Maximum difference between two subsets of m elements in C

The task is to find the greatest difference between the sum of m elements in an array. Suppose we have an array and a number m, then we will first find the sum of highest m numbers and then subtract the sum of lowest m numbers from it to get the maximum difference. So the main thing is to find two subsets of m numbers which have the highest sum and lowest sum.

Let’s now understand what we have to do using an example −

Input 

arr = {1,2,3,4,5} ; m=3

Output 

Maximum difference here is : 6

Explanation − Here the highest 3 numbers are 3,4,5 and the sum is 12. Lowest 3 numbers are 1,2,3 and sum is 6. So the highest or maximum difference is 12-6 which is 6.

Input 

arr = {10,13,22,8,16,14}; m=4

Output 

Maximum difference here is : 20

Explanation − Here the highest 4 numbers are 22,16,14,13 and the sum is 65. Lowest 4 numbers are 8,10,13,14 and the sum is 45 . So the highest or maximum difference is 65-45 which is 20.

Approach used in the below program as follows

• Take input array arr[] and a number m for making sets

• In the find_diff() function we are passing the input array and it’s length and returning the maximum difference of the sum of sets of m elements.

• Here we will first sort the elements of array arr[].

• Then we will find the sum of first m and last m elements as these will be least m and highest m numbers of arr[] .

• At last we return the difference.

• Note − sort(arr[],int) is assumed to return the sorted array.

Example

#include<stdio.h>
//create function to calculate maximum difference between sum of highest and lowest m elements of array
int find_diff(int arr[],int length,int m){
   //for sorting the array
   sort(arr,length);
   int maxsum=0, minsum=0;
   //calculate now max difference between two subsets of m elements
   for(int i=0;i<m;i++){
      minsum+=arr[i];
      maxsum+=arr[length-i-1];
   }
   return(maxsum-minsum);
}
// Driver program
int main(){
   int arr[]={1,1,2,3,5,7,1};
   int m=3;
   cout << find_diff(arr,7,m);
   return 0;
}

Output

If we run the above code we will get the following output −

12