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<a href="../binary_tree/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.1 Binary tree
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
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|
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|
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<span class="md-ellipsis">
|
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7.2 Binary tree traversal
|
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</span>
|
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|
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|
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<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
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<a href="./" class="md-nav__link md-nav__link--active">
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|
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|
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<span class="md-ellipsis">
|
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7.2 Binary tree traversal
|
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</span>
|
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|
||
|
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</a>
|
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|
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|
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|
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<nav class="md-nav md-nav--secondary" aria-label="Table of contents">
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7.2.1 Level-order traversal
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</a>
|
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|
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<nav class="md-nav" aria-label="7.2.1 Level-order traversal">
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|
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1. Code implementation
|
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|
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|
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|
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|
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2. Complexity analysis
|
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|
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|
||
</li>
|
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|
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|
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|
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|
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<span class="md-ellipsis">
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7.2.2 Preorder, inorder, and postorder traversal
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|
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|
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|
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|
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1. Code implementation
|
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|
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2. Complexity analysis
|
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|
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|
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|
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|
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|
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|
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|
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<span class="md-ellipsis">
|
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7.3 Array Representation of tree
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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<li class="md-nav__item">
|
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<a href="../binary_search_tree/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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7.4 Binary Search tree
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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|
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7.5 AVL tree *
|
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</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
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<a href="../summary/" class="md-nav__link">
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|
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7.6 Summary
|
||
</span>
|
||
|
||
|
||
</a>
|
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|
||
|
||
|
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|
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||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
Chapter 8. Heap
|
||
</span>
|
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|
||
|
||
</a>
|
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|
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|
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<span class="md-nav__icon md-icon"></span>
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Chapter 8. Heap
|
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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|
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|
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<a href="../../chapter_heap/heap/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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8.1 Heap
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
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|
||
|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_heap/build_heap/" class="md-nav__link">
|
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|
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|
||
<span class="md-ellipsis">
|
||
8.2 Building a heap
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_heap/top_k/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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8.3 Top-k problem
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_heap/summary/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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8.4 Summary
|
||
</span>
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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</ul>
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</nav>
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|
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|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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<li class="md-nav__item md-nav__item--nested">
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|
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
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<span class="md-ellipsis">
|
||
Chapter 9. Graph
|
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</span>
|
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|
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|
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</a>
|
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Chapter 9. Graph
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
|
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<a href="../../chapter_graph/graph/" class="md-nav__link">
|
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|
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<span class="md-ellipsis">
|
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9.1 Graph
|
||
</span>
|
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|
||
|
||
</a>
|
||
</li>
|
||
|
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<li class="md-nav__item">
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<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
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<span class="md-ellipsis">
|
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9.2 Basic graph operations
|
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</span>
|
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|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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<li class="md-nav__item">
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<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
|
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<span class="md-ellipsis">
|
||
9.3 Graph traversal
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_graph/summary/" class="md-nav__link">
|
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<span class="md-ellipsis">
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9.4 Summary
|
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</span>
|
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|
||
|
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|
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|
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|
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|
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<span class="md-ellipsis">
|
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Chapter 10. Searching
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</span>
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</a>
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Chapter 10. Searching
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10.1 Binary search
|
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</span>
|
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|
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|
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</a>
|
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</li>
|
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<li class="md-nav__item">
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<span class="md-ellipsis">
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10.2 Binary search insertion
|
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</span>
|
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|
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|
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</a>
|
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</li>
|
||
|
||
|
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|
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|
||
|
||
|
||
|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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10.3 Binary search boundaries
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
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|
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|
