Minimum pairs required to be removed such that the array does not contain any pair with sum K

Given an array arr[] of size N and an integer K, the task is to find the minimum count of pairs required to be removed such that no pair exists in the array whose sum of elements is equal to K.

Examples:

Input: arr[] = { 3, 1, 3, 4, 3 }, K = 6 
Output: 1 
Explanation:
Removing the pair (arr[0], arr[2]) modifies arr[] to arr[] = { 1, 4, 3 } 
Since no pair exists in arr[] whose sum of elements is equal to K(=6), the required output is 1.

Input: arr = { 1, 2, 3, 4 }, K = 5 
Output: 2 
Explanation:
Removing the pair (arr[0], arr[3]) modifies arr[] to arr[] = { 2, 3 } 
Removing the pair (arr[0], arr[1]) modifies arr[] to arr[] = { } 
Since no pair exists in arