diff --git a/codes/cpp/chapter_tree/binary_tree_bfs.cpp b/codes/cpp/chapter_tree/binary_tree_bfs.cpp index eeec2a18e..30c2d6007 100644 --- a/codes/cpp/chapter_tree/binary_tree_bfs.cpp +++ b/codes/cpp/chapter_tree/binary_tree_bfs.cpp @@ -15,12 +15,12 @@ vector hierOrder(TreeNode* root) { vector vec; while (!queue.empty()) { TreeNode* node = queue.front(); - queue.pop(); // 队列出队 - vec.push_back(node->val); // 保存结点 + queue.pop(); // 队列出队 + vec.push_back(node->val); // 保存结点 if (node->left != nullptr) - queue.push(node->left); // 左子结点入队 + queue.push(node->left); // 左子结点入队 if (node->right != nullptr) - queue.push(node->right); // 右子结点入队 + queue.push(node->right); // 右子结点入队 } return vec; } diff --git a/codes/python/chapter_tree/avl_tree.py b/codes/python/chapter_tree/avl_tree.py new file mode 100644 index 000000000..d0ff48cba --- /dev/null +++ b/codes/python/chapter_tree/avl_tree.py @@ -0,0 +1,208 @@ +""" +File: avl_tree.py +Created Time: 2022-12-20 +Author: a16su (lpluls001@gmail.com) +""" + +import sys, os.path as osp +import typing + +sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__)))) +from include import * + + +class AVLTree: + def __init__(self, root: typing.Optional[TreeNode] = None): + self.root = root + + """ 获取结点高度 """ + def height(self, node: typing.Optional[TreeNode]) -> int: + # 空结点高度为 -1 ,叶结点高度为 0 + if node is not None: + return node.height + return -1 + + """ 更新结点高度 """ + def __update_height(self, node: TreeNode): + # 结点高度等于最高子树高度 + 1 + node.height = max([self.height(node.left), self.height(node.right)]) + 1 + + """ 获取平衡因子 """ + def balance_factor(self, node: TreeNode) -> int: + # 空结点平衡因子为 0 + if node is None: + return 0 + # 结点平衡因子 = 左子树高度 - 右子树高度 + return self.height(node.left) - self.height(node.right) + + """ 右旋操作 """ + def __right_rotate(self, node: TreeNode) -> TreeNode: + child = node.left + grand_child = child.right + # 以 child 为原点,将 node 向右旋转 + child.right = node + node.left = grand_child + # 更新结点高度 + self.__update_height(node) + self.__update_height(child) + # 返回旋转后子树的根节点 + return child + + """ 左旋操作 """ + def __left_rotate(self, node: TreeNode) -> TreeNode: + child = node.right + grand_child = child.left + # 以 child 为原点,将 node 向左旋转 + child.left = node + node.right = grand_child + # 更新结点高度 + self.__update_height(node) + self.__update_height(child) + # 返回旋转后子树的根节点 + return child + + """ 执行旋转操作,使该子树重新恢复平衡 """ + def __rotate(self, node: TreeNode) -> TreeNode: + # 获取结点 node 的平衡因子 + balance_factor = self.balance_factor(node) + # 左偏树 + if balance_factor > 1: + if self.balance_factor(node.left) >= 0: + # 右旋 + return self.__right_rotate(node) + else: + # 先左旋后右旋 + node.left = self.__left_rotate(node.left) + return self.__right_rotate(node) + # 右偏树 + elif balance_factor < -1: + if self.balance_factor(node.right) <= 0: + # 左旋 + return self.__left_rotate(node) + else: + # 先右旋后左旋 + node.right = self.__right_rotate(node.right) + return self.__left_rotate(node) + # 平衡树,无需旋转,直接返回 + return node + + """ 插入结点 """ + def insert(self, val) -> TreeNode: + self.root = self.