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|
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|
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|
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|
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|
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10.4 Hashing optimization strategies
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<span class="md-ellipsis">
|
||
10.5 Search algorithms revisited
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
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|
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|
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|
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|
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<span class="md-ellipsis">
|
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10.6 Summary
|
||
</span>
|
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|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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|
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</ul>
|
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</nav>
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|
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|
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Chapter 11. Sorting
|
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Chapter 11. Sorting
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11.1 Sorting algorithms
|
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</span>
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|
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|
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</a>
|
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</li>
|
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11.2 Selection sort
|
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</span>
|
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|
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|
||
</a>
|
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</li>
|
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|
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|
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11.3 Bubble sort
|
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</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
|
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|
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|
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11.4 Insertion sort
|
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</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
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|
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|
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|
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<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
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|
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<span class="md-ellipsis">
|
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11.5 Quick sort
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
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|
||
|
||
|
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|
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|
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|
||
<li class="md-nav__item">
|
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<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
|
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|
||
|
||
<span class="md-ellipsis">
|
||
11.6 Merge sort
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
||
<li class="md-nav__item">
|
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<a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
|
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|
||
|
||
<span class="md-ellipsis">
|
||
11.7 Heap sort
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
|
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|
||
|
||
<span class="md-ellipsis">
|
||
11.8 Bucket sort
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.9 Counting sort
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.10 Radix sort
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_sorting/summary/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
||
11.11 Summary
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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|
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</ul>
|
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</nav>
|
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|
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|
||
|
||
|
||
|
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|
||
|
||
|
||
|
||
|
||
|
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|
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|
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<span class="md-ellipsis">
|
||
Chapter 12. Divide and conquer
|
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</span>
|
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|
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|
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</a>
|
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<label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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Chapter 12. Divide and conquer
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<a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
|
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<span class="md-ellipsis">
|
||
12.1 Divide and conquer algorithms
|
||
</span>
|
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|
||
|
||
</a>
|
||
</li>
|
||
|
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
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|
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|
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<span class="md-ellipsis">
|
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12.2 Divide and conquer search strategy
|
||
</span>
|
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|
||
|
||
</a>
|
||
</li>
|
||
|
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<li class="md-nav__item">
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|
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12.3 Building binary tree problem
|
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</span>
|
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|
||
|
||
</a>
|
||
</li>
|
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12.4 Tower of Hanoi Problem
|
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|
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|
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|
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</a>
|
||
</li>
|
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|
||
12.5 Summary
|
||
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|
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|
||
|
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|
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Chapter 13. Backtracking
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Chapter 13. Backtracking
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13.1 Backtracking algorithms
|
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|
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</a>
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</li>
|
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13.2 Permutation problem
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</a>
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</li>
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13.3 Subset sum problem
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|
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</a>
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</li>
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13.4 n queens problem
|
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|
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|
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|
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</a>
|
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</li>
|
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|
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13.5 Summary
|
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|
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|
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|
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<h1 id="72-binary-tree-traversal">7.2 Binary tree traversal<a class="headerlink" href="#72-binary-tree-traversal" title="Permanent link">¶</a></h1>
|
||
<p>From the perspective of physical structure, a tree is a data structure based on linked lists, hence its traversal method involves accessing nodes one by one through pointers. However, a tree is a non-linear data structure, which makes traversing a tree more complex than traversing a linked list, requiring the assistance of search algorithms to achieve.</p>
|
||
<p>Common traversal methods for binary trees include level-order traversal, preorder traversal, inorder traversal, and postorder traversal, among others.</p>
|
||
<h2 id="721-level-order-traversal">7.2.1 Level-order traversal<a class="headerlink" href="#721-level-order-traversal" title="Permanent link">¶</a></h2>
|
||
<p>As shown in Figure 7-9, <u>level-order traversal</u> traverses the binary tree from top to bottom, layer by layer, and accesses nodes in each layer in a left-to-right order.</p>
|
||
<p>Level-order traversal essentially belongs to <u>breadth-first traversal</u>, also known as <u>breadth-first search (BFS)</u>, which embodies a "circumferentially outward expanding" layer-by-layer traversal method.</p>
|
||
<p><a class="glightbox" href="../binary_tree_traversal.assets/binary_tree_bfs.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Level-order traversal of a binary tree" class="animation-figure" src="../binary_tree_traversal.assets/binary_tree_bfs.png" /></a></p>
|
||
<p align="center"> Figure 7-9 Level-order traversal of a binary tree </p>
|
||
|
||
<h3 id="1-code-implementation">1. Code implementation<a class="headerlink" href="#1-code-implementation" title="Permanent link">¶</a></h3>
|
||
