Binary 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 MoreArrays: Why Are They the Cornerstone of Data Structures? A Must-Learn for Beginners
This article introduces the core position of arrays as a basic data structure. An array is a sequence of elements of the same type, enabling random access through indices (starting from 0). It features simplicity, intuitive design, continuous storage, and efficient index-based access. As a foundational structure, arrays underpin complex data structures like stacks, queues, and hash tables (e.g., stacks use arrays for Last-In-First-Out behavior, while queues utilize circular arrays for First-In-First-Out operations). They also form the basis of multi-dimensional arrays (e.g., matrices). Arrays support fundamental operations such as traversal, search, and sorting, with a random access time complexity of O(1), significantly outperforming linked lists' O(n). However, arrays have limitations: fixed size (static arrays) and inefficient insertion/deletion (requiring element shifting). In summary, arrays serve as the "key to entry" in data structures, and mastering them lays the foundation for learning complex structures and algorithms.
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