__insert_helper(self.root, val) + return self.root + + """ 递归插入结点(辅助函数)""" + def __insert_helper(self, node: typing.Optional[TreeNode], val: int) -> TreeNode: + if node is None: + return TreeNode(val) + # 1. 查找插入位置,并插入结点 + if val < node.val: + node.left = self.__insert_helper(node.left, val) + elif val > node.val: + node.right = self.__insert_helper(node.right, val) + else: + # 重复结点不插入,直接返回 + return node + # 更新结点高度 + self.__update_height(node) + # 2. 执行旋转操作,使该子树重新恢复平衡 + return self.__rotate(node) + + """ 删除结点 """ + def remove(self, val: int): + root = self.__remove_helper(self.root, val) + return root + + """ 递归删除结点(辅助函数) """ + def __remove_helper(self, node: typing.Optional[TreeNode], val: int) -> typing.Optional[TreeNode]: + if node is None: + return None + # 1. 查找结点,并删除之 + if val < node.val: + node.left = self.__remove_helper(node.left, val) + elif val > node.val: + node.right = self.__remove_helper(node.right, val) + else: + if node.left is None or node.right is None: + child = node.left or node.right + # 子结点数量 = 0 ,直接删除 node 并返回 + if child is None: + return None + # 子结点数量 = 1 ,直接删除 node + else: + node = child + else: # 子结点数量 = 2 ,则将中序遍历的下个结点删除,并用该结点替换当前结点 + temp = self.__min_node(node.right) + node.right = self.__remove_helper(node.right, temp.val) + node.val = temp.val + # 更新结点高度 + self.__update_height(node) + # 2. 执行旋转操作,使该子树重新恢复平衡 + return self.__rotate(node) + + """ 获取最小结点 """ + def __min_node(self, node: typing.Optional[TreeNode]) -> typing.Optional[TreeNode]: + if node is None: + return None + # 循环访问左子结点,直到叶结点时为最小结点,跳出 + while node.left is not None: + node = node.left + return node + + """ 查找结点 """ + def search(self, val: int): + cur = self.root + # 循环查找,越过叶结点后跳出 + while cur is not None: + # 目标结点在 root 的右子树中 + if cur.val < val: + cur = cur.right + # 目标结点在 root 的左子树中 + elif cur.val > val: + cur = cur.left + # 找到目标结点,跳出循环 + else: + break + # 返回目标结点 + return cur + + +""" Driver Code """ +if __name__ == "__main__": + def test_insert(tree: AVLTree, val: int): + tree.insert(val) + print("\n插入结点 {} 后,AVL 树为".format(val)) + print_tree(tree.root) + + def test_remove(tree: AVLTree, val: int): + tree.remove(val) + print("\n删除结点 {} 后,AVL 树为".format(val)) + print_tree(tree.root) + + # 初始化空 AVL 树 + avl_tree = AVLTree() + + # 插入结点 + # 请关注插入结点后,AVL 树是如何保持平衡的 + test_insert(avl_tree, 1) + test_insert(avl_tree, 2) + test_insert(avl_tree, 3) + test_insert(avl_tree, 4) + test_insert(avl_tree, 5) + test_insert(avl_tree, 8) + test_insert(avl_tree, 7) + test_insert(avl_tree, 9) + test_insert(avl_tree, 10) + test_insert(avl_tree, 6) + + # 插入重复结点 + test_insert(avl_tree, 7) + + # 删除结点 + # 请关注删除结点后,AVL 树是如何保持平衡的 + test_remove(avl_tree, 8) # 删除度为 0 的结点 + test_remove(avl_tree, 5) # 删除度为 1 的结点 + test_remove(avl_tree, 4) # 删除度为 2 的结点 + + result_node = avl_tree.search(7) + print("\n查找到的结点对象为 {},结点值 = {}".format(result_node, result_node.val)) diff --git a/codes/python/chapter_tree/binary_search_tree.py b/codes/python/chapter_tree/binary_search_tree.py index 0f855f279..23e341854 100644 --- a/codes/python/chapter_tree/binary_search_tree.py +++ b/codes/python/chapter_tree/binary_search_tree.py @@ -1,10 +1,167 @@ """ File: binary_search_tree.py -Created Time: 2022-11-25 -Author: Krahets (krahets@163.com) +Created Time: 2022-12-20 +Author: a16su (lpluls001@gmail.com) """ import sys, os.path as osp +import typing + sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__)))) from include import * + +""" 二叉搜索树 """ +class BinarySearchTree: + def __init__(self, nums: typing.List[int]) -> None: + nums.sort() + self.