subtree</u> can be defined.</p> <p>Each node has two references (pointers), pointing respectively to the <u>left-child node</u> and <u>right-child node</u>. This node is called the <u>parent node</u> of these two child nodes. When given a node of a binary tree, we call the tree formed by this node's left child and all nodes below it the <u>left subtree</u> of this node. Similarly, the <u>right subtree</u> can be defined.</p>
<p><strong>In a binary tree, except for leaf nodes, all other nodes contain child nodes and non-empty subtrees.</strong> As shown in Figure 7-1, if "Node 2" is considered as the parent node, then its left and right child nodes are "Node 4" and "Node 5," respectively. The left subtree is "the tree formed by Node 4 and all nodes under it," and the right subtree is "the tree formed by Node 5 and all nodes under it."</p> <p><strong>In a binary tree, except leaf nodes, all other nodes contain child nodes and non-empty subtrees.</strong> As shown in Figure 7-1, if "Node 2" is regarded as a parent node, its left and right child nodes are "Node 4" and "Node 5" respectively. The left subtree is formed by "Node 4" and all nodes beneath it, while the right subtree is formed by "Node 5" and all nodes beneath it.</p>
<p><a class="glightbox" href="../binary_tree.assets/binary_tree_definition.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Parent Node, child Node, subtree" class="animation-figure" src="../binary_tree.assets/binary_tree_definition.png" /></a></p> <p><a class="glightbox" href="../binary_tree.assets/binary_tree_definition.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Parent Node, child Node, subtree" class="animation-figure" src="../binary_tree.assets/binary_tree_definition.png" /></a></p>
<p align="center"> Figure 7-1 &nbsp; Parent Node, child Node, subtree </p> <p align="center"> Figure 7-1 &nbsp; Parent Node, child Node, subtree </p>
<h2 id="711-common-terminology-of-binary-trees">7.1.1 &nbsp; Common terminology of binary trees<a class="headerlink" href="#711-common-terminology-of-binary-trees" title="Permanent link">&para;</a></h2> <h2 id="711-common-terminology-of-binary-trees">7.1.1 &nbsp; Common terminology of binary trees<a class="headerlink" href="#711-common-terminology-of-binary-trees" title="Permanent link">&para;</a></h2>
<p>The commonly used terminology of binary trees is shown in Figure 7-2.</p> <p>The commonly used terminology of binary trees is shown in Figure 7-2.</p>
<ul> <ul>
<li><u>Root node</u>: The node at the top level of the binary tree, which has no parent node.</li> <li><u>Root node</u>: The node at the top level of a binary tree, which does not have a parent node.</li>
<li><u>Leaf node</u>: A node with no children, both of its pointers point to <code>None</code>.</li> <li><u>Leaf node</u>: A node that does not have any child nodes, with both of its pointers pointing to <code>None</code>.</li>
<li><u>Edge</u>: The line segment connecting two nodes, i.e., node reference (pointer).</li> <li><u>Edge</u>: A line segment that connects two nodes, representing a reference (pointer) between the nodes.</li>
<li>The <u>level</u> of a node: Incrementing from top to bottom, with the root node's level being 1.</li> <li>The <u>level</u> of a node: It increases from top to bottom, with the root node being at level 1.</li>
<li>The <u>degree</u> of a node: The number of children a node has. In a binary tree, the degree can be 0, 1, or 2.</li> <li>The <u>degree</u> of a node: The number of child nodes that a node has. In a binary tree, the degree can be 0, 1, or 2.</li>
<li>The <u>height</u> of a binary tree: The number of edges passed from the root node to the farthest leaf node.</li> <li>The <u>height</u> of a binary tree: The number of edges from the root node to the farthest leaf node.</li>
<li>The <u>depth</u> of a node: The number of edges passed from the root node to the node.</li> <li>The <u>depth</u> of a node: The number of edges from the root node to the node.</li>
<li>The <u>height</u> of a node: The number of edges from the farthest leaf node to the node.</li> <li>The <u>height</u> of a node: The number of edges from the farthest leaf node to the node.</li>
</ul> </ul>
<p><a class="glightbox" href="../binary_tree.assets/binary_tree_terminology.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Common Terminology of Binary Trees" class="animation-figure" src="../binary_tree.assets/binary_tree_terminology.png" /></a></p> <p><a class="glightbox" href="../binary_tree.assets/binary_tree_terminology.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Common Terminology of Binary Trees" class="animation-figure" src="../binary_tree.assets/binary_tree_terminology.png" /></a></p>
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<div class="admonition tip"> <div class="admonition tip">
<p class="admonition-title">Tip</p> <p class="admonition-title">Tip</p>
<p>Please note that we typically define "height" and "depth" as "the number of edges traversed", but some problems or textbooks may define them as "the number of nodes traversed". In such cases, both height and depth need to be incremented by 1.</p> <p>Please note that we usually define "height" and "depth" as "the number of edges traversed", but some questions or textbooks may define them as "the number of nodes traversed". In this case, both height and depth need to be incremented by 1.</p>
</div> </div>
<h2 id="712-basic-operations-of-binary-trees">7.1.2 &nbsp; Basic operations of binary trees<a class="headerlink" href="#712-basic-operations-of-binary-trees" title="Permanent link">&para;</a></h2> <h2 id="712-basic-operations-of-binary-trees">7.1.2 &nbsp; Basic operations of binary trees<a class="headerlink" href="#712-basic-operations-of-binary-trees" title="Permanent link">&para;</a></h2>
<h3 id="1-initializing-a-binary-tree">1. &nbsp; Initializing a binary tree<a class="headerlink" href="#1-initializing-a-binary-tree" title="Permanent link">&para;</a></h3> <h3 id="1-initializing-a-binary-tree">1. &nbsp; Initializing a binary tree<a class="headerlink" href="#1-initializing-a-binary-tree" title="Permanent link">&para;</a></h3>
<p>Similar to a linked list, begin by initialize nodes, then construct references (pointers).</p> <p>Similar to a linked list, the initialization of a binary tree involves first creating the nodes and then establishing the references (pointers) between them.</p>
<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div> <div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
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</details> </details>
<div class="admonition tip"> <div class="admonition tip">
<p class="admonition-title">Tip</p> <p class="admonition-title">Tip</p>
<p>It's important to note that inserting nodes may change the original logical structure of the binary tree, while removing nodes typically involves removing the node and all its subtrees. Therefore, in a binary tree, insertion and removal are usually performed through a coordinated set of operations to achieve meaningful outcomes.</p> <p>It should be noted that inserting nodes may change the original logical structure of the binary tree, while removing nodes typically involves removing the node and all its subtrees. Therefore, in a binary tree, insertion and removal are usually performed through a set of operations to achieve meaningful outcomes.</p>
</div> </div>
<h2 id="713-common-types-of-binary-trees">7.1.3 &nbsp; Common types of binary trees<a class="headerlink" href="#713-common-types-of-binary-trees" title="Permanent link">&para;</a></h2> <h2 id="713-common-types-of-binary-trees">7.1.3 &nbsp; Common types of binary trees<a class="headerlink" href="#713-common-types-of-binary-trees" title="Permanent link">&para;</a></h2>
