Maximum Circular Subarray Sum in C++

We are given an array and the task is to form the subarrays such that the sum of subarrays in a circular fashion will result in a maximum value.

Input − int arr[] = {1, 2, 8, 4, 3, 0, 7}

Output − Maximum circular subarray sum is − 22

Explanation − we are given an array containing {1, 2, 8, 4, 3, 0, 7} and the subarray of it with maximum sum will be 7 + 1 + 2+ 8 + 4 is 22.

Input − int arr[] = { 2, 5, -1, 6, 9, 4, -5 }

Output − Maximum circular subarray sum is − 25

Explanation − we are given an array containing {2, 5, -1, 6, 9, 4, -5} and the subarray of it with maximum sum will be 4 + 2 + 5 - 1 + 6 + 9 is 25.

Approach used in the below program is as follows

• Input an array of integer elements containing both positive and negative values.

• Calculate the size of an array.

• Pass an array and the size to the function for further processing.

• Create a temporary variable as total and set it to 0

• Start loop FOR from i to 0 till the size of an array

• Inside the loop, Set total with total + arr[i]

• Set temp = arr[0], temp_2 = arr[0], temp_3 = arr[0], temp_4 = arr[0]

• Start the loop FOR from i to 1 till the size of an array

• Inside the loop set temp = max(temp + arr[i], arr[i]), temp_2 = max(temp_2, temp), temp_3 = min(temp_3 + arr[i], arr[i]), temp_4 = min(temp_4, temp_3)

• Check IF size == 1 then return arr[0]

• Check IF temp_4 == total then return temp_2

• Set max_sum = max(temp_3, total - temp_4)

• Return max_sum

• Print the result.

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
int maximum(int arr[], int size){
   int total = 0;
   for (int i = 0; i < size; i++){
      total += arr[i];
   }
   int temp = arr[0];
   int temp_2 = arr[0];
   int temp_3 = arr[0];
   int temp_4 = arr[0];
   for (int i = 1; i < size; i++){
      temp = max(temp + arr[i], arr[i]);
      temp_2 = max(temp_2, temp);
      temp_3 = min(temp_3 + arr[i], arr[i]);
      temp_4 = min(temp_4, temp_3);
   }
   if (size == 1){
      return arr[0];
   }
   if (temp_4 == total){
      return temp_2;
   }
   int max_sum = max(temp_3, total - temp_4);
   return max_sum;
}
int main(){
   int arr[] = { 2, 5, -1, 6, 9, 4, -5 };
   int size = sizeof(arr) / sizeof(arr[0]);
   cout<<"Maximum circular subarray sum is: "<<maximum(arr, size) << endl;
   return 0;
}

Output

If we run the above code it will generate the following output −

Maximum circular subarray sum is: 25