<p>Breadth-first traversal is usually implemented with the help of a "queue". The queue follows the "first in, first out" rule, while breadth-first traversal follows the "layer-by-layer progression" rule, the underlying ideas of the two are consistent. The implementation code is as follows:</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_bfs.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span> <span class="nf">level_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-></span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""Level-order traversal"""</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="c1"># Initialize queue, add root node</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">queue</span><span class="p">:</span> <span class="n">deque</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]</span> <span class="o">=</span> <span class="n">deque</span><span class="p">()</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="c1"># Initialize a list to store the traversal sequence</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="k">while</span> <span class="n">queue</span><span class="p">:</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">=</span> <span class="n">queue</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span> <span class="c1"># Queue dequeues</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">)</span> <span class="c1"># Save node value</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="k">if</span> <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span> <span class="c1"># Left child node enqueues</span>
|
||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="k">if</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span> <span class="c1"># Right child node enqueues</span>
|
||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a> <span class="k">return</span> <span class="n">res</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_bfs.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">levelOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_bfs.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* Level-order traversal */</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="nf">levelOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w"> </span><span class="c1">// Initialize queue, add root node</span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="n">Queue</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">LinkedList</span><span class="o"><></span><span class="p">();</span>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="c1">// Initialize a list to store the traversal sequence</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">list</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">();</span>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">queue</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w"> </span><span class="n">TreeNode</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">queue</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// Queue dequeues</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w"> </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">);</span><span class="w"> </span><span class="c1">// Save node value</span>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
|
||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// Left child node enqueues</span>
|
||
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
|
||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// Right child node enqueues</span>
|
||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">list</span><span class="p">;</span>
|
||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_bfs.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_tree_bfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">LevelOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_bfs.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">levelOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_bfs.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">levelOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_bfs.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">levelOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_bfs.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">levelOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_bfs.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">levelOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_bfs.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">level_order</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_bfs.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">levelOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_bfs.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">levelOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">level_order</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_bfs.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">levelOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="2-complexity-analysis">2. Complexity analysis<a class="headerlink" href="#2-complexity-analysis" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li><strong>Time complexity is <span class="arithmatex">\(O(n)\)</span></strong>: All nodes are visited once, using <span class="arithmatex">\(O(n)\)</span> time, where <span class="arithmatex">\(n\)</span> is the number of nodes.</li>
|
||
<li><strong>Space complexity is <span class="arithmatex">\(O(n)\)</span></strong>: In the worst case, i.e., a full binary tree, before traversing to the lowest level, the queue can contain at most <span class="arithmatex">\((n + 1) / 2\)</span> nodes at the same time, occupying <span class="arithmatex">\(O(n)\)</span> space.</li>
|
||
</ul>
|
||
<h2 id="722-preorder-inorder-and-postorder-traversal">7.2.2 Preorder, inorder, and postorder traversal<a class="headerlink" href="#722-preorder-inorder-and-postorder-traversal" title="Permanent link">¶</a></h2>
|
||
<p>Correspondingly, preorder, inorder, and postorder traversal all belong to <u>depth-first traversal</u>, also known as <u>depth-first search (DFS)</u>, which embodies a "proceed to the end first, then backtrack and continue" traversal method.</p>
|
||
<p>Figure 7-10 shows the working principle of performing a depth-first traversal on a binary tree. <strong>Depth-first traversal is like walking around the perimeter of the entire binary tree</strong>, encountering three positions at each node, corresponding to preorder traversal, inorder traversal, and postorder traversal.</p>
|
||
<p><a class="glightbox" href="../binary_tree_traversal.assets/binary_tree_dfs.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Preorder, inorder, and postorder traversal of a binary search tree" class="animation-figure" src="../binary_tree_traversal.assets/binary_tree_dfs.png" /></a></p>
|
||
<p align="center"> Figure 7-10 Preorder, inorder, and postorder traversal of a binary search tree </p>
|
||
|
||
<h3 id="1-code-implementation_1">1. Code implementation<a class="headerlink" href="#1-code-implementation_1" title="Permanent link">¶</a></h3>
|
||
<p>Depth-first search is usually implemented based on recursion:</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-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_dfs.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span> <span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">):</span>
|
||
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w"> </span><span class="sd">"""Pre-order traversal"""</span>
|
||
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a> <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a> <span class="k">return</span>
|
||
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a> <span class="c1"># Visit priority: root node -> left subtree -> right subtree</span>
|
||
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a> <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a> <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
|
||
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a> <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
|
||
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>
|
||
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="k">def</span> <span class="nf">in_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">):</span>
|
||
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w"> </span><span class="sd">"""In-order traversal"""</span>
|
||
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a> <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a> <span class="k">return</span>
|
||
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a> <span class="c1"># Visit priority: left subtree -> root node -> right subtree</span>
|
||
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a> <span class="n">in_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
|
||
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a> <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a> <span class="n">in_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
|
||
<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>
|
||
<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="k">def</span> <span class="nf">post_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">):</span>
|
||
<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w"> </span><span class="sd">"""Post-order traversal"""</span>
|
||
<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a> <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||
<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a> <span class="k">return</span>
|
||
<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a> <span class="c1"># Visit priority: left subtree -> right subtree -> root node</span>
|
||
<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a> <span class="n">post_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
|
||
<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a> <span class="n">post_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
|
||
<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a> <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_dfs.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
|
||
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a>
|
||
<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">inOrder</span><span class="p">}</span>
|
||
<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a>
|
||
<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">postOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_dfs.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* Pre-order traversal */</span>
|
||
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
|
||
<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w"> </span><span class="c1">// Visit priority: root node -> left subtree -> right subtree</span>
|
||
<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w"> </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
|
||
<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
|
||
<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w"> </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
|
||
<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span>
|
||
<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a>
|
||
<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="cm">/* In-order traversal */</span>