<h3 id="1-perfect-binary-tree">1. &nbsp; Perfect binary tree<a class="headerlink" href="#1-perfect-binary-tree" title="Permanent link">&para;</a></h3> <h3 id="1-perfect-binary-tree">1. &nbsp; Perfect binary tree<a class="headerlink" href="#1-perfect-binary-tree" title="Permanent link">&para;</a></h3>
<p>As shown in Figure 7-4, in a <u>perfect binary tree</u>, all levels of nodes are fully filled. In a perfect binary tree, the degree of leaf nodes is <span class="arithmatex">\(0\)</span>, while the degree of all other nodes is <span class="arithmatex">\(2\)</span>; if the tree's height is <span class="arithmatex">\(h\)</span>, then the total number of nodes is <span class="arithmatex">\(2^{h+1} - 1\)</span>, showing a standard exponential relationship, reflecting the common phenomenon of cell division in nature.</p> <p>As shown in Figure 7-4, in a <u>perfect binary tree</u>, all levels are completely filled with nodes. In a perfect binary tree, leaf nodes have a degree of <span class="arithmatex">\(0\)</span>, while all other nodes have a degree of <span class="arithmatex">\(2\)</span>. The total number of nodes can be calculated as <span class="arithmatex">\(2^{h+1} - 1\)</span>, where <span class="arithmatex">\(h\)</span> is the height of the tree. This exhibits a standard exponential relationship, reflecting the common phenomenon of cell division in nature.</p>
<div class="admonition tip"> <div class="admonition tip">
<p class="admonition-title">Tip</p> <p class="admonition-title">Tip</p>
<p>Please note that in the Chinese community, a perfect binary tree is often referred to as a <u>full binary tree</u>.</p> <p>Please note that in the Chinese community, a perfect binary tree is often referred to as a <u>full binary tree</u>.</p>
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<p align="center"> Figure 7-4 &nbsp; Perfect binary tree </p> <p align="center"> Figure 7-4 &nbsp; Perfect binary tree </p>
<h3 id="2-complete-binary-tree">2. &nbsp; Complete binary tree<a class="headerlink" href="#2-complete-binary-tree" title="Permanent link">&para;</a></h3> <h3 id="2-complete-binary-tree">2. &nbsp; Complete binary tree<a class="headerlink" href="#2-complete-binary-tree" title="Permanent link">&para;</a></h3>
<p>As shown in Figure 7-5, a <u>complete binary tree</u> has only the bottom level nodes not fully filled, and the bottom level nodes are filled as far left as possible.</p> <p>As shown in Figure 7-5, a <u>complete binary tree</u> is a binary tree where only the nodes in the bottom level are not completely filled, and the nodes in the bottom level are filled from left to right as much as possible. Please note that a perfect binary tree is also a complete binary tree.</p>
<p><a class="glightbox" href="../binary_tree.assets/complete_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Complete binary tree" class="animation-figure" src="../binary_tree.assets/complete_binary_tree.png" /></a></p> <p><a class="glightbox" href="../binary_tree.assets/complete_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Complete binary tree" class="animation-figure" src="../binary_tree.assets/complete_binary_tree.png" /></a></p>
<p align="center"> Figure 7-5 &nbsp; Complete binary tree </p> <p align="center"> Figure 7-5 &nbsp; Complete binary tree </p>
<h3 id="3-full-binary-tree">3. &nbsp; Full binary tree<a class="headerlink" href="#3-full-binary-tree" title="Permanent link">&para;</a></h3> <h3 id="3-full-binary-tree">3. &nbsp; Full binary tree<a class="headerlink" href="#3-full-binary-tree" title="Permanent link">&para;</a></h3>
<p>As shown in Figure 7-6, a <u>full binary tree</u> has all nodes except leaf nodes having two children.</p> <p>As shown in Figure 7-6, a <u>full binary tree</u>, except for the leaf nodes, has two child nodes for all other nodes.</p>
<p><a class="glightbox" href="../binary_tree.assets/full_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Full binary tree" class="animation-figure" src="../binary_tree.assets/full_binary_tree.png" /></a></p> <p><a class="glightbox" href="../binary_tree.assets/full_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Full binary tree" class="animation-figure" src="../binary_tree.assets/full_binary_tree.png" /></a></p>
<p align="center"> Figure 7-6 &nbsp; Full binary tree </p> <p align="center"> Figure 7-6 &nbsp; Full binary tree </p>
<h3 id="4-balanced-binary-tree">4. &nbsp; Balanced binary tree<a class="headerlink" href="#4-balanced-binary-tree" title="Permanent link">&para;</a></h3> <h3 id="4-balanced-binary-tree">4. &nbsp; Balanced binary tree<a class="headerlink" href="#4-balanced-binary-tree" title="Permanent link">&para;</a></h3>
<p>As shown in Figure 7-7, in a <u>balanced binary tree</u>, the absolute difference in height between the left and right subtrees of any node does not exceed 1.</p> <p>As shown in Figure 7-7, in a <u>balanced binary tree</u>, the absolute difference between the height of the left and right subtrees of any node does not exceed 1.</p>
<p><a class="glightbox" href="../binary_tree.assets/balanced_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Balanced binary tree" class="animation-figure" src="../binary_tree.assets/balanced_binary_tree.png" /></a></p> <p><a class="glightbox" href="../binary_tree.assets/balanced_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Balanced binary tree" class="animation-figure" src="../binary_tree.assets/balanced_binary_tree.png" /></a></p>
<p align="center"> Figure 7-7 &nbsp; Balanced binary tree </p> <p align="center"> Figure 7-7 &nbsp; Balanced binary tree </p>
<h2 id="714-degeneration-of-binary-trees">7.1.4 &nbsp; Degeneration of binary trees<a class="headerlink" href="#714-degeneration-of-binary-trees" title="Permanent link">&para;</a></h2> <h2 id="714-degeneration-of-binary-trees">7.1.4 &nbsp; Degeneration of binary trees<a class="headerlink" href="#714-degeneration-of-binary-trees" title="Permanent link">&para;</a></h2>
<p>Figure 7-8 shows the ideal and degenerate structures of binary trees. A binary tree becomes a "perfect binary tree" when every level is filled; while it degenerates into a "linked list" when all nodes are biased toward one side.</p> <p>Figure 7-8 shows the ideal and degenerate structures of binary trees. A binary tree becomes a "perfect binary tree" when every level is filled; while it degenerates into a "linked list" when all nodes are biased toward one side.</p>
<ul> <ul>
<li>The perfect binary tree is the ideal situation, fully leveraging the "divide and conquer" advantage of binary trees.</li> <li>A perfect binary tree is an ideal scenario where the "divide and conquer" advantage of a binary tree can be fully utilized.</li>
<li>A linked list is another extreme, where operations become linear, degrading the time complexity to <span class="arithmatex">\(O(n)\)</span>.</li> <li>On the other hand, a linked list represents another extreme where all operations become linear, resulting in a time complexity of <span class="arithmatex">\(O(n)\)</span>.</li>
</ul> </ul>
<p><a class="glightbox" href="../binary_tree.assets/binary_tree_best_worst_cases.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="The Best and Worst Structures of Binary Trees" class="animation-figure" src="../binary_tree.assets/binary_tree_best_worst_cases.png" /></a></p> <p><a class="glightbox" href="../binary_tree.assets/binary_tree_best_worst_cases.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="The Best and Worst Structures of Binary Trees" class="animation-figure" src="../binary_tree.assets/binary_tree_best_worst_cases.png" /></a></p>
<p align="center"> Figure 7-8 &nbsp; The Best and Worst Structures of Binary Trees </p> <p align="center"> Figure 7-8 &nbsp; The Best and Worst Structures of Binary Trees </p>