__root = self.build_tree(nums, 0, len(nums) - 1) + + """ 构建二叉搜索树 """ + def build_tree(self, nums: typing.List[int], start_index: int, end_index: int) -> typing.Optional[TreeNode]: + if start_index > end_index: + return None + + # 将数组中间结点作为根结点 + mid = (start_index + end_index) // 2 + root = TreeNode(nums[mid]) + # 递归建立左子树和右子树 + root.left = self.build_tree(nums=nums, start_index=start_index, end_index=mid - 1) + root.right = self.build_tree(nums=nums, start_index=mid + 1, end_index=end_index) + return root + + @property + def root(self) -> typing.Optional[TreeNode]: + return self.__root + + """ 查找结点 """ + def search(self, num: int) -> typing.Optional[TreeNode]: + cur = self.root + # 循环查找,越过叶结点后跳出 + while cur is not None: + # 目标结点在 root 的右子树中 + if cur.val < num: + cur = cur.right + # 目标结点在 root 的左子树中 + elif cur.val > num: + cur = cur.left + # 找到目标结点,跳出循环 + else: + break + return cur + + """ 插入结点 """ + def insert(self, num: int) -> typing.Optional[TreeNode]: + root = self.root + # 若树为空,直接提前返回 + if root is None: + return None + + cur = root + pre = None + + # 循环查找,越过叶结点后跳出 + while cur is not None: + # 找到重复结点,直接返回 + if cur.val == num: + return None + pre = cur + + if cur.val < num: # 插入位置在 root 的右子树中 + cur = cur.right + else: # 插入位置在 root 的左子树中 + cur = cur.left + + # 插入结点 val + node = TreeNode(num) + if pre.val < num: + pre.right = node + else: + pre.left = node + return node + + """ 删除结点 """ + def remove(self, num: int) -> typing.Optional[TreeNode]: + root = self.root + # 若树为空,直接提前返回 + if root is None: + return None + + cur = root + pre = None + + # 循环查找,越过叶结点后跳出 + while cur is not None: + # 找到待删除结点,跳出循环 + if cur.val == num: + break + pre = cur + if cur.val < num: # 待删除结点在 root 的右子树中 + cur = cur.right + else: # 待删除结点在 root 的左子树中 + cur = cur.left + + # 若无待删除结点,则直接返回 + if cur is None: + return None + + # 子结点数量 = 0 or 1 + if cur.left is None or cur.right is None: + # 当子结点数量 = 0 / 1 时, child = null / 该子结点 + child = cur.left or cur.right + # 删除结点 cur + if pre.left == cur: + pre.left = child + else: + pre.right = child + # 子结点数量 = 2 + else: + # 获取中序遍历中 cur 的下一个结点 + nex = self.min(cur.right) + tmp = nex.val + # 递归删除结点 nex + self.remove(nex.val) + # 将 nex 的值复制给 cur + cur.val = tmp + return cur + + """ 获取最小结点 """ + def min(self, root: typing.Optional[TreeNode]) -> typing.Optional[TreeNode]: + if root is None: + return root + + # 循环访问左子结点,直到叶结点时为最小结点,跳出 + while root.left is not None: + root = root.left + return root + + +""" Driver Code """ +if __name__ == "__main__": + # 初始化二叉搜索树 + nums = list(range(1, 16)) + bst = BinarySearchTree(nums=nums) + print("\n初始化的二叉树为\n") + print_tree(bst.root) + + # 查找结点 + node = bst.search(5) + print("\n查找到的结点对象为: {},结点值 = {}".format(node, node.val)) + + # 插入结点 + ndoe = bst.insert(16) + print("\n插入结点 