# Max Array Sum

### Problem Statement :

```Given an array of integers, find the subset of non-adjacent elements with the maximum sum. Calculate the sum of that subset. It is possible that the maximum sum is 0, the case when all elements are negative.

For example, given an array arr = [ -2, 1 , 3, -4, 5 ]  we have the following possible subsets. These exclude the empty subset and single element subsets which are also valid.

Subset      Sum
[-2, 3, 5]   6
[-2, 3]      1
[-2, -4]    -6
[-2, 5]      3
[1, -4]     -3
[1, 5]       6
[3, 5]       8
Our maximum subset sum is 8. Note that any individual element is a subset as well.

Function Description

Complete the maxSubsetSum function in the editor below. It should return an integer representing the maximum subset sum for the given array.

maxSubsetSum has the following parameter(s):

arr: an array of integers

Input Format

The first line contains an integer, n.
The second line contains n space-separated integers arr[ i ].

Constraints

1  <=   n   <=   10^5
- 10^4   <=   arr[ i ]   <=   10^4

Output Format

Return the maximum sum described in the statement.

Sample Input 0

5
3 7 4 6 5
Sample Output 0

13```

### Solution :

```                            ```Solution in C :

int dp[100005];

int maxSubsetSum(vector<int> arr) {

dp[0]=max(0,arr[0]);
if(arr.size()==1)
return dp[0];
for(int i=1;i<arr.size();i++)
{
dp[i]=max(dp[i-2],max(dp[i-1],dp[i-2]+arr[i]));
}
int n=arr.size();
return max(dp[n-1],dp[n-2]);
}```
```

## 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