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 :



title-img 


                            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]);
}








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