# Find Height of Binary Tree represented by Parent array in C++

In this problem, we are given an array arr[] of size n that denotes a tree. Our task is to find height of Binary Tree represented by Parent array.

A Binary Search Tree (BST) is a tree in which all the nodes follow the below-mentioned properties −

• The value of the key of the left sub-tree is less than the value of its parent (root) node's key.
• The value of the key of the right subtree is greater than or equal to the value of its parent (root) node's key.

Height of a tree is the number of nodes traversed when going from root node to the farthest leaf node.

Solution Approach:

A simple solution to the problem is by creating a tree from the parent array. Finding the root of this tree and recurring for the found index making left and right subtree and then returns the maximum height.

A more efficient method would be calculating the depth of nodes from the array and store then store it in depth array. From this array return the maximum depth.

## Example

Live Demo

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

void findAllDepths(int arr[], int i, int nodeDepth[]) {

if (nodeDepth[i])
return;
if (arr[i] == -1) {

nodeDepth[i] = 1;
return;
}
if (nodeDepth[arr[i]] == 0)
findAllDepths(arr, arr[i], nodeDepth);
nodeDepth[i] = nodeDepth[arr[i]] + 1;
}

int findMaxHeightBT(int arr[], int n) {

int nodeDepth[n];
for (int i = 0; i < n; i++)
nodeDepth[i] = 0;
for (int i = 0; i < n; i++)
findAllDepths(arr, i, nodeDepth);
int maxHeight = nodeDepth[0];
for (int i=1; i<n; i++)
if (maxHeight < nodeDepth[i])
maxHeight = nodeDepth[i];
return maxHeight;
}

int main() {

int arr[] = {-1, 0, 0, 1, 1};
int n = sizeof(arr)/sizeof(arr[0]);
cout<<"The maximum height of binary Tree is "<<findMaxHeightBT(arr, n);
return 0;
}

## Output −

The maximum height of binary Tree is 3