# Find maximum sum array of length less than or equal to m in C++

C++Server Side ProgrammingProgramming

In the problem, we are given n arrays of different length. Our task is to Find the maximum sum array of length less than or equal to m.

We need to find sub-arrays from the arrays to maximise the sum and make the length of all subarrays combined equal to m.

Let’s take an example to understand the problem,

## Input

n = 3, m = 4
arrOfArr[][] = {
{5, 2, -1, 4, -3}
{3, -2, 1, 6}
{-2, 0, 5}
}

## Output

20

## Explanation

SubArrays are {5, 4}, {6}, {5},
length = 2 + 1 + 1 = 4
Sum = 5 + 4 + 6 + 5 = 20

## Solution Approach

The problem can be solved using a dynamic programming approach. We will create a DP array and compute the cumulative array sums of length k which varies from 0 to m.

In the DP array, store the maximum array sum for all lengths from 0 to m for each array in the 2D DP. Then return the maximum sum which will be at the last row of the array.

Program to illustrate the working of our solution,

## Example

#include <bits/stdc++.h>
using namespace std;
#define N 5
int findMax(int a, int b){
if(a > b)
return a;
return b;
}
int findMaxSumArray(int arr[][N], int M) {
int DP[N][M];
int sumArray[M];
int sum[M];
memset(DP, -1, sizeof(DP) * N * M);
sumArray = 0;
DP = 0;
for (int i = 1; i <= 5; i++) {
int len = arr[i - 1];
for (int j = 1; j <= len; j++) {
sumArray[j] = arr[i - 1][j];
sumArray[j] += sumArray[j - 1];
sum[j] = -100;
}
for (int j = 1; j <= len && j <= 6; j++)
for (int k = 1; k <= len; k++)
if (j + k - 1 <= len)
sum[j] = findMax(sum[j], sumArray[j + k - 1] - sumArray[k - 1]);
for (int j = 0; j <= 6; j++)
DP[i][j] = DP[i - 1][j];
for (int j = 1; j <= 6; j++)
for (int cur = 1; cur <= j && cur <= len; cur++)
DP[i][j] = findMax(DP[i][j], DP[i - 1][j - cur] + sum[cur]);
}
int maxSum = 0;
for (int i = 0; i <= 6; i++)
maxSum = findMax(maxSum, DP[i]);
return maxSum;
}
int main() {
int arr[][N] = { { 3, 2, -1, 6 },
{ 2, 7, -1 },
{ 3, 2, 2, -4 } };
int m = 4;
cout<<"Maximum sum array of length less than or equal to "<<m<<" : "<<findMaxSumArray(arr, m);
}

## Output

Maximum sum array of length less than or equal to 4 : 15