Largest Sum Contiguous Subarray

An array of integers is given. We have to find the sum of all elements which are contiguous, whose sum is largest, that will be sent as output.

Using dynamic programming we will store the maximum sum up to current term. It will help to find the sum for contiguous elements in the array.

Input and Output

Input:
An array of integers. {-2, -3, 4, -1, -2, 1, 5, -3}
Output:
Maximum Sum of the Subarray is: 7

Algorithm

maxSum(array, n)

Input − The main array, the size of the array.

Output − maximum sum.

Begin
   tempMax := array[0]
   currentMax = tempMax
   for i := 1 to n-1, do
      currentMax = maximum of (array[i] and currentMax+array[i])
      tempMax = maximum of (currentMax and tempMax)
   done
   return tempMax
End

Example

#include<iostream>
using namespace std;

int maxSum( int arr[], int n) {
   int tempMax = arr[0];
   int currentMax = tempMax;

   for (int i = 1; i < n; i++ ) { //find the max value
      currentMax = max(arr[i], currentMax+arr[i]);
      tempMax = max(tempMax, currentMax);
   }
   return tempMax;
}

int main() {
   int arr[] = {-2, -3, 4, -1, -2, 1, 5, -3};
   int n = 8;
   cout << "Maximum Sum of the Sub-array is: "<< maxSum( arr, n );
}

Output

Maximum Sum of the Sub-array is: 7