Problem

Calculate the height of the given binary tree.

Brute force approach

We can traverse each and calculate the diameter for each node.

max(lh + rh + 1, max(left_dia, right_dia)); .

TC – O(N2)

Better Approach

We can traverse each node one by one and keep its height and diameter(if diameter passes through that node) in a variable, and we will keep updating the global diameter of the tree.

#include<bits/stdc++.h>
using namespace std;

struct Node{
	int data;
  	Node* left;
  	Node* right;
  	Node(int data){
    	this->data = data;
      	left = right = NULL;
    }
};

int diameterOfTree(Node* root, int &result){
	if(!root) return 0;

  	int lh = diameterOfTree(root->left, result);
  	int rh = diameterOfTree(root->right, result);
	
  	int heightOfCurrNode = max(lh, rh) + 1;
  	int currDiameter = lh + rh;
  	result = max(currDiameter, result); // this contains the diameter
  	return heightOfCurrNode;
}


int main() {
/*
         1
       /    \
      2      3
    /   \   /  \
   4     5 6    7
*/
    struct Node* root = new Node(1);
  	root->left = new Node(2);
  	root->left->left = new Node(4);
  	root->left->right = new Node(5);
  	root->left->right->left = new Node(15);
  	root->right = new Node(3);
  	root->right->left = new Node(6);
  	root->right->right = new Node(7);
  	int result = INT_MIN;
  	diameterOfTree(root, result);
  	cout<<result;
    return 0;
}

 

TC – O(N)

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