<p>As shown in Table 7-1, in the best and worst structures, the number of leaf nodes, total number of nodes, and height of the binary tree reach their maximum or minimum values.</p> <p>As shown in Table 7-1, in the best and worst structures, the binary tree achieves either maximum or minimum values for leaf node count, total number of nodes, and height.</p>
<p align="center"> Table 7-1 &nbsp; The Best and Worst Structures of Binary Trees </p> <p align="center"> Table 7-1 &nbsp; The Best and Worst Structures of Binary Trees </p>
<div class="center-table"> <div class="center-table">

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Contributors Contributors
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<p> <p>
This book has been optimized by the efforts of over 180 contributors. We sincerely thank them for their invaluable time and contributions! This book has been refined by the efforts of over 180 contributors. We sincerely thank them for their invaluable time and contributions!
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<div class="highlight"><span class="filename">heap.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 初始化堆積 */</span> <div class="highlight"><span class="filename">heap.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 初始化堆積 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// 初始化小頂堆積</span> <a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// 初始化小頂堆積</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span> <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="c1">// 初始化大頂堆積（使用 lambda 表示式修改 Comparator 即可）</span> <a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="c1">// 初始化大頂堆積（使用 lambda 表示式修改 Comparer 即可）</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">Comparer</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">.</span><span class="n">Create</span><span class="p">((</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">y</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">x</span><span class="p">));</span> <a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">Comparer</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">.</span><span class="n">Create</span><span class="p">((</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">y</span><span class="p">.</span><span class="n">CompareTo</span><span class="p">(</span><span class="n">x</span><span class="p">)));</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a> <a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm">/* 元素入堆積 */</span> <a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm">/* 元素入堆積 */</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">1</span><span class="p">);</span> <a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>

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<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="p">}</span> <a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="p">}</span>
<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a> <a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a>
<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="cm">/* 雜湊表元素插入 */</span> <a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="cm">/* 雜湊表元素插入 */</span>
<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">HashTable</span><span class="w"> </span><span class="o">**</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w"> </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">t</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">find</span><span class="p">(</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">);</span> <a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w"> </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">t</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">find</span><span class="p">(</span><span class="o">*</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">);</span>
<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">t</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">t</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w"> </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">HashTable</span><span class="p">));</span> <a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w"> </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">HashTable</span><span class="p">));</span>
<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span> <a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w"> </span><span class="n">HASH_ADD_INT</span><span class="p">(</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">);</span> <a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w"> </span><span class="n">HASH_ADD_INT</span><span class="p">(</span><span class="o">*</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">);</span>
<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w"> </span><span class="n">t</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span> <a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w"> </span><span class="n">t</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w"> </span><span class="p">}</span>
@ -4059,7 +4059,7 @@
<a id="__codelineno-24-35" name="__codelineno-24-35" href="#__codelineno-24-35"></a><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span> <a id="__codelineno-24-35" name="__codelineno-24-35" href="#__codelineno-24-35"></a><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
<a id="__codelineno-24-36" name="__codelineno-24-36" href="#__codelineno-24-36"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span> <a id="__codelineno-24-36" name="__codelineno-24-36" href="#__codelineno-24-36"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a id="__codelineno-24-37" name="__codelineno-24-37" href="#__codelineno-24-37"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-24-37" name="__codelineno-24-37" href="#__codelineno-24-37"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-24-38" name="__codelineno-24-38" href="#__codelineno-24-38"></a><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="n">hashtable</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="p">);</span> <a id="__codelineno-24-38" name="__codelineno-24-38" href="#__codelineno-24-38"></a><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="o">&amp;</span><span class="n">hashtable</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-24-39" name="__codelineno-24-39" href="#__codelineno-24-39"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-24-39" name="__codelineno-24-39" href="#__codelineno-24-39"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-24-40" name="__codelineno-24-40" href="#__codelineno-24-40"></a><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span> <a id="__codelineno-24-40" name="__codelineno-24-40" href="#__codelineno-24-40"></a><span class="w"> </span><span class="o">*</span><span class="n">returnSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-24-41" name="__codelineno-24-41" href="#__codelineno-24-41"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span> <a id="__codelineno-24-41" name="__codelineno-24-41" href="#__codelineno-24-41"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>

5
zh-hant/chapter_sorting/counting_sort/index.html
View file

@ -4406,8 +4406,9 @@
<a id="__codelineno-24-30" name="__codelineno-24-30" href="#__codelineno-24-30"></a><span class="w"> </span><span class="c1">// 使用結果陣列 res 覆蓋原陣列 nums</span> <a id="__codelineno-24-30" name="__codelineno-24-30" href="#__codelineno-24-30"></a><span class="w"> </span><span class="c1">// 使用結果陣列 res 覆蓋原陣列 nums</span>
<a id="__codelineno-24-31" name="__codelineno-24-31" href="#__codelineno-24-31"></a><span class="w"> </span><span class="n">memcpy</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span> <a id="__codelineno-24-31" name="__codelineno-24-31" href="#__codelineno-24-31"></a><span class="w"> </span><span class="n">memcpy</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
