Minimum sum obtained by choosing N number from given N pairs

Given an array arr[] of N pairs of integers (A, B) where N is even, the task is to find the minimum sum of choosing N elements such that value A and B from all the pairs are chosen exactly (N/2) times.
Examples: 
 

Input: N = 4, arr[][] = { {7, 20}, {300, 50}, {30, 200}, {30, 20} } 
Output: 107 
Explanation: 
Choose value-A from 1st pair = 7. 
Choose value-B from 2nd pair = 50. 
Choose value-A from 3rd pair = 30. 
Choose value-B from 4th pair = 20. 
The minimum sum is 7 + 50 + 30 + 20 = 107.
Input: N = 4, arr[][] = { {10, 20}, {400, 50}, {30, 200}, {30, 20} } 
Output: 110 
Explanation: 
Choose value-A from 1st pair = 10. 
Choose value-B from 2nd pair = 50. 
Choose value-A from 3rd pair = 30. 
Choose value-B from 4th pair = 20. 
The minimum sum is 10 + 50 + 30 + 20 = 110. 
 

Approach: This problem can be solved using Greedy Approach. Below are the steps: 
 

1. For each pair (A, B) in the given array, store the value of (B - A) with the corresponding index in temporary array(say temp[]). The value (B - A) actually defines how much cost is minimized if A is chosen over B for each element.
2. The objective is to minimize the total cost. Hence, sort the array temp[] in decreasing order.
3. Pick the first N/2 elements from the array temp[] by choosing A as first N/2 elements will have the maximum sum when A is chosen over B.
4. For remaining N/2 elements choose B as the sum of values can be minimized.

Below is the implementation of the above approach:
 

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to choose the elements A
// and B such the sum of all elements
// is minimum
int minSum(int arr[][2], int n)
{

    // Create an array of pair to
    // store Savings and index
    pair<int, int> temp[n];

    // Traverse the given array of pairs
    for (int i = 0; i < 2 * n; i++) {

        // Sum minimized when A
        // is chosen over B for
        // i-th element.
        temp[i].first = arr[i][1]
                        - arr[i][0];

        // Store index for the
        // future reference.
        temp[i].second = i;
    }

    // Sort savings array in
    // non-increasing order.
    sort(temp, temp + 2 * n,
         greater<pair<int, int> >());

    // Storing result
    int res = 0;

    for (int i = 0; i < 2 * n; i++) {

        // First n elements choose
        // A and rest choose B
        if (i < n)
            res += arr[temp[i].second][0];
        else
            res += arr[temp[i].second][1];
    }

    // Return the final Sum
    return res;
}

// Driver Code
int main()
{
    // Given array of pairs
    int arr[4][2] = { { 7, 20 },
                      { 300, 50 },
                      { 30, 200 },
                      { 30, 20 } };

    // Function Call
    cout << minSum(arr, 2);
}

/*package whatever //do not write package name here */
import java.util.*;
public class GFG{

  static class Pair<K,V>{

    K first;
    V second;

    Pair(K k, V v){
      first = k;
      second = v;
    }

  }

  // Function to choose the elements A
  // and B such the sum of all elements
  // is minimum
  static int minSum(int arr[][], int n)
  {

    // Create an array of pair to
    // store Savings and index
    Pair<Integer, Integer> temp[] = new Pair[2*n];

    // Traverse the given array of pairs
    for (int i = 0; i < 2 * n; i++) {

      // Sum minimized when A
      // is chosen over B for
      // i-th element.
      temp[i] = new Pair(arr[i][1] - arr[i][0],i);

      // Store index for the
      // future reference.
    }

    // Sort savings array in
    // non-increasing order.
    Arrays.sort(temp,(a,b)->b.first-a.first);

    // Storing result
    int res = 0;

    for (int i = 0; i < 2 * n; i++) {

      // First n elements choose
      // A and rest choose B
      if (i < n)
        res += arr[temp[i].second][0];
      else
        res += arr[temp[i].second][1];
    }

    // Return the final Sum
    return res;
  }

  public static void main(String[] args) {

    // Given array of pairs
    int arr[][] = { { 7, 20 }, { 300, 50 }, { 30, 200 }, { 30, 20 } };

    // Function Call
    System.out.println(minSum(arr, 2));
  }
}

// This code is contributed by aadityaburujwale.

