# Largest Tree Sum Path - Google Top Interview Questions

### Problem Statement :

```Given a binary tree root, return the largest sum of any path between any two nodes.

Constraints

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

Example 1

Input

root = [-6, [5, null, null], [4, [7, [4, [2, null, null], null], [8, null, null]], [12, null, null]]]

Output

31

Explanation
The largest sum path is: [8, 7, 4, 12]```

### Solution :

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

int helper(Tree* root, int& ans) {
if (!root) return 0;
int a = helper(root->left, ans);
int b = helper(root->right, ans);
ans = max(ans, max(root->val + a + b, root->val));
return max(a + root->val, b + root->val);
}

int solve(Tree* root) {
int ans = INT_MIN;
helper(root, ans);
return ans;
}```
```

```                        ```Solution in Java :

import java.util.*;

/**
* public class Tree {
*   int val;
*   Tree left;
*   Tree right;
* }
*/
class Solution {
private int ans = Integer.MIN_VALUE;
public int solve(Tree root) {
traversal(root);
return ans;
}

private int traversal(Tree root) {
if (root == null) {
return 0;
}
int left = traversal(root.left);
int right = traversal(root.right);

int onePath = Math.max(Math.max(left, right) + root.val, root.val);
int topSum = Math.max(onePath, left + right + root.val);
ans = Math.max(ans, topSum);

return onePath;
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, root):
ans = -math.inf

def dfs(root):
if root is None:
return 0

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

single = max(left + root.val, right + root.val, root.val)

top = max(single, left + right + root.val)

nonlocal ans
ans = max(ans, top)

return single

dfs(root)
return ans```
```

## 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

## Print the Elements of a Linked List

This is an to practice traversing a linked list. Given a pointer to the head node of a linked list, print each node's data element, one per line. If the head pointer is null (indicating the list is empty), there is nothing to print. Function Description: Complete the printLinkedList function in the editor below. printLinkedList has the following parameter(s): 1.SinglyLinkedListNode

## Insert a Node at the Tail of a Linked List

You are given the pointer to the head node of a linked list and an integer to add to the list. Create a new node with the given integer. Insert this node at the tail of the linked list and return the head node of the linked list formed after inserting this new node. The given head pointer may be null, meaning that the initial list is empty. Input Format: You have to complete the SinglyLink