Diameter of a Binary Tree in O(n) [A new method]
The diameter of a tree is the number of nodes on the longest path between two leaves in the tree. The diagram below shows two trees each with diameter nine, the leaves that form the ends of the longest path are colored (note that there may be more than one path in the tree of the same diameter).
Examples:
Input : 1
/ \
2 3
/ \
4 5
Output : 4
Input : 1
/ \
2 3
/ \ . \
4 5 . 6
Output : 5We have discussed a solution in below post.
Diameter of a Binary Tree
In this post a new simple O(n) method is discussed. Diameter of a tree can be calculated by only using the height function, because the diameter of a tree is nothing but maximum value of (left_height + right_height + 1) for each node. So we need to calculate this value (left_height + right_height + 1) for each node and update the result. Time complexity – O(n)
C++14
// Simple C++ program to find diameter// of a binary tree.#include <bits/stdc++.h>using namespace std;/* Tree node structure used in the program */struct Node { int data; Node* left, *right;};/* Function to find height of a tree */int height(Node* root, int& ans){ if (root == NULL) return 0; int left_height = height(root->left, ans); int right_height = height(root->right, ans); // update the answer, because diameter of a // tree is nothing but maximum value of // (left_height + right_height + 1) for each node ans = max(ans, 1 + left_height + right_height); return 1 + max(left_height, right_height);}/* Computes the diameter of binary tree with given root. */int diameter(Node* root){ if (root == NULL) return 0; int ans = INT_MIN; // This will store the final answer height(root, ans); return ans;}struct Node* newNode(int data){ struct Node* node = new Node; node->data = data; node->left = node->right = NULL; return (node);}// Driver codeint main(){ struct Node* root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); printf("Diameter is %d\n", diameter(root)); return 0;} |
Java
// Simple Java program to find diameter// of a binary tree.class GfG {/* Tree node structure used in the program */static class Node{ int data; Node left, right;}static class A{ int ans = Integer.MIN_VALUE;}/* Function to find height of a tree */static int height(Node root, A a){ if (root == null) return 0; int left_height = height(root.left, a); int right_height = height(root.right, a); // update the answer, because diameter of a // tree is nothing but maximum value of // (left_height + right_height + 1) for each node a.ans = Math.max(a.ans, 1 + left_height + right_height); return 1 + Math.max(left_height, right_height);}/* Computes the diameter of binarytree with given root. */static int diameter(Node root){ if (root == null) return 0; // This will store the final answer A a = new A(); int height_of_tree = height(root, a); return a.ans;}static Node newNode(int data){ Node node = new Node(); node.data = data; node.left = null; node.right = null; return (node);}// Driver codepublic static void main(String[] args){ Node root = newNode(1); root.left = newNode(2); root.right = newNode(3); root.left.left = newNode(4); root.left.right = newNode(5); System.out.println("Diameter is " + diameter(root));}}// This code is contributed by Prerna Saini. |
Python3
# Simple Python3 program to find diameter# of a binary tree.class newNode: def __init__(self, data): self.data = data self.left = self.right = None# Function to find height of a treedef height(root, ans): if (root == None): return 0 left_height = height(root.left, ans) right_height = height(root.right, ans) # update the answer, because diameter # of a tree is nothing but maximum # value of (left_height + right_height + 1) # for each node ans[0] = max(ans[0], 1 + left_height + right_height) return 1 + max(left_height, right_height)# Computes the diameter of binary# tree with given root.def diameter(root): if (root == None): return 0 ans = [-999999999999] # This will store # the final answer height_of_tree = height(root, ans) return ans[0]# Driver codeif __name__ == '__main__': root = newNode(1) root.left = newNode(2) root.right = newNode(3) root.left.left = newNode(4) root.left.right = newNode(5) print("Diameter is", diameter(root))# This code is contributed by PranchalK |
C#
// Simple C# program to find diameter// of a binary tree.using System;class GfG{/* Tree node structure used in the program */class Node{ public int data; public Node left, right;}class A{ public int ans = int.MinValue;}/* Function to find height of a tree */static int height(Node root, A a){ if (root == null) return 0; int left_height = height(root.left, a); int right_height = height(root.right, a); // update the answer, because diameter of a // tree is nothing but maximum value of // (left_height + right_height + 1) for each node a.ans = Math.Max(a.ans, 1 + left_height + right_height); return 1 + Math.Max(left_height, right_height);}/* Computes the diameter of binarytree with given root. */static int diameter(Node root){ if (root == null) return 0; // This will store the final answer A a = new A(); int height_of_tree = height(root, a); return a.ans;}static Node newNode(int data){ Node node = new Node(); node.data = data; node.left = null; node.right = null; return (node);}// Driver codepublic static void Main(){ Node root = newNode(1); root.left = newNode(2); root.right = newNode(3); root.left.left = newNode(4); root.left.right = newNode(5); Console.WriteLine("Diameter is " + diameter(root));}}/* This code is contributed by Rajput-Ji*/ |
Output
Diameter is 4
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