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 a longest path are colored (note that there may be more than one path in tree of same diameter).

Examples:



Input :     1
          /   \
        2      3
      /  \
    4     5

Output : 4

Input :     1
          /   \
        2      3
      /  \ .    \
    4     5 .    6

Output : 5

We 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++

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// 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
    int height_of_tree = 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 code
int 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;
}

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Java

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// 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 binary 
tree 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 code 
public 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.

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Python3

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# Simple C++ 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 tree 
def 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 code 
if __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

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C#

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// 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
    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 binary 
tree 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 code 
public 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*/

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Output:

Diameter is 4

This article is contributed by Pooja Kamal. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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