# Tree: Height of a Binary Tree

### Problem Statement :

```The height of a binary tree is the number of edges between the tree's root and its furthest leaf. For example, the following binary tree is of height :

image
Function Description

Complete the getHeight or height function in the editor. It must return the height of a binary tree as an integer.

getHeight or height has the following parameter(s):

root: a reference to the root of a binary tree.
Note -The Height of binary tree with single node is taken as zero.

Input Format

The first line contains an integer , the number of nodes in the tree.
Next line contains  space separated integer where th integer denotes node[i].data.

Note: Node values are inserted into a binary search tree before a reference to the tree's root node is passed to your function. In a binary search tree, all nodes on the left branch of a node are less than the node value. All values on the right branch are greater than the node value.

Output Format

Your function should return a single integer denoting the height of the binary tree.```

### Solution :

```                            ```Solution in C :

In C++ :

/*The tree node has data, left child and right child
struct node
{
int data;
node* left;
node* right;
};

*/
int height(node * root)
{
if(root==NULL) return 0;
else
{
int l=height(root->left);
int r=height(root->right);
if(l>r)
return l+1;
else
return r+1;
}
}

In Java :

/*

class Node
int data;
Node left;
Node right;
*/
int height(Node root){
if (root == null){
return 0;
}
else{
return 1+Math.max(height(root.left), height(root.right));
}
}

In C :

int getHeight(Node* root){
int h;
Node *r=root;
h=Height(r);
// Write your code here

return h-1;
}
int  Height(Node* r){
if (r == NULL)
return 0;

// Compute height of each tree
int heightLeft = Height(r->left);
int heightRight = Height(r->right);

/* use the larger one */
if (heightLeft > heightRight)
return(heightLeft + 1);
else
return(heightRight + 1);
}

In python3 :

def getHeight(self,root):
#Write your code here
leftHeight = 0
rightHeight = 0
if( root.left):
leftHeight = self.getHeight(root.left) + 1

if( root.right):
rightHeight = self.getHeight(root.right) + 1

if( leftHeight > rightHeight ):
return leftHeight
else:
return rightHeight```
```

## Balanced Forest

Greg has a tree of nodes containing integer data. He wants to insert a node with some non-zero integer value somewhere into the tree. His goal is to be able to cut two edges and have the values of each of the three new trees sum to the same amount. This is called a balanced forest. Being frugal, the data value he inserts should be minimal. Determine the minimal amount that a new node can have to a

## Jenny's Subtrees

Jenny loves experimenting with trees. Her favorite tree has n nodes connected by n - 1 edges, and each edge is ` unit in length. She wants to cut a subtree (i.e., a connected part of the original tree) of radius r from this tree by performing the following two steps: 1. Choose a node, x , from the tree. 2. Cut a subtree consisting of all nodes which are not further than r units from node x .

## Tree Coordinates

We consider metric space to be a pair, , where is a set and such that the following conditions hold: where is the distance between points and . Let's define the product of two metric spaces, , to be such that: , where , . So, it follows logically that is also a metric space. We then define squared metric space, , to be the product of a metric space multiplied with itself: . For

## Array Pairs

Consider an array of n integers, A = [ a1, a2, . . . . an] . Find and print the total number of (i , j) pairs such that ai * aj <= max(ai, ai+1, . . . aj) where i < j. Input Format The first line contains an integer, n , denoting the number of elements in the array. The second line consists of n space-separated integers describing the respective values of a1, a2 , . . . an .

## Self Balancing Tree

An AVL tree (Georgy Adelson-Velsky and Landis' tree, named after the inventors) is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. We define balance factor for each node as : balanceFactor = height(left subtree) - height(righ

## Array and simple queries

Given two numbers N and M. N indicates the number of elements in the array A[](1-indexed) and M indicates number of queries. You need to perform two types of queries on the array A[] . You are given queries. Queries can be of two types, type 1 and type 2. Type 1 queries are represented as 1 i j : Modify the given array by removing elements from i to j and adding them to the front. Ty