16 后,二叉树为\n") + print_tree(bst.root) + + # 删除结点 + bst.remove(1) + print("\n删除结点 1 后,二叉树为\n") + print_tree(bst.root) + + bst.remove(2) + print("\n删除结点 2 后,二叉树为\n") + print_tree(bst.root) + + bst.remove(4) + print("\n删除结点 4 后,二叉树为\n") + print_tree(bst.root) diff --git a/codes/python/chapter_tree/binary_tree.py b/codes/python/chapter_tree/binary_tree.py index 81828b5cf..d99026352 100644 --- a/codes/python/chapter_tree/binary_tree.py +++ b/codes/python/chapter_tree/binary_tree.py @@ -1,10 +1,40 @@ """ File: binary_tree.py -Created Time: 2022-11-25 -Author: Krahets (krahets@163.com) +Created Time: 2022-12-20 +Author: a16su (lpluls001@gmail.com) """ import sys, os.path as osp + sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__)))) from include import * + +""" Driver Code """ +if __name__ == "__main__": + """ 初始化二叉树 """ + # 初始化节点 + n1 = TreeNode(val=1) + n2 = TreeNode(val=2) + n3 = TreeNode(val=3) + n4 = TreeNode(val=4) + n5 = TreeNode(val=5) + # 构建引用指向(即指针) + n1.left = n2 + n1.right = n3 + n2.left = n4 + n2.right = n5 + print("\n初始化二叉树\n") + print_tree(n1) + + """ 插入与删除结点 """ + P = TreeNode(0) + # 在 n1 -> n2 中间插入节点 P + n1.left = P + P.left = n2 + print("\n插入结点 P 后\n") + print_tree(n1) + # 删除结点 + n1.left = n2 + print("\n删除结点 P 后\n"); + print_tree(n1) diff --git a/codes/python/chapter_tree/binary_tree_bfs.py b/codes/python/chapter_tree/binary_tree_bfs.py index 9ae1b3594..0320a08dd 100644 --- a/codes/python/chapter_tree/binary_tree_bfs.py +++ b/codes/python/chapter_tree/binary_tree_bfs.py @@ -1,10 +1,42 @@ """ File: binary_tree_bfs.py -Created Time: 2022-11-25 -Author: Krahets (krahets@163.com) +Created Time: 2022-12-20 +Author: a16su (lpluls001@gmail.com) """ import sys, os.path as osp +import typing + sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__)))) from include import * + +""" 层序遍历 """ +def hier_order(root: TreeNode): + # 初始化队列,加入根结点 + queue = collections.deque() + queue.append(root) + # 初始化一个列表,用于保存遍历序列 + res = [] + while queue: + node = queue.popleft() # 队列出队 + res.append(node.val) # 保存节点值 + if node.left is not None: + queue.append(node.left) # 左子结点入队 + if node.right is not None: + queue.append(node.right) # 右子结点入队 + return res + + +""" Driver Code """ +if __name__ == "__main__": + # 初始化二叉树 + # 这里借助了一个从数组直接生成二叉树的函数 + root = list_to_tree(arr=[1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, None, None]) + print("\n初始化二叉树\n") + print_tree(root) + + # 层序遍历 + res = hier_order(root) + print("\n层序遍历的结点打印序列 = ", res) + assert res == [1, 2, 3, 4, 5, 6, 7] diff --git a/codes/python/chapter_tree/binary_tree_dfs.py b/codes/python/chapter_tree/binary_tree_dfs.py index 094bd4cb5..11ee8339c 100644 --- a/codes/python/chapter_tree/binary_tree_dfs.py +++ b/codes/python/chapter_tree/binary_tree_dfs.py @@ -1,10 +1,68 @@ """ File: binary_tree_dfs.py -Created Time: 2022-11-25 -Author: Krahets (krahets@163.com) +Created Time: 2022-12-20 +Author: a16su (lpluls001@gmail.com) """ import sys, os.path as osp +import typing + sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__)))) from include import * + +res = [] + +""" 前序遍历 """ +def