Maximum difference between two subsets of m elements
Given an array of n integers and a number m, find the maximum possible difference between two sets of m elements chosen from given array.
Examples:
Input : arr[] = 1 2 3 4 5
m = 4
Output : 4
The maximum four elements are 2, 3,
4 and 5. The minimum four elements are
1, 2, 3 and 4. The difference between
two sums is (2 + 3 + 4 + 5) - (1 + 2
+ 3 + 4) = 4
Input : arr[] = 5 8 11 40 15
m = 2
Output : 42
The difference is (40 + 15) - (5 + 8)
The idea is to first sort the array, then find sum of first m elements and sum of last m elements. Finally return difference between two sums.
CPP
// C++ program to find difference // between max and min sum of array #include <bits/stdc++.h> using namespace std; // utility function int find_difference(int arr[], int n, int m) { int max = 0, min = 0; // sort array sort(arr, arr + n); for (int i = 0, j = n - 1; i < m; i++, j--) { min += arr[i]; max += arr[j]; } return (max - min); } // Driver code int main() { int arr[] = { 1, 2, 3, 4, 5 }; int n = sizeof(arr) / sizeof(arr[0]); int m = 4; cout << find_difference(arr, n, m); return 0; } |
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Java
// Java program to find difference // between max and min sum of array import java.util.Arrays; class GFG { // utility function static int find_difference(int arr[], int n, int m) { int max = 0, min = 0; // sort array Arrays.sort(arr); for (int i = 0, j = n - 1; i < m; i++, j--) { min += arr[i]; max += arr[j]; } return (max - min); } // Driver program public static void main(String arg[]) { int arr[] = { 1, 2, 3, 4, 5 }; int n = arr.length; int m = 4; System.out.print(find_difference(arr, n, m)); } } // This code is contributed by Anant Agarwal. |
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Python3
# Python program to # find difference # between max and # min sum of array def find_difference(arr, n, m): max = 0; min = 0 # sort array arr.sort(); j = n-1 for i in range(m): min += arr[i] max += arr[j] j = j - 1 return (max - min) # Driver code if __name__ == "__main__": arr = [1, 2, 3, 4, 5] n = len(arr) m = 4 print(find_difference(arr, n, m)) # This code is contributed by # Harshit Saini |
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C#
// C# program to find difference // between max and min sum of array using System; class GFG { // utility function static int find_difference(int[] arr, int n, int m) { int max = 0, min = 0; // sort array Array.Sort(arr); for (int i = 0, j = n - 1; i < m; i++, j--) { min += arr[i]; max += arr[j]; } return (max - min); } // Driver program public static void Main() { int[] arr = { 1, 2, 3, 4, 5 }; int n = arr.Length; int m = 4; Console.Write(find_difference(arr, n, m)); } } // This code is contributed by nitin mittal |
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PHP
<?php // PHP program to find difference // between max and min sum of array // utility function function find_difference($arr, $n, $m) { $max = 0; $min = 0; // sort array sort($arr); sort( $arr,$n); for($i = 0, $j = $n - 1; $i <$m; $i++, $j--) { $min += $arr[$i]; $max += $arr[$j]; } return ($max - $min); } // Driver code { $arr = array(1, 2, 3, 4, 5); $n = sizeof($arr) / sizeof($arr[0]); $m = 4; echo find_difference($arr, $n, $m); return 0; } // This code is contributed by nitin mittal. ?> |
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Output:
4
We can optimize the above solution using more efficient approaches discussed in below post.
k largest(or smallest) elements in an array | added Min Heap method
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