<a id="__codelineno-24-32" name="__codelineno-24-32" href="#__codelineno-24-32"></a><span class="w"> </span><span class="c1">// 5. 釋放記憶體</span> <a id="__codelineno-24-32" name="__codelineno-24-32" href="#__codelineno-24-32"></a><span class="w"> </span><span class="c1">// 5. 釋放記憶體</span>
<a id="__codelineno-24-33" name="__codelineno-24-33" href="#__codelineno-24-33"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">counter</span><span class="p">);</span> <a id="__codelineno-24-33" name="__codelineno-24-33" href="#__codelineno-24-33"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-24-34" name="__codelineno-24-34" href="#__codelineno-24-34"></a><span class="p">}</span> <a id="__codelineno-24-34" name="__codelineno-24-34" href="#__codelineno-24-34"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">counter</span><span class="p">);</span>
<a id="__codelineno-24-35" name="__codelineno-24-35" href="#__codelineno-24-35"></a><span class="p">}</span>
</code></pre></div> </code></pre></div>
</div> </div>
<div class="tabbed-block"> <div class="tabbed-block">

88
zh-hant/chapter_sorting/radix_sort/index.html
View file

@ -4141,48 +4141,52 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSortDigit</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSortDigit</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w"> </span><span class="c1">// 十進位制的位範圍為 0~9 ，因此需要長度為 10 的桶陣列</span> <a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w"> </span><span class="c1">// 十進位制的位範圍為 0~9 ，因此需要長度為 10 的桶陣列</span>
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">((</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">10</span><span class="p">));</span> <a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">((</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">10</span><span class="p">));</span>
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w"> </span><span class="c1">// 統計 0~9 各數字的出現次數</span> <a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w"> </span><span class="n">memset</span><span class="p">(</span><span class="n">counter</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">10</span><span class="p">);</span><span class="w"> </span><span class="c1">// 初始化為 0 以支持後續記憶體釋放</span>
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w"> </span><span class="c1">// 統計 0~9 各數字的出現次數</span>
<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w"> </span><span class="c1">// 獲取 nums[i] 第 k 位，記為 d</span> <a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span> <a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w"> </span><span class="c1">// 獲取 nums[i] 第 k 位，記為 d</span>
<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w"> </span><span class="c1">// 統計數字 d 的出現次數</span> <a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">++</span><span class="p">;</span> <a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w"> </span><span class="c1">// 統計數字 d 的出現次數</span>
<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w"> </span><span class="c1">// 求前綴和，將“出現個數”轉換為“陣列索引”</span> <a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w"> </span><span class="c1">// 求前綴和，將“出現個數”轉換為“陣列索引”</span>
<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span> <a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w"> </span><span class="c1">// 倒序走訪，根據桶內統計結果，將各元素填入 res</span> <a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">size</span><span class="p">);</span> <a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w"> </span><span class="c1">// 倒序走訪，根據桶內統計結果，將各元素填入 res</span>
<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">size</span><span class="p">);</span>
<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span> <a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 獲取 d 在陣列中的索引 j</span> <a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span><span class="w"> </span><span class="c1">// 將當前元素填入索引 j</span> <a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 獲取 d 在陣列中的索引 j</span>
<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 將 d 的數量減 1</span> <a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span><span class="w"> </span><span class="c1">// 將當前元素填入索引 j</span>
<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 將 d 的數量減 1</span>
<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w"> </span><span class="c1">// 使用結果覆蓋原陣列 nums</span> <a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w"> </span><span class="c1">// 使用結果覆蓋原陣列 nums</span>
<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">];</span> <a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="p">}</span> <a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a> <a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="w"> </span><span class="c1">// 釋放記憶體</span>
<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a><span class="cm">/* 基數排序 */</span> <a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a><span class="kt">void</span><span class="w"> </span><span class="nf">radixSort</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">counter</span><span class="p">);</span>
<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="w"> </span><span class="c1">// 獲取陣列的最大元素，用於判斷最大位數</span> <a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a><span class="p">}</span>
<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">INT32_MIN</span><span class="p">;</span> <a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a>
<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">size_t</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="cm">/* 基數排序 */</span>
<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">max</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a><span class="kt">void</span><span class="w"> </span><span class="nf">radixSort</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span> <a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a><span class="w"> </span><span class="c1">// 獲取陣列的最大元素，用於判斷最大位數</span>
<a id="__codelineno-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">INT32_MIN</span><span class="p">;</span>
<a id="__codelineno-10-44" name="__codelineno-10-44" href="#__codelineno-10-44"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-10-44" name="__codelineno-10-44" href="#__codelineno-10-44"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-45" name="__codelineno-10-45" href="#__codelineno-10-45"></a><span class="w"> </span><span class="c1">// 按照從低位到高位的順序走訪</span> <a id="__codelineno-10-45" name="__codelineno-10-45" href="#__codelineno-10-45"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">max</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">exp</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span> <a id="__codelineno-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-10-47" name="__codelineno-10-47" href="#__codelineno-10-47"></a><span class="w"> </span><span class="c1">// 對陣列元素的第 k 位執行計數排序</span> <a id="__codelineno-10-47" name="__codelineno-10-47" href="#__codelineno-10-47"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-48" name="__codelineno-10-48" href="#__codelineno-10-48"></a><span class="w"> </span><span class="c1">// k = 1 -&gt; exp = 1</span> <a id="__codelineno-10-48" name="__codelineno-10-48" href="#__codelineno-10-48"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-49" name="__codelineno-10-49" href="#__codelineno-10-49"></a><span class="w"> </span><span class="c1">// k = 2 -&gt; exp = 10</span> <a id="__codelineno-10-49" name="__codelineno-10-49" href="#__codelineno-10-49"></a><span class="w"> </span><span class="c1">// 按照從低位到高位的順序走訪</span>
<a id="__codelineno-10-50" name="__codelineno-10-50" href="#__codelineno-10-50"></a><span class="w"> </span><span class="c1">// 即 exp = 10^(k-1)</span> <a id="__codelineno-10-50" name="__codelineno-10-50" href="#__codelineno-10-50"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">exp</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
