Walk of a Tree

A tree walk refers to a process of visiting each node in a tree data structure in a systematic way. Common walks include pre-order, in-order, post-order, and level-order.

Java - Pre-order traversal:

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void preOrder(TreeNode root) {
  if (root == null) return;
  
  System.out.print(root.val + " ");
  preOrder(root.left);
  preOrder(root.right);
} 

C++ - In-order traversal:

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void inOrder(TreeNode* root) {
  if (!root) return;

  inOrder(root->left);
  cout << root->val << " ";
  inOrder(root->right);
}

Python - Post-order traversal:

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def post_order(root):
  if root is None:
    return
  
  post_order(root.left)
  post_order(root.right)
  print(root.val, end=' ')

Key properties:

Visits each node systematically once
Different orderings produce different walks
Useful for tree operations like copying

Tree walks provide mechanisms to visit nodes in structured manner. Allow implementing traversal, serialization, etc.

A “walk” in the context of a tree refers to a sequence of vertices and edges that starts and ends at the same vertex, in which each edge and vertex is visited exactly once. The concept of a “walk” is crucial for various algorithms in tree traversal, including Depth First Search (DFS) and Breadth First Search (BFS).

The concept of a “walk” in a tree refers to traversing the tree’s nodes in a particular sequence. In a walk, you start at one node and move along the edges to reach another node. You can revisit nodes and edges.

Visual Representation:

Imagine a tree with the following structure, where each letter represents a node and the lines represent edges between nodes.

A walk from node A to node F could be: A -> B -> A -> C -> F

In this example, the “walk” starts at node A, goes down to node B, then returns to A, then goes to C, and finally reaches F.

Key Takeaway:

The concept of a “walk” allows us to describe the various ways we can navigate from one point to another within a tree. Understanding walks is fundamental in tree-related algorithms like depth-first and breadth-first search.

Solution

In the code examples below, we demonstrate how to perform a simple walk of a binary tree using DFS in Java, C++, and Python. The DFS algorithm starts at the root and explores as far as possible along each branch before backtracking.

Java

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class TreeNode {
    int value;
    TreeNode left;
    TreeNode right;
    TreeNode(int value) {
        this.value = value;
    }
}

public class TreeWalk {
    public static void dfs(TreeNode node) {
        if (node == null) return;
        System.out.println(node.value);  // Process the current node
        dfs(node.left);  // Walk the left subtree
        dfs(node.right);  // Walk the right subtree
    }

    public static void main(String[] args) {
        TreeNode root = new TreeNode(1);
        root.left = new TreeNode(2);
        root.right = new TreeNode(3);
        dfs(root);  // Output will be 1 2 3
    }
}

C++

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#include <iostream>

struct TreeNode {
    int value;
    TreeNode* left;
    TreeNode* right;
    TreeNode(int val) : value(val), left(NULL), right(NULL) {}
};

void dfs(TreeNode* node) {
    if (node == NULL) return;
    std::cout << node->value << " ";  // Process the current node
    dfs(node->left);  // Walk the left subtree
    dfs(node->right);  // Walk the right subtree
}

int main() {
    TreeNode* root = new TreeNode(1);
    root->left = new TreeNode(2);
    root->right = new TreeNode(3);
    dfs(root);  // Output will be "1 2 3"
    return 0;
}

Python

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class TreeNode:
    def __init__(self, value):
        self.value = value
        self.left = None
        self.right = None

def dfs(node):
    if node is None:
        return
    print(node.value, end=' ')  # Process the current node
    dfs(node.left)  # Walk the left subtree
    dfs(node.right)  # Walk the right subtree

if __name__ == "__main__":
    root = TreeNode(1)
    root.left = TreeNode(2)
    root.right = TreeNode(3)
    dfs(root)  # Output will be "1 2 3"

Key Takeaways

A “walk” in a tree refers to a specific sequence of vertices and edges.
Tree walks are essential for traversal algorithms like DFS and BFS.
DFS is a commonly used method to perform a walk in a tree. It explores as far as possible along each branch before backtracking.