pre_order(root: typing.Optional[TreeNode]): + if root is None: + return + # 访问优先级:根结点 -> 左子树 -> 右子树 + res.append(root.val) + pre_order(root=root.left) + pre_order(root=root.right) + +""" 中序遍历 """ +def in_order(root: typing.Optional[TreeNode]): + if root is None: + return + # 访问优先级:左子树 -> 根结点 -> 右子树 + in_order(root=root.left) + res.append(root.val) + in_order(root=root.right) + +""" 后序遍历 """ +def post_order(root: typing.Optional[TreeNode]): + if root is None: + return + # 访问优先级:左子树 -> 右子树 -> 根结点 + post_order(root=root.left) + post_order(root=root.right) + res.append(root.val) + + +""" Driver Code """ +if __name__ == "__main__": + # 初始化二叉树 + # 这里借助了一个从数组直接生成二叉树的函数 + root = list_to_tree(arr=[1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, None, None]) + print("\n初始化二叉树\n") + print_tree(root) + + # 前序遍历 + res.clear() + pre_order(root) + print("\n前序遍历的结点打印序列 = ", res) + assert res == [1, 2, 4, 5, 3, 6, 7] + + # 中序遍历 + res.clear() + in_order(root) + print("\n中序遍历的结点打印序列 = ", res) + assert res == [4, 2, 5, 1, 6, 3, 7] + + # 后序遍历 + res.clear() + post_order(root) + print("\n后序遍历的结点打印序列 = ", res) + assert res == [4, 5, 2, 6, 7, 3, 1] diff --git a/codes/python/include/binary_tree.py b/codes/python/include/binary_tree.py index de2569e42..670fd18ce 100644 --- a/codes/python/include/binary_tree.py +++ b/codes/python/include/binary_tree.py @@ -10,9 +10,19 @@ class TreeNode: """Definition for a binary tree node """ def __init__(self, val=0, left=None, right=None): - self.val = val - self.left = left - self.right = right + self.val = val # 结点值 + self.height = 0 # 结点高度 + self.left = left # 左子结点引用 + self.right = right # 右子结点引用 + + def __str__(self): + val = self.val + left_node_val = self.left.val if self.left else None + right_node_val = self.right.val if self.right else None + return "".format(val, left_node_val, right_node_val) + + __repr__ = __str__ + def list_to_tree(arr): """Generate a binary tree with a list diff --git a/docs/chapter_tree/avl_tree.md b/docs/chapter_tree/avl_tree.md index 2b1ad08f0..bc4493520 100644 --- a/docs/chapter_tree/avl_tree.md +++ b/docs/chapter_tree/avl_tree.md @@ -48,7 +48,21 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit === "Python" ```python title="avl_tree.py" - + """ AVL 树结点类 """ + class TreeNode: + def __init__(self, val=None, left=None, right=None): + self.val = val # 结点值 + self.height = 0 # 结点高度, avl 树会用到 + self.left = left # 左子结点引用 + self.right = right # 右子结点引用 + + def __str__(self): # 直接print时会好看一点 + val = self.val + left_node_val = self.left.val if self.left else None + right_node_val = self.right.val if self.right else None + return "".format(val, left_node_val, right_node_val) + + __repr__ = __str__ ``` === "Go" @@ -115,7 +129,17 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit === "Python" ```python title="avl_tree.py" - + """ 获取结点高度 """ + def height(self, node: typing.Optional[TreeNode]) -> int: + # 空结点高度为 -1 ,叶结点高度为 0 + if node is not None: + return node.height + return -1 + + """ 更新结点高度 """ + def __update_height(self, node: TreeNode): + # 结点高度等于最高子树高度 + 1 + node.height = max([self.height(node.left), self.height(node.right)]) + 