BFS of Tree: Implementation Steps for Breadth-First Search and Level Order Traversal
BFS is a classic tree traversal method that accesses nodes in a "breadth-first" (level order) manner, with its core implementation relying on a queue (FIFO). The steps are as follows: initialize the queue by enqueueing the root node, then repeatedly dequeue the front node for access, enqueue its left and right children (in natural order) until the queue is empty. BFS is suitable for tree hierarchy problems, such as calculating tree height, determining a perfect binary tree, and finding the shortest root-to-leaf path. For the binary tree `1(2(4,5),3)`, the level order traversal sequence is 1→2→3→4→5. Key points: The queue ensures level order, the enqueue order of children (left→right), time complexity O(n) (where n is the number of nodes), and space complexity O(n) (worst-case scenario with n/2 nodes in the queue). Mastering BFS enables efficient solution of level-related problems and serves as a foundation for more complex algorithms.
Read MoreBinary Trees: Three Traversal Methods of Binary Trees, Recursive Implementation Made Super Simple
This article introduces three classic traversal methods of binary trees (pre-order, in-order, and post-order), implemented recursively, with the core being clarifying the position of root node access. Each node in a binary tree has at most left and right subtrees. Traversal refers to visiting nodes in a specific order. Recursion is key here, similar to "matryoshka dolls," where the function calls itself with a narrowed scope until empty nodes are encountered, terminating the recursion. The differences between the three traversal orders are: - Pre-order: Root → Left → Right; - In-order: Left → Root → Right; - Post-order: Left → Right → Root. Using an example tree (root 1 with left child 2 and right child 3; node 2 has left child 4 and right child 5), the traversal results are: - Pre-order: 1 2 4 5 3; - In-order: 4 2 5 1 3; - Post-order: 4 5 2 3 1. The core of recursive implementation lies in the termination condition (returning for empty nodes) and recursively traversing left and right subtrees in the traversal order. By clarifying the root position and recursive logic, the traversal process can be clearly understood.
Read MoreHow to Learn Tree Traversal? Easily Understand Preorder, Inorder, and Postorder Traversals
Trees are fundamental data structures, and traversal is the process of visiting all nodes. This article focuses on explaining the preorder, inorder, and postorder traversals of binary trees, with their core difference lying in the timing of visiting the root node. - **Preorder Traversal (Root → Left → Right)**: Visit the root first, then recursively traverse the left subtree, and finally the right subtree. Example: 1→2→4→5→3→6→7. - **Inorder Traversal (Left → Root → Right)**: Recursively traverse the left subtree first, then visit the root, and finally the right subtree. Example: 4→2→5→1→6→3→7. - **Postorder Traversal (Left → Right → Root)**: Recursively traverse the left subtree first, then the right subtree, and finally visit the root. Example: 4→5→2→6→7→3→1. Memory mnemonic: Preorder has the root first, inorder has the root in the middle, postorder has the root last. In applications, preorder is used for tree copying, inorder sorts binary search trees, and postorder is used for node deletion. Traversal essentially embodies the recursive thought; mastering the order and scenarios enables proficiency.
Read MoreDrawing Binary Trees Step by Step: The First Lesson in Data Structure Fundamentals
A binary tree is a fundamental data structure where each node has at most two child nodes (left and right), and nodes with no descendants are called leaves. Core terms include: root node (the topmost starting point), leaf node (node with no children), child node (a node on the next level below its parent), and left/right subtrees (the left/right children and their descendants of a node). Construction starts from the root node, with child nodes added incrementally. Each node can have at most two children, and child positions are ordered (left vs. right). A binary tree must satisfy: each node has ≤2 children, and child positions are clearly defined (left or right). Traversal methods include pre-order (root → left → right), in-order (left → root → right), and post-order (left → right → root). Drawing the tree is crucial for understanding core relationships, as it intuitively visualizes node connections and forms the foundation for complex structures (e.g., heaps, red-black trees) and algorithms (sorting, searching).
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