Distance of each node of a Binary Tree from the root node using BFS
Last Updated : 21 Jun, 2021
Given a Binary tree consisting of N nodes with values in the range [1, N], the task is to find the distance from the root node to every node of the tree.
Examples:
Input:
1 / \ 2 3 / \ \ 4 5 6
Output: 0 1 1 2 2 2
Explanation:
The distance from the root to node 1 is 0.
The distance from the root to node 2 is 1.
The distance from the root to node 3 is 1.
The distance from the root to node 4 is 2.
The distance from the root to node 5 is 2.
The distance from the root to node 6 is 2.
Input:
5 / \ 4 6 / \ 3 7 / \ 1 2
Output: 3 3 2 1 0 1 2
Approach: The problem can be solved using BFS technique. The idea is to use the fact that the distance from the root to a node is equal to the level of that node in the binary tree. Follow the steps below to solve the problem:
- Initialize a queue, say Q, to store the nodes at each level of the tree.
- Initialize an array, say dist[], where dist[i] stores the distance from the root node to ith of the tree.
- Traverse the tree using BFS. For every ith node encountered, update dist[i] to the level of that node in the binary tree.
- Finally, print the dist[] array.
Below is the implementation of the above approach:
C++ // C++ program to implement // the above approach #include <bits/stdc++.h> using namespace std; struct Node { // Stores data value // of the node int data; // Stores left subtree // of a node Node* left; // Stores right subtree // of a node Node* right; Node(int x) { data = x; left = right = NULL; } }; void findDistance(Node* root, int N) { // Store nodes at each level // of the binary tree queue<Node*> Q; // Insert root into Q Q.push(root); // Stores level of a node int level = 0; // dist[i]: Stores the distance // from root node to node i int dist[N + 1]; // Traverse tree using BFS while (!Q.empty()) { // Stores count of nodes // at current level int M = Q.size(); // Traverse the nodes at // current level for (int i = 0; i < M; i++) { // Stores front element // of the queue root = Q.front(); // Pop front element // of the queue Q.pop(); // Stores the distance from // root node to current node dist[root->data] = level; if (root->left) { // Push left subtree Q.push(root->left); } if (root->right) { // Push right subtree Q.push(root->right); } } // Update level level += 1; } for (int i = 1; i <= N; i++) { cout << dist[i] << " "; } } // Driver Code int main() { int N = 7; Node* root = new Node(5); root->left = new Node(4); root->right = new Node(6); root->left->left = new Node(3); root->left->right = new Node(7); root->left->left->left = new Node(1); root->left->left->right = new Node(2); findDistance(root, N); } // Java program to implement // the above approach import java.util.*; class GFG { static class Node { // Stores data value // of the node int data; // Stores left subtree // of a node Node left; // Stores right subtree // of a node Node right; Node(int x) { data = x; left = right = null; } }; static void findDistance(Node root, int N) { // Store nodes at each level // of the binary tree Queue<Node> Q = new LinkedList<>(); // Insert root into Q Q.add(root); // Stores level of a node int level = 0; // dist[i]: Stores the distance // from root node to node i int []dist = new int[N + 1]; // Traverse tree using BFS while (!Q.isEmpty()) { // Stores count of nodes // at current level int M = Q.size(); // Traverse the nodes at // current level for (int i = 0; i < M; i++) { // Stores front element // of the queue root = Q.peek(); // Pop front element // of the queue Q.remove(); // Stores the distance from // root node to current node dist[root.data] = level; if (root.left != null) { // Push left subtree Q.add(root.left); } if (root.right != null) { // Push right subtree Q.add(root.right); } } // Update level level += 1; } for (int i = 1; i <= N; i++) { System.out.print(dist[i] + " "); } } // Driver Code public static void main(String[] args) { int N = 7; Node root = new Node(5); root.left = new Node(4); root.right = new Node(6); root.left.left = new Node(3); root.left.right = new Node(7); root.left.left.left = new Node(1); root.left.left.right = new Node(2); findDistance(root, N); } } // This code is contributed by shikhasingrajput # Python3 program