<a id="__codelineno-10-51" name="__codelineno-10-51" href="#__codelineno-10-51"></a><span class="w"> </span><span class="n">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span> <a id="__codelineno-10-51" name="__codelineno-10-51" href="#__codelineno-10-51"></a><span class="w"> </span><span class="c1">// 對陣列元素的第 k 位執行計數排序</span>
<a id="__codelineno-10-52" name="__codelineno-10-52" href="#__codelineno-10-52"></a><span class="p">}</span> <a id="__codelineno-10-52" name="__codelineno-10-52" href="#__codelineno-10-52"></a><span class="w"> </span><span class="c1">// k = 1 -&gt; exp = 1</span>
<a id="__codelineno-10-53" name="__codelineno-10-53" href="#__codelineno-10-53"></a><span class="w"> </span><span class="c1">// k = 2 -&gt; exp = 10</span>
<a id="__codelineno-10-54" name="__codelineno-10-54" href="#__codelineno-10-54"></a><span class="w"> </span><span class="c1">// 即 exp = 10^(k-1)</span>
<a id="__codelineno-10-55" name="__codelineno-10-55" href="#__codelineno-10-55"></a><span class="w"> </span><span class="n">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
<a id="__codelineno-10-56" name="__codelineno-10-56" href="#__codelineno-10-56"></a><span class="p">}</span>
</code></pre></div> </code></pre></div>
</div> </div>
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zh-hant/chapter_tree/array_representation_of_tree/index.html
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<a id="__codelineno-23-41" name="__codelineno-23-41" href="#__codelineno-23-41"></a> <a id="__codelineno-23-41" name="__codelineno-23-41" href="#__codelineno-23-41"></a>
<a id="__codelineno-23-42" name="__codelineno-23-42" href="#__codelineno-23-42"></a><span class="w"> </span><span class="cm">/* 層序走訪 */</span> <a id="__codelineno-23-42" name="__codelineno-23-42" href="#__codelineno-23-42"></a><span class="w"> </span><span class="cm">/* 層序走訪 */</span>
<a id="__codelineno-23-43" name="__codelineno-23-43" href="#__codelineno-23-43"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">level_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-43" name="__codelineno-23-43" href="#__codelineno-23-43"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">level_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-44" name="__codelineno-23-44" href="#__codelineno-23-44"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span> <a id="__codelineno-23-44" name="__codelineno-23-44" href="#__codelineno-23-44"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">tree</span><span class="p">.</span><span class="n">iter</span><span class="p">().</span><span class="n">filter_map</span><span class="p">(</span><span class="o">|&amp;</span><span class="n">x</span><span class="o">|</span><span class="w"> </span><span class="n">x</span><span class="p">).</span><span class="n">collect</span><span class="p">()</span>
<a id="__codelineno-23-45" name="__codelineno-23-45" href="#__codelineno-23-45"></a><span class="w"> </span><span class="c1">// 直接走訪陣列</span> <a id="__codelineno-23-45" name="__codelineno-23-45" href="#__codelineno-23-45"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-46" name="__codelineno-23-46" href="#__codelineno-23-46"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-46" name="__codelineno-23-46" href="#__codelineno-23-46"></a>
<a id="__codelineno-23-47" name="__codelineno-23-47" href="#__codelineno-23-47"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-47" name="__codelineno-23-47" href="#__codelineno-23-47"></a><span class="w"> </span><span class="cm">/* 深度優先走訪 */</span>
<a id="__codelineno-23-48" name="__codelineno-23-48" href="#__codelineno-23-48"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <a id="__codelineno-23-48" name="__codelineno-23-48" href="#__codelineno-23-48"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">dfs</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span>: <span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">order</span>: <span class="kp">&amp;</span><span class="o">&#39;</span><span class="nb">static</span> <span class="kt">str</span><span class="p">,</span><span class="w"> </span><span class="n">res</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-49" name="__codelineno-23-49" href="#__codelineno-23-49"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-23-49" name="__codelineno-23-49" href="#__codelineno-23-49"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-50" name="__codelineno-23-50" href="#__codelineno-23-50"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-23-50" name="__codelineno-23-50" href="#__codelineno-23-50"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-23-51" name="__codelineno-23-51" href="#__codelineno-23-51"></a><span class="w"> </span><span class="n">res</span> <a id="__codelineno-23-51" name="__codelineno-23-51" href="#__codelineno-23-51"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-52" name="__codelineno-23-52" href="#__codelineno-23-52"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-23-52" name="__codelineno-23-52" href="#__codelineno-23-52"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="n">unwrap</span><span class="p">();</span>
<a id="__codelineno-23-53" name="__codelineno-23-53" href="#__codelineno-23-53"></a> <a id="__codelineno-23-53" name="__codelineno-23-53" href="#__codelineno-23-53"></a><span class="w"> </span><span class="c1">// 前序走訪</span>
<a id="__codelineno-23-54" name="__codelineno-23-54" href="#__codelineno-23-54"></a><span class="w"> </span><span class="cm">/* 深度優先走訪 */</span> <a id="__codelineno-23-54" name="__codelineno-23-54" href="#__codelineno-23-54"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-55" name="__codelineno-23-55" href="#__codelineno-23-55"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">dfs</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span>: <span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">order</span>: <span class="kp">&amp;</span><span class="kt">str</span><span class="p">,</span><span class="w"> </span><span class="n">res</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-55" name="__codelineno-23-55" href="#__codelineno-23-55"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-23-56" name="__codelineno-23-56" href="#__codelineno-23-56"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-56" name="__codelineno-23-56" href="#__codelineno-23-56"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-57" name="__codelineno-23-57" href="#__codelineno-23-57"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span> <a id="__codelineno-23-57" name="__codelineno-23-57" href="#__codelineno-23-57"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-23-58" name="__codelineno-23-58" href="#__codelineno-23-58"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-23-58" name="__codelineno-23-58" href="#__codelineno-23-58"></a><span class="w"> </span><span class="c1">// 中序走訪</span>
<a id="__codelineno-23-59" name="__codelineno-23-59" href="#__codelineno-23-59"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="n">unwrap</span><span class="p">();</span> <a id="__codelineno-23-59" name="__codelineno-23-59" href="#__codelineno-23-59"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-60" name="__codelineno-23-60" href="#__codelineno-23-60"></a><span class="w"> </span><span class="c1">// 前序走訪</span> <a id="__codelineno-23-60" name="__codelineno-23-60" href="#__codelineno-23-60"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-23-61" name="__codelineno-23-61" href="#__codelineno-23-61"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-61" name="__codelineno-23-61" href="#__codelineno-23-61"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-62" name="__codelineno-23-62" href="#__codelineno-23-62"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">);</span> <a id="__codelineno-23-62" name="__codelineno-23-62" href="#__codelineno-23-62"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-23-63" name="__codelineno-23-63" href="#__codelineno-23-63"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-23-63" name="__codelineno-23-63" href="#__codelineno-23-63"></a><span class="w"> </span><span class="c1">// 後序走訪</span>
<a id="__codelineno-23-64" name="__codelineno-23-64" href="#__codelineno-23-64"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span> <a id="__codelineno-23-64" name="__codelineno-23-64" href="#__codelineno-23-64"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-65" name="__codelineno-23-65" href="#__codelineno-23-65"></a><span class="w"> </span><span class="c1">// 中序走訪</span> <a id="__codelineno-23-65" name="__codelineno-23-65" href="#__codelineno-23-65"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-23-66" name="__codelineno-23-66" href="#__codelineno-23-66"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-66" name="__codelineno-23-66" href="#__codelineno-23-66"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-67" name="__codelineno-23-67" href="#__codelineno-23-67"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">);</span> <a id="__codelineno-23-67" name="__codelineno-23-67" href="#__codelineno-23-67"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-68" name="__codelineno-23-68" href="#__codelineno-23-68"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-23-68" name="__codelineno-23-68" href="#__codelineno-23-68"></a>
<a id="__codelineno-23-69" name="__codelineno-23-69" href="#__codelineno-23-69"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span> <a id="__codelineno-23-69" name="__codelineno-23-69" href="#__codelineno-23-69"></a><span class="w"> </span><span class="cm">/* 前序走訪 */</span>
<a id="__codelineno-23-70" name="__codelineno-23-70" href="#__codelineno-23-70"></a><span class="w"> </span><span class="c1">// 後序走訪</span> <a id="__codelineno-23-70" name="__codelineno-23-70" href="#__codelineno-23-70"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">pre_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-71" name="__codelineno-23-71" href="#__codelineno-23-71"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-71" name="__codelineno-23-71" href="#__codelineno-23-71"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
<a id="__codelineno-23-72" name="__codelineno-23-72" href="#__codelineno-23-72"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">);</span> <a id="__codelineno-23-72" name="__codelineno-23-72" href="#__codelineno-23-72"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-23-73" name="__codelineno-23-73" href="#__codelineno-23-73"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-23-73" name="__codelineno-23-73" href="#__codelineno-23-73"></a><span class="w"> </span><span class="n">res</span>
<a id="__codelineno-23-74" name="__codelineno-23-74" href="#__codelineno-23-74"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-23-74" name="__codelineno-23-74" href="#__codelineno-23-74"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-75" name="__codelineno-23-75" href="#__codelineno-23-75"></a> <a id="__codelineno-23-75" name="__codelineno-23-75" href="#__codelineno-23-75"></a>
<a id="__codelineno-23-76" name="__codelineno-23-76" href="#__codelineno-23-76"></a><span class="w"> </span><span class="cm">/* 前序走訪 */</span> <a id="__codelineno-23-76" name="__codelineno-23-76" href="#__codelineno-23-76"></a><span class="w"> </span><span class="cm">/* 中序走訪 */</span>
<a id="__codelineno-23-77" name="__codelineno-23-77" href="#__codelineno-23-77"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">pre_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-77" name="__codelineno-23-77" href="#__codelineno-23-77"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">in_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-78" name="__codelineno-23-78" href="#__codelineno-23-78"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span> <a id="__codelineno-23-78" name="__codelineno-23-78" href="#__codelineno-23-78"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
<a id="__codelineno-23-79" name="__codelineno-23-79" href="#__codelineno-23-79"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span> <a id="__codelineno-23-79" name="__codelineno-23-79" href="#__codelineno-23-79"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-23-80" name="__codelineno-23-80" href="#__codelineno-23-80"></a><span class="w"> </span><span class="n">res</span> <a id="__codelineno-23-80" name="__codelineno-23-80" href="#__codelineno-23-80"></a><span class="w"> </span><span class="n">res</span>
<a id="__codelineno-23-81" name="__codelineno-23-81" href="#__codelineno-23-81"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-23-81" name="__codelineno-23-81" href="#__codelineno-23-81"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-82" name="__codelineno-23-82" href="#__codelineno-23-82"></a> <a id="__codelineno-23-82" name="__codelineno-23-82" href="#__codelineno-23-82"></a>
<a id="__codelineno-23-83" name="__codelineno-23-83" href="#__codelineno-23-83"></a><span class="w"> </span><span class="cm">/* 中序走訪 */</span> <a id="__codelineno-23-83" name="__codelineno-23-83" href="#__codelineno-23-83"></a><span class="w"> </span><span class="cm">/* 後序走訪 */</span>
<a id="__codelineno-23-84" name="__codelineno-23-84" href="#__codelineno-23-84"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">in_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-84" name="__codelineno-23-84" href="#__codelineno-23-84"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">post_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-85" name="__codelineno-23-85" href="#__codelineno-23-85"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span> <a id="__codelineno-23-85" name="__codelineno-23-85" href="#__codelineno-23-85"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
<a id="__codelineno-23-86" name="__codelineno-23-86" href="#__codelineno-23-86"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span> <a id="__codelineno-23-86" name="__codelineno-23-86" href="#__codelineno-23-86"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-23-87" name="__codelineno-23-87" href="#__codelineno-23-87"></a><span class="w"> </span><span class="n">res</span> <a id="__codelineno-23-87" name="__codelineno-23-87" href="#__codelineno-23-87"></a><span class="w"> </span><span class="n">res</span>
<a id="__codelineno-23-88" name="__codelineno-23-88" href="#__codelineno-23-88"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-23-88" name="__codelineno-23-88" href="#__codelineno-23-88"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-89" name="__codelineno-23-89" href="#__codelineno-23-89"></a> <a id="__codelineno-23-89" name="__codelineno-23-89" href="#__codelineno-23-89"></a><span class="p">}</span>
<a id="__codelineno-23-90" name="__codelineno-23-90" href="#__codelineno-23-90"></a><span class="w"> </span><span class="cm">/* 後序走訪 */</span>
<a id="__codelineno-23-91" name="__codelineno-23-91" href="#__codelineno-23-91"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">post_order</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-92" name="__codelineno-23-92" href="#__codelineno-23-92"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
<a id="__codelineno-23-93" name="__codelineno-23-93" href="#__codelineno-23-93"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-23-94" name="__codelineno-23-94" href="#__codelineno-23-94"></a><span class="w"> </span><span class="n">res</span>
<a id="__codelineno-23-95" name="__codelineno-23-95" href="#__codelineno-23-95"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-96" name="__codelineno-23-96" href="#__codelineno-23-96"></a><span class="p">}</span>
</code></pre></div> </code></pre></div>
</div> </div>
<div class="tabbed-block"> <div class="tabbed-block">

2
zh-hant/chapter_tree/avl_tree/index.html
View file

@ -4005,7 +4005,7 @@
</div> </div>
<div class="tabbed-block"> <div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* AVL 樹節點結構體 */</span> <div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* AVL 樹節點結構體 */</span>
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span> <a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span> <a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span>
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">;</span> <a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">;</span>

8
zh-hant/chapter_tree/binary_search_tree/index.html
View file

@ -5070,7 +5070,7 @@
<a id="__codelineno-37-38" name="__codelineno-37-38" href="#__codelineno-37-38"></a><span class="w"> </span><span class="c1">// 刪除節點 cur</span> <a id="__codelineno-37-38" name="__codelineno-37-38" href="#__codelineno-37-38"></a><span class="w"> </span><span class="c1">// 刪除節點 cur</span>
<a id="__codelineno-37-39" name="__codelineno-37-39" href="#__codelineno-37-39"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">Rc</span>::<span class="n">ptr_eq</span><span class="p">(</span><span class="o">&amp;</span><span class="n">cur</span><span class="p">,</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">as_ref</span><span class="p">().</span><span class="n">unwrap</span><span class="p">())</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-37-39" name="__codelineno-37-39" href="#__codelineno-37-39"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">Rc</span>::<span class="n">ptr_eq</span><span class="p">(</span><span class="o">&amp;</span><span class="n">cur</span><span class="p">,</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">as_ref</span><span class="p">().</span><span class="n">unwrap</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-37-40" name="__codelineno-37-40" href="#__codelineno-37-40"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span> <a id="__codelineno-37-40" name="__codelineno-37-40" href="#__codelineno-37-40"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
<a id="__codelineno-37-41" name="__codelineno-37-41" href="#__codelineno-37-41"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">left</span><span class="p">.</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">Rc</span>::<span class="n">ptr_eq</span><span class="p">(</span><span class="o">&amp;</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">().</span><span class="n">unwrap</span><span class="p">(),</span><span class="w"> </span><span class="o">&amp;</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-37-41" name="__codelineno-37-41" href="#__codelineno-37-41"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">left</span><span class="p">.</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">Rc</span>::<span class="n">ptr_eq</span><span class="p">(</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">().</span><span class="n">unwrap</span><span class="p">(),</span><span class="w"> </span><span class="o">&amp;</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-37-42" name="__codelineno-37-42" href="#__codelineno-37-42"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span> <a id="__codelineno-37-42" name="__codelineno-37-42" href="#__codelineno-37-42"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-37-43" name="__codelineno-37-43" href="#__codelineno-37-43"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-37-43" name="__codelineno-37-43" href="#__codelineno-37-43"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-37-44" name="__codelineno-37-44" href="#__codelineno-37-44"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span> <a id="__codelineno-37-44" name="__codelineno-37-44" href="#__codelineno-37-44"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
@ -5091,11 +5091,11 @@
<a id="__codelineno-37-59" name="__codelineno-37-59" href="#__codelineno-37-59"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span> <a id="__codelineno-37-59" name="__codelineno-37-59" href="#__codelineno-37-59"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-37-60" name="__codelineno-37-60" href="#__codelineno-37-60"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-37-60" name="__codelineno-37-60" href="#__codelineno-37-60"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-37-61" name="__codelineno-37-61" href="#__codelineno-37-61"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-37-61" name="__codelineno-37-61" href="#__codelineno-37-61"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-37-62" name="__codelineno-37-62" href="#__codelineno-37-62"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">tmpval</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">;</span> <a id="__codelineno-37-62" name="__codelineno-37-62" href="#__codelineno-37-62"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">tmp_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-37-63" name="__codelineno-37-63" href="#__codelineno-37-63"></a><span class="w"> </span><span class="c1">// 遞迴刪除節點 tmp</span> <a id="__codelineno-37-63" name="__codelineno-37-63" href="#__codelineno-37-63"></a><span class="w"> </span><span class="c1">// 遞迴刪除節點 tmp</span>
<a id="__codelineno-37-64" name="__codelineno-37-64" href="#__codelineno-37-64"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">tmpval</span><span class="p">);</span> <a id="__codelineno-37-64" name="__codelineno-37-64" href="#__codelineno-37-64"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">tmp_val</span><span class="p">);</span>
<a id="__codelineno-37-65" name="__codelineno-37-65" href="#__codelineno-37-65"></a><span class="w"> </span><span class="c1">// 用 tmp 覆蓋 cur</span> <a id="__codelineno-37-65" name="__codelineno-37-65" href="#__codelineno-37-65"></a><span class="w"> </span><span class="c1">// 用 tmp 覆蓋 cur</span>
<a id="__codelineno-37-66" name="__codelineno-37-66" href="#__codelineno-37-66"></a><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmpval</span><span class="p">;</span> <a id="__codelineno-37-66" name="__codelineno-37-66" href="#__codelineno-37-66"></a><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp_val</span><span class="p">;</span>
<a id="__codelineno-37-67" name="__codelineno-37-67" href="#__codelineno-37-67"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-37-67" name="__codelineno-37-67" href="#__codelineno-37-67"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-37-68" name="__codelineno-37-68" href="#__codelineno-37-68"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-37-68" name="__codelineno-37-68" href="#__codelineno-37-68"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-37-69" name="__codelineno-37-69" href="#__codelineno-37-69"></a><span class="p">}</span> <a id="__codelineno-37-69" name="__codelineno-37-69" href="#__codelineno-37-69"></a><span class="p">}</span>

84
zh-hant/chapter_tree/binary_tree_traversal/index.html
View file

@ -4335,40 +4335,56 @@
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">fn</span> <span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span>: <span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">fn</span> <span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span>: <span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span> <a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a> <a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a>
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">root</span>: <span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w"> </span><span class="c1">// 訪問優先順序：根節點 -&gt; 左子樹 -&gt; 右子樹</span> <a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w"> </span><span class="n">result</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">);</span> <a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w"> </span><span class="c1">// 訪問優先順序：根節點 -&gt; 左子樹 -&gt; 右子樹</span>
