# Height Balanced Tree - Amazon Top Interview Questions

### Problem Statement :

```Given the root of a binary tree, return whether its height is balanced. That is, for every node in the tree, the absolute difference of the height of its left subtree and the height of its right subtree is 0 or 1.

Constraints

n ≤ 100,000 where n is the number of nodes in root

Example 1

Input

root = [1, null, [4, null, [12, null, null]]]

Output

False

Explanation

This is false since the root's right subtree has height of 2, and left has height of 0.

Example 2

Input

root = [1, [0, null, null], [4, null, [12, null, null]]]

Output

True```

### Solution :

```                        ```Solution in C++ :

int height(Tree* root) {
if (root == NULL) return 0;
return max(height(root->left), height(root->right)) + 1;
}
bool solve(Tree* root) {
if (root == NULL) return true;

return solve(root->left) && solve(root->right) &&
abs(height(root->left) - height(root->right)) <= 1;
}```
```

```                        ```Solution in Java :

import java.util.*;

/**
* public class Tree {
*   int val;
*   Tree left;
*   Tree right;
* }
*/
class Solution {
public boolean ans = true;

public int traverse(Tree root) {
if (root == null)
return 0;
int left = traverse(root.left);
int right = traverse(root.right);
ans = ans && (Math.abs(left - right) < 2);
return Math.max(left, right) + 1;
}

public boolean solve(Tree root) {
traverse(root);
return ans;
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, root):
isBalanced = True

def dfs(depth, root):
nonlocal isBalanced
if not root:
return depth

left = dfs(depth + 1, root.left)
right = dfs(depth + 1, root.right)

if abs(left - right) > 1:
isBalanced = False

return max(left, right)

dfs(0, root)
return isBalanced```
```

## Costly Intervals

Given an array, your goal is to find, for each element, the largest subarray containing it whose cost is at least k. Specifically, let A = [A1, A2, . . . , An ] be an array of length n, and let be the subarray from index l to index r. Also, Let MAX( l, r ) be the largest number in Al. . . r. Let MIN( l, r ) be the smallest number in Al . . .r . Let OR( l , r ) be the bitwise OR of the

## The Strange Function

One of the most important skills a programmer needs to learn early on is the ability to pose a problem in an abstract way. This skill is important not just for researchers but also in applied fields like software engineering and web development. You are able to solve most of a problem, except for one last subproblem, which you have posed in an abstract way as follows: Given an array consisting

## Self-Driving Bus

Treeland is a country with n cities and n - 1 roads. There is exactly one path between any two cities. The ruler of Treeland wants to implement a self-driving bus system and asks tree-loving Alex to plan the bus routes. Alex decides that each route must contain a subset of connected cities; a subset of cities is connected if the following two conditions are true: There is a path between ever

## Unique Colors

You are given an unrooted tree of n nodes numbered from 1 to n . Each node i has a color, ci. Let d( i , j ) be the number of different colors in the path between node i and node j. For each node i, calculate the value of sum, defined as follows: Your task is to print the value of sumi for each node 1 <= i <= n. Input Format The first line contains a single integer, n, denoti

## Fibonacci Numbers Tree

Shashank loves trees and math. He has a rooted tree, T , consisting of N nodes uniquely labeled with integers in the inclusive range [1 , N ]. The node labeled as 1 is the root node of tree , and each node in is associated with some positive integer value (all values are initially ). Let's define Fk as the Kth Fibonacci number. Shashank wants to perform 22 types of operations over his tree, T

## Pair Sums

Given an array, we define its value to be the value obtained by following these instructions: Write down all pairs of numbers from this array. Compute the product of each pair. Find the sum of all the products. For example, for a given array, for a given array [7,2 ,-1 ,2 ] Note that ( 7 , 2 ) is listed twice, one for each occurrence of 2. Given an array of integers, find the largest v