to implement # the above approach class Node: def __init__(self, data): # Stores data value # of the node self.data = data # Stores left subtree # of a node self.left = None # Stores right subtree # of a node self.right = None def findDistance(root, N): # Store nodes at each level # of the binary tree Q = [] # Insert root into Q Q.append(root) # Stores level of a node level = 0 # dist[i]: Stores the distance # from root node to node i dist = [0 for i in range(N + 1)] # Traverse tree using BFS while Q: # Stores count of nodes # at current level M = len(Q) # Traverse the nodes at # current level for i in range(0, M): # Stores front element # of the queue root = Q[0] # Pop front element # of the queue Q.pop(0) # Stores the distance from # root node to current node dist[root.data] = level if root.left: # Push left subtree Q.append(root.left) if root.right: # Push right subtree Q.append(root.right) # Update level level += 1 for i in range(1, N + 1): print(dist[i], end = " ") # Driver code if __name__ == '__main__': N = 7 root = Node(5) root.left = Node(4) root.right = Node(6) root.left.left = Node(3) root.left.right = Node(7) root.left.left.left = Node(1) root.left.left.right = Node(2) findDistance(root, N) # This code is contributed by MuskanKalra1
// C# program to implement // the above approach using System; using System.Collections.Generic; class GFG { class Node { // Stores data value // of the node public int data; // Stores left subtree // of a node public Node left; // Stores right subtree // of a node public Node right; public Node(int x) { data = x; left = right = null; } }; static void findDistance(Node root, int N) { // Store nodes at each level // of the binary tree Queue<Node> Q = new Queue<Node>(); // Insert root into Q Q.Enqueue(root); // Stores level of a node int level = 0; // dist[i]: Stores the distance // from root node to node i int []dist = new int[N + 1]; // Traverse tree using BFS while (Q.Count != 0) { // Stores count of nodes // at current level int M = Q.Count; // Traverse the nodes at // current level for (int i = 0; i < M; i++) { // Stores front element // of the queue root = Q.Peek(); // Pop front element // of the queue Q.Dequeue(); // Stores the distance from // root node to current node dist[root.data] = level; if (root.left != null) { // Push left subtree Q.Enqueue(root.left); } if (root.right != null) { // Push right subtree Q.Enqueue(root.right); } } // Update level level += 1; } for (int i = 1; i <= N; i++) { Console.Write(dist[i] + " "); } } // Driver Code public static void Main(String[] args) { int N = 7; Node root = new Node(5); root.left = new Node(4); root.right = new Node(6); root.left.left = new Node(3); root.left.right = new Node(7); root.left.left.left = new Node(1); root.left.left.right = new Node(2); findDistance(root, N); } } // This code is contributed by shikhasingrajput <script> // JavaScript program to implement the above approach // Structure of a tree node class Node { constructor(x) { this.left = null; this.right = null; this.data = x; } } function findDistance(root, N) { // Store nodes at each level // of the binary tree let Q = []; // Insert root into Q Q.push(root); // Stores level of a node let level = 0; // dist[i]: Stores the distance // from root node to node i let dist = new Array(N + 1); // Traverse tree using BFS while (Q.length > 0) { // Stores count of nodes // at current level let M = Q.length; // Traverse the nodes at // current level for (let i = 0; i < M; i++) { // Stores front element // of the queue root = Q[0]; // Pop front element // of the queue Q.shift(); // Stores the distance from // root node to current node dist[root.data] = level; if (root.left != null) { // Push left subtree Q.push(root.left); } if (root.right != null) { // Push right subtree Q.push(root.right); } } // Update level level += 1; } for (let i = 1; i <= N; i++) { document.write(dist[i] + " "); } } let N = 7; let root = new Node(5); root.left = new Node(4); root.right = new Node(6); root.left.left = new Node(3); root.left.right = new Node(7); root.left.left.left = new Node(1); root.left.left.right = new Node(2); findDistance(root, N); </script> Time Complexity: O(N)
Auxiliary Space: O(N)
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