# Python3 program for the above approach

# Function to choose the elements A
# and B such the sum of all elements
# is minimum
def minSum(arr, n):

    # Create an array of pair to
    # store Savings and index
    temp = [None]*(2*n)

    # Traverse the given array of pairs
    for i in range(2 * n):

        # Sum minimized when A
        # is chosen over B for
        # i-th element.
        temp[i] = (arr[i][1] - arr[i][0], i)

    # Sort savings array in
    # non-increasing order.
    temp.sort(reverse=True)

    # Storing result
    res = 0

    for i in range(2 * n):

        # First n elements choose
        # A and rest choose B
        if (i < n):
            res += arr[temp[i][1]][0]
        else:
            res += arr[temp[i][1]][1]

    # Return the final Sum
    return res


# Driver Code
if __name__ == '__main__':
    # Given array of pairs
    arr = [[7, 20],
           [300, 50],
           [30, 200],
           [30, 20]]

    # Function Call
    print(minSum(arr, 2))

using System;
using System.Linq;

class GFG 
{

  // Function to choose the elements A
  // and B such the sum of all elements
  // is minimum
  public static int MinSum(int[,] arr, int n) 
  {

    // Create an array of Tuple to store savings and index
    Tuple<int, int>[] temp = new Tuple<int, int>[2 * n];

    // Traverse the given array of pairs
    for (int i = 0; i < 2 * n; i++)
    {

      // Sum minimized when A is chosen over B for i-th element.
      temp[i] = new Tuple<int, int>(arr[i, 1] - arr[i, 0], i);
    }

    // Sort savings array in non-increasing order.
    Array.Sort(temp, (x, y) => y.Item1.CompareTo(x.Item1));

    // Storing result
    int res = 0;

    for (int i = 0; i < 2 * n; i++)
    {

      // First n elements choose A and rest choose B
      if (i < n) {
        res += arr[temp[i].Item2, 0];
      } else {
        res += arr[temp[i].Item2, 1];
      }
    }

    // Return the final Sum
    return res;
  }

  public static void Main(string[] args)
  {

    // Given array of pairs
    int[,] arr = { { 7, 20 }, { 300, 50 }, { 30, 200 }, { 30, 20 } };
    Console.WriteLine(MinSum(arr, 2));
  }
}

// This code is contributed by poojaagarwal2.

// Javascript program for the above approach

// Function to choose the elements A
// and B such the sum of all elements
// is minimum
function minSum(arr, n) {

    // Create an array of pair to
    // store Savings and index
    let temp = new Array(2 * n).fill(null);

    // Traverse the given array of pairs
    for (let i = 0; i < 2 * n; i++) {

        // Sum minimized when A
        // is chosen over B for
        // i-th element.
        temp[i] = [arr[i][1] - arr[i][0], i]
    }

    // Sort savings array in
    // non-increasing order.
    temp.sort((a, b) => b[0] - a[0]);

    // Storing result
    let res = 0

    for (let i = 0; i < 2 * n; i++) {

        // First n elements choose
        // A and rest choose B
        if (i < n)
            res += arr[temp[i][1]][0]
        else
            res += arr[temp[i][1]][1]

    }

    // Return the final Sum
    return res
}


// Driver Code

// Given array of pairs
let arr = [[7, 20],
[300, 50],
[30, 200],
[30, 20]]

// Function Call
console.log(minSum(arr, 2))

// This code is contributed by saurabh_jaiswal.

107

Time Complexity: O(N*log(N)) 
Auxiliary Space Complexity: O(N)