|
||
<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
|
||
<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w"> </span><span class="c1">// Visit priority: left subtree -> root node -> right subtree</span>
|
||
<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w"> </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
|
||
<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w"> </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
|
||
<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w"> </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
|
||
<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="p">}</span>
|
||
<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a>
|
||
<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="cm">/* Post-order traversal */</span>
|
||
<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
|
||
<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w"> </span><span class="c1">// Visit priority: left subtree -> right subtree -> root node</span>
|
||
<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w"> </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
|
||
<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w"> </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
|
||
<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w"> </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
|
||
<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_dfs.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_tree_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PreOrder</span><span class="p">}</span>
|
||
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
|
||
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_tree_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">InOrder</span><span class="p">}</span>
|
||
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a>
|
||
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_tree_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PostOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_dfs.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
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<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">inOrder</span><span class="p">}</span>
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<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a>
|
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<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">postOrder</span><span class="p">}</span>
|
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</code></pre></div>
|
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</div>
|
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">binary_tree_dfs.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
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<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">inOrder</span><span class="p">}</span>
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<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a>
|
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<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">postOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
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<div class="tabbed-block">
|
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<div class="highlight"><span class="filename">binary_tree_dfs.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
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<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
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<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">inOrder</span><span class="p">}</span>
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<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a>
|
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<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">postOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
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<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_dfs.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
|
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<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
|
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<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">inOrder</span><span class="p">}</span>
|
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<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a>
|
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<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">postOrder</span><span class="p">}</span>
|
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</code></pre></div>
|
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</div>
|
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<div class="tabbed-block">
|
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<div class="highlight"><span class="filename">binary_tree_dfs.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
|
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<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
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<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">inOrder</span><span class="p">}</span>
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<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a>
|
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<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">postOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_dfs.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pre_order</span><span class="p">}</span>
|
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|
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<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="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">post_order</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_dfs.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
|
||
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
|
||
<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">inOrder</span><span class="p">}</span>
|
||
<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a>
|
||
<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">postOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_dfs.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">preOrder</span><span class="p">}</span>
|
||
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
|
||
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">inOrder</span><span class="p">}</span>
|
||
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>
|
||
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">postOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pre_order</span><span class="p">}</span>
|
||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
|
||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">in_order</span><span class="p">}</span>
|
||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>
|
||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">post_order</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">binary_tree_dfs.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
|
||
<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a>
|
||
<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">inOrder</span><span class="p">}</span>
|
||
<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a>
|
||
<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">postOrder</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="admonition tip">
|
||
<p class="admonition-title">Tip</p>
|
||
<p>Depth-first search can also be implemented based on iteration, interested readers can study this on their own.</p>
|
||
</div>
|
||
<p>Figure 7-11 shows the recursive process of preorder traversal of a binary tree, which can be divided into two opposite parts: "recursion" and "return".</p>
|
||
<ol>
|
||
<li>"Recursion" means starting a new method, the program accesses the next node in this process.</li>
|
||
<li>"Return" means the function returns, indicating the current node has been fully accessed.</li>
|
||
</ol>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="3:11"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1"><1></label><label for="__tabbed_3_2"><2></label><label for="__tabbed_3_3"><3></label><label for="__tabbed_3_4"><4></label><label for="__tabbed_3_5"><5></label><label for="__tabbed_3_6"><6></label><label for="__tabbed_3_7"><7></label><label for="__tabbed_3_8"><8></label><label for="__tabbed_3_9"><9></label><label for="__tabbed_3_10"><10></label><label for="__tabbed_3_11"><11></label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="The recursive process of preorder traversal" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step1.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step2" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step2.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step3" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step3.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step4" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step4.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step5" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step5.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step6" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step6.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step7" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step7.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step8" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step8.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step9" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step9.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step10" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step10.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step11.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step11" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step11.png" /></a></p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p align="center"> Figure 7-11 The recursive process of preorder traversal </p>
|
||
|
||
<h3 id="2-complexity-analysis_1">2. Complexity analysis<a class="headerlink" href="#2-complexity-analysis_1" title="Permanent link">¶</a></h3>
|
||
<ul>
|
||
<li><strong>Time complexity is <span class="arithmatex">\(O(n)\)</span></strong>: All nodes are visited once, using <span class="arithmatex">\(O(n)\)</span> time.</li>
|
||
<li><strong>Space complexity is <span class="arithmatex">\(O(n)\)</span></strong>: In the worst case, i.e., the tree degrades into a linked list, the recursion depth reaches <span class="arithmatex">\(n\)</span>, the system occupies <span class="arithmatex">\(O(n)\)</span> stack frame space.</li>
|
||
</ul>
|
||
|
||
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