1 ``` === "Go" @@ -185,7 +209,13 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit === "Python" ```python title="avl_tree.py" - + """ 获取平衡因子 """ + def balance_factor(self, node: TreeNode) -> int: + # 空结点平衡因子为 0 + if node is None: + return 0 + # 结点平衡因子 = 左子树高度 - 右子树高度 + return self.height(node.left) - self.height(node.right) ``` === "Go" @@ -281,7 +311,18 @@ AVL 树的独特之处在于「旋转 Rotation」的操作,其可 **在不影 === "Python" ```python title="avl_tree.py" - + """ 右旋操作 """ + def __right_rotate(self, node: TreeNode) -> TreeNode: + child = node.left + grand_child = child.right + # 以 child 为原点,将 node 向右旋转 + child.right = node + node.left = grand_child + # 更新结点高度 + self.__update_height(node) + self.__update_height(child) + # 返回旋转后子树的根节点 + return child ``` === "Go" @@ -363,7 +404,18 @@ AVL 树的独特之处在于「旋转 Rotation」的操作,其可 **在不影 === "Python" ```python title="avl_tree.py" - + """ 左旋操作 """ + def __left_rotate(self, node: TreeNode) -> TreeNode: + child = node.right + grand_child = child.left + # 以 child 为原点,将 node 向左旋转 + child.left = node + node.right = grand_child + # 更新结点高度 + self.__update_height(node) + self.__update_height(child) + # 返回旋转后子树的根节点 + return child ``` === "Go" @@ -485,7 +537,30 @@ AVL 树的独特之处在于「旋转 Rotation」的操作,其可 **在不影 === "Python" ```python title="avl_tree.py" - + """ 执行旋转操作,使该子树重新恢复平衡 """ + def __rotate(self, node: TreeNode) -> TreeNode: + # 获取结点 node 的平衡因子 + balance_factor = self.balance_factor(node) + # 左偏树 + if balance_factor > 1: + if self.balance_factor(node.left) >= 0: + # 右旋 + return self.__right_rotate(node) + else: + # 先左旋后右旋 + node.left = self.__left_rotate(node.left) + return self.__right_rotate(node) + # 右偏树 + elif balance_factor < -1: + if self.balance_factor(node.right) <= 0: + # 左旋 + return self.__left_rotate(node) + else: + # 先右旋后左旋 + node.right = self.__right_rotate(node.right) + return self.__left_rotate(node) + # 平衡树,无需旋转,直接返回 + return node ``` === "Go" @@ -597,7 +672,27 @@ AVL 树的独特之处在于「旋转 Rotation」的操作,其可 **在不影 === "Python" ```python title="avl_tree.py" - + """ 插入结点 """ + def insert(self, val) -> TreeNode: + self.root = self.__insert_helper(self.root, val) + return self.root + + """ 递归插入结点(辅助函数)""" + def __insert_helper(self, node: typing.Optional[TreeNode], val: int) -> TreeNode: + if node is None: + return TreeNode(val) + # 1. 查找插入位置,并插入结点 + if val < node.val: + node.left = self.__insert_helper(node.left, val) + elif val > node.val: + node.right = self.__insert_helper(node.right, val) + else: + # 重复结点不插入,直接返回 + return node + # 更新结点高度 + self.__update_height(node) + # 2. 执行旋转操作,使该子树重新恢复平衡 + return self.__rotate(node) ``` === "Go" @@ -717,7 +812,46 @@ AVL 树的独特之处在于「旋转 Rotation」的操作,其可 **在不影 === "Python" ```python title="avl_tree.py" - + """ 删除结点 """ + def remove(self, val: int): + root = self.__remove_helper(self.root, val) + return root + + """ 递归删除结点(辅助函数) """ + def __remove_helper(self, node: typing.Optional[TreeNode], val: int) -> typing.Optional[TreeNode]: + if node is None: + return None + # 1. 查找结点,并删除之 + if val < node.val: + node.left = self.__remove_helper(node.left, val) + elif val > node.val: + node.right = self.