# Subtree with Maximum Value - Facebook Top Interview Questions

### Problem Statement :

```Given a binary tree root, return the maximum sum of a subtree.

A subtree is defined to be some node in root including all of its descendants.

A subtree sum is the sum of all the node values in the subtree.

A subtree can be null in which case its sum is 0.

Constraints

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

Example 1

Input

root = [3, [0, null, null], [2, [0, null, null], null]]

Output

5```

### Solution :

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

int ans;
int go(Tree* root) {
if (!root) return 0;
int val = go(root->left) + go(root->right) + root->val;
ans = max(ans, val);
return val;
}
int solve(Tree* root) {
ans = 0;
go(root);
return ans;
}```
```

```                        ```Solution in Java :

import java.util.*;

class Solution {
public int solve(Tree root) {
dfs(root);
return max;
}
int max = 0;
public int dfs(Tree root) {
if (root == null)
return 0;

int left = dfs(root.left);
int right = dfs(root.right);

max = Math.max(max, root.val + left + right);
return root.val + left + right;
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, root):
sol = 0

def subsum(node):
nonlocal sol
lhs = subsum(node.left) if node.left else 0
rhs = subsum(node.right) if node.right else 0
res = node.val + lhs + rhs
sol = max(sol, res)
return res

subsum(root)
return sol```
```

## Array-DS

An array is a type of data structure that stores elements of the same type in a contiguous block of memory. In an array, A, of size N, each memory location has some unique index, i (where 0<=i<N), that can be referenced as A[i] or Ai. Reverse an array of integers. Note: If you've already solved our C++ domain's Arrays Introduction challenge, you may want to skip this. Example: A=[1,2,3

## 2D Array-DS

Given a 6*6 2D Array, arr: 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 An hourglass in A is a subset of values with indices falling in this pattern in arr's graphical representation: a b c d e f g There are 16 hourglasses in arr. An hourglass sum is the sum of an hourglass' values. Calculate the hourglass sum for every hourglass in arr, then print t

## Dynamic Array

Create a list, seqList, of n empty sequences, where each sequence is indexed from 0 to n-1. The elements within each of the n sequences also use 0-indexing. Create an integer, lastAnswer, and initialize it to 0. There are 2 types of queries that can be performed on the list of sequences: 1. Query: 1 x y a. Find the sequence, seq, at index ((x xor lastAnswer)%n) in seqList.

## Left Rotation

A left rotation operation on an array of size n shifts each of the array's elements 1 unit to the left. Given an integer, d, rotate the array that many steps left and return the result. Example: d=2 arr=[1,2,3,4,5] After 2 rotations, arr'=[3,4,5,1,2]. Function Description: Complete the rotateLeft function in the editor below. rotateLeft has the following parameters: 1. int d

## Sparse Arrays

There is a collection of input strings and a collection of query strings. For each query string, determine how many times it occurs in the list of input strings. Return an array of the results. Example: strings=['ab', 'ab', 'abc'] queries=['ab', 'abc', 'bc'] There are instances of 'ab', 1 of 'abc' and 0 of 'bc'. For each query, add an element to the return array, results=[2,1,0]. Fun

## Array Manipulation

Starting with a 1-indexed array of zeros and a list of operations, for each operation add a value to each of the array element between two given indices, inclusive. Once all operations have been performed, return the maximum value in the array. Example: n=10 queries=[[1,5,3], [4,8,7], [6,9,1]] Queries are interpreted as follows: a b k 1 5 3 4 8 7 6 9 1 Add the valu