<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w"> </span><span class="n">result</span><span class="p">.</span><span class="n">extend</span><span class="p">(</span><span class="n">pre_order</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">()));</span> <a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">();</span>
<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w"> </span><span class="n">result</span><span class="p">.</span><span class="n">extend</span><span class="p">(</span><span class="n">pre_order</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">()));</span> <a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w"> </span><span class="n">result</span> <a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="p">}</span> <a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a> <a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="cm">/* 中序走訪 */</span> <a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="p">);</span>
<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="k">fn</span> <span class="nf">in_order</span><span class="p">(</span><span class="n">root</span>: <span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a>
<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span> <a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w"> </span><span class="n">result</span>
<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a> <a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="p">}</span>
<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a>
<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w"> </span><span class="c1">// 訪問優先順序：左子樹 -&gt; 根節點 -&gt; 右子樹</span> <a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="cm">/* 中序走訪 */</span>
<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w"> </span><span class="n">result</span><span class="p">.</span><span class="n">extend</span><span class="p">(</span><span class="n">in_order</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">()));</span> <a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="k">fn</span> <span class="nf">in_order</span><span class="p">(</span><span class="n">root</span>: <span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w"> </span><span class="n">result</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">);</span> <a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w"> </span><span class="n">result</span><span class="p">.</span><span class="n">extend</span><span class="p">(</span><span class="n">in_order</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">()));</span> <a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a>
<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">root</span>: <span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w"> </span><span class="n">result</span> <a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="p">}</span> <a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="w"> </span><span class="c1">// 訪問優先順序：左子樹 -&gt; 根節點 -&gt; 右子樹</span>
<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a> <a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">();</span>
<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="cm">/* 後序走訪 */</span> <a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="k">fn</span> <span class="nf">post_order</span><span class="p">(</span><span class="n">root</span>: <span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span> <a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a> <a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="w"> </span><span class="c1">// 訪問優先順序：左子樹 -&gt; 右子樹 -&gt; 根節點</span> <a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="p">);</span>
<a id="__codelineno-23-33" name="__codelineno-23-33" href="#__codelineno-23-33"></a><span class="w"> </span><span class="n">result</span><span class="p">.</span><span class="n">extend</span><span class="p">(</span><span class="n">post_order</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">()));</span> <a id="__codelineno-23-33" name="__codelineno-23-33" href="#__codelineno-23-33"></a>
<a id="__codelineno-23-34" name="__codelineno-23-34" href="#__codelineno-23-34"></a><span class="w"> </span><span class="n">result</span><span class="p">.</span><span class="n">extend</span><span class="p">(</span><span class="n">post_order</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">()));</span> <a id="__codelineno-23-34" name="__codelineno-23-34" href="#__codelineno-23-34"></a><span class="w"> </span><span class="n">result</span>
<a id="__codelineno-23-35" name="__codelineno-23-35" href="#__codelineno-23-35"></a><span class="w"> </span><span class="n">result</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">);</span> <a id="__codelineno-23-35" name="__codelineno-23-35" href="#__codelineno-23-35"></a><span class="p">}</span>
<a id="__codelineno-23-36" name="__codelineno-23-36" href="#__codelineno-23-36"></a><span class="w"> </span><span class="p">}</span> <a id="__codelineno-23-36" name="__codelineno-23-36" href="#__codelineno-23-36"></a>
<a id="__codelineno-23-37" name="__codelineno-23-37" href="#__codelineno-23-37"></a><span class="w"> </span><span class="n">result</span> <a id="__codelineno-23-37" name="__codelineno-23-37" href="#__codelineno-23-37"></a><span class="cm">/* 後序走訪 */</span>
<a id="__codelineno-23-38" name="__codelineno-23-38" href="#__codelineno-23-38"></a><span class="p">}</span> <a id="__codelineno-23-38" name="__codelineno-23-38" href="#__codelineno-23-38"></a><span class="k">fn</span> <span class="nf">post_order</span><span class="p">(</span><span class="n">root</span>: <span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-39" name="__codelineno-23-39" href="#__codelineno-23-39"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
<a id="__codelineno-23-40" name="__codelineno-23-40" href="#__codelineno-23-40"></a>
<a id="__codelineno-23-41" name="__codelineno-23-41" href="#__codelineno-23-41"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">root</span>: <span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-42" name="__codelineno-23-42" href="#__codelineno-23-42"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-43" name="__codelineno-23-43" href="#__codelineno-23-43"></a><span class="w"> </span><span class="c1">// 訪問優先順序：左子樹 -&gt; 右子樹 -&gt; 根節點</span>
<a id="__codelineno-23-44" name="__codelineno-23-44" href="#__codelineno-23-44"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">();</span>
<a id="__codelineno-23-45" name="__codelineno-23-45" href="#__codelineno-23-45"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-23-46" name="__codelineno-23-46" href="#__codelineno-23-46"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">.</span><span class="n">as_ref</span><span class="p">(),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-23-47" name="__codelineno-23-47" href="#__codelineno-23-47"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-23-48" name="__codelineno-23-48" href="#__codelineno-23-48"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-49" name="__codelineno-23-49" href="#__codelineno-23-49"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-50" name="__codelineno-23-50" href="#__codelineno-23-50"></a>
<a id="__codelineno-23-51" name="__codelineno-23-51" href="#__codelineno-23-51"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">result</span><span class="p">);</span>
<a id="__codelineno-23-52" name="__codelineno-23-52" href="#__codelineno-23-52"></a>
<a id="__codelineno-23-53" name="__codelineno-23-53" href="#__codelineno-23-53"></a><span class="w"> </span><span class="n">result</span>
<a id="__codelineno-23-54" name="__codelineno-23-54" href="#__codelineno-23-54"></a><span class="p">}</span>
</code></pre></div> </code></pre></div>
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