__remove_helper(node.right, val) + else: + if node.left is None or node.right is None: + child = node.left or node.right + # 子结点数量 = 0 ,直接删除 node 并返回 + if child is None: + return None + # 子结点数量 = 1 ,直接删除 node + else: + node = child + else: # 子结点数量 = 2 ,则将中序遍历的下个结点删除,并用该结点替换当前结点 + temp = self.min_node(node.right) + node.right = self.__remove_helper(node.right, temp.val) + node.val = temp.val + # 更新结点高度 + self.__update_height(node) + # 2. 执行旋转操作,使该子树重新恢复平衡 + return self.__rotate(node) + + """ 获取最小结点 """ + def min_node(self, node: typing.Optional[TreeNode]) -> typing.Optional[TreeNode]: + if node is None: + return None + # 循环访问左子结点,直到叶结点时为最小结点,跳出 + while node.left is not None: + node = node.left + return node ``` === "Go" diff --git a/docs/chapter_tree/binary_search_tree.md b/docs/chapter_tree/binary_search_tree.md index c2551e749..32ebb3736 100644 --- a/docs/chapter_tree/binary_search_tree.md +++ b/docs/chapter_tree/binary_search_tree.md @@ -82,7 +82,21 @@ comments: true === "Python" ```python title="binary_search_tree.py" - + """ 查找结点 """ + def search(self, num: int) -> typing.Optional[TreeNode]: + cur = self.root + # 循环查找,越过叶结点后跳出 + while cur is not None: + # 目标结点在 root 的右子树中 + if cur.val < num: + cur = cur.right + # 目标结点在 root 的左子树中 + elif cur.val > num: + cur = cur.left + # 找到目标结点,跳出循环 + else: + break + return cur ``` === "Go" @@ -244,7 +258,35 @@ comments: true === "Python" ```python title="binary_search_tree.py" + """ 插入结点 """ + def insert(self, num: int) -> typing.Optional[TreeNode]: + root = self.root + # 若树为空,直接提前返回 + if root is None: + return None + cur = root + pre = None + + # 循环查找,越过叶结点后跳出 + while cur is not None: + # 找到重复结点,直接返回 + if cur.val == num: + return None + pre = cur + + if cur.val < num: # 插入位置在 root 的右子树中 + cur = cur.right + else: # 插入位置在 root 的左子树中 + cur = cur.left + + # 插入结点 val + node = TreeNode(num) + if pre.val < num: + pre.right = node + else: + pre.left = node + return node ``` === "Go" @@ -525,7 +567,60 @@ comments: true === "Python" ```python title="binary_search_tree.py" + """ 删除结点 """ + def remove(self, num: int) -> typing.Optional[TreeNode]: + root = self.root + # 若树为空,直接提前返回 + if root is None: + return None + cur = root + pre = None + + # 循环查找,越过叶结点后跳出 + while cur is not None: + # 找到待删除结点,跳出循环 + if cur.val == num: + break + pre = cur + if cur.val < num: # 待删除结点在 root 的右子树中 + cur = cur.right + else: # 待删除结点在 root 的左子树中 + cur = cur.left + + # 若无待删除结点,则直接返回 + if cur is None: + return None + + # 子结点数量 = 0 or 1 + if cur.left is None or cur.right is None: + # 当子结点数量 = 0 / 1 时, child = null / 该子结点 + child = cur.left or cur.right + # 删除结点 cur + if pre.left == cur: + pre.left = child + else: + pre.right = child + # 子结点数量 = 2 + else: + # 获取中序遍历中 cur 的下一个结点 + nex = self.min(cur.right) + tmp = nex.val + # 递归删除结点 nex + self.remove(nex.val) + # 将 nex 的值复制给 cur + cur.val = tmp + return cur + + """ 获取最小结点 """ + def min(self, root: typing.Optional[TreeNode]) -> typing.Optional[TreeNode]: + if root is None: + return root + + # 循环访问左子结点,直到叶结点时为最小结点,跳出 + while root.left is not None: + root = root.left + return root ``` === "Go" diff --git a/docs/chapter_tree/binary_tree.md b/docs/chapter_tree/binary_tree.md index 22478b847..4de1e4c1b 100644 --- a/docs/chapter_tree/binary_tree.md +++ b/docs/chapter_tree/binary_tree.md @@ -35,7 +35,7 @@ comments: true ```python title="" """ 链表结点类 """ class TreeNode: - def __init__(self, val=0, left=None, right=None): + def __init__(self, val=None, left=None, right=None): self.val = val # 结点值 self.left = left # 左子结点指针 self.right = right # 右子结点指针 @@ -175,7 +175,18 @@ comments: true === "Python" ```python title="binary_tree.py" - + """ 初始化二叉树 """ + # 初始化节点 + n1 = TreeNode(val=1) + n2 = TreeNode(val=2) + n3 = TreeNode(val=3) + n4 = TreeNode(val=4) + n5 = TreeNode(val=5) + # 构建引用指向(即指针) + n1.left = n2 + n1.right = n3 + n2.left = n4 + n2.right = n5 ``` === "Go" @@ -284,7 +295,13 @@ comments: true === "Python" ```python title="binary_tree.py" - + """ 插入与删除结点 """ + p = TreeNode(0) + # 在 n1 -> n2 中间插入结点 P + n1.left = p + p.left = n2 + # 删除节点 P + n1.left = n2 ``` === "Go" @@ -437,7 +454,7 @@ comments: true === "Python" ```python title="" - “”“ 二叉树的数组表示 ”“” + """ 二叉树的数组表示 """ # 直接使用 None 来表示空位 tree = [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15] ``` diff --git a/docs/chapter_tree/binary_tree_traversal.md b/docs/chapter_tree/binary_tree_traversal.md index 971d24cc5..f46348412 100644 --- a/docs/chapter_tree/binary_tree_traversal.md +++ b/docs/chapter_tree/binary_tree_traversal.md @@ -51,12 +51,12 @@ comments: true vector vec; while (!queue.empty()) { TreeNode* node = queue.front(); - queue.pop(); // 队列出队 - vec.push_back(node->val); // 保存结点 + queue.pop(); // 队列出队 + vec.push_back(node->val); // 保存结点 if (node->left != nullptr) - queue.push(node->left); // 左子结点入队 + queue.push(node->left); // 左子结点入队 if (node->right != nullptr) - queue.push(node->right); // 右子结点入队 + queue.push(node->right); // 右子结点入队 } return vec; } @@ -65,7 +65,21 @@ comments: true === "Python" ```python title="binary_tree_bfs.py" - + """ 层序遍历 """ + def hier_order(root: TreeNode): + # 初始化队列,加入根结点 + queue = collections.deque() + queue.append(root) + # 初始化一个列表,用于保存遍历序列 + res = [] + while queue: + node = queue.popleft() # 队列出队 + res.append(node.val) # 保存节点值 + if node.left is not None: + queue.append(node.left) # 左子结点入队 + if node.right is not None: + queue.append(node.right) # 右子结点入队 + return res ``` === "Go" @@ -256,7 +270,32 @@ comments: true === "Python" ```python title="binary_tree_dfs.py" - + """ 前序遍历 """ + def pre_order(root: typing.Optional[TreeNode]): + if root is None: + return + # 访问优先级:根结点 -> 左子树 -> 右子树 + res.append(root.val) + pre_order(root=root.left) + pre_order(root=root.right) + + """ 中序遍历 """ + def in_order(root: typing.Optional[TreeNode]): + if root is None: + return + # 访问优先级:左子树 -> 根结点 -> 右子树 + in_order(root=root.left) + res.append(root.val) + in_order(root=root.right) + + """ 后序遍历 """ + def post_order(root: typing.Optional[TreeNode]): + if root is None: + return + # 访问优先级:左子树 -> 右子树 -> 根结点 + post_order(root=root.left) + post_order(root=root.right) + res.append(root.val) ``` === "Go" @@ -402,7 +441,6 @@ comments: true postOrder(root.right); list.Add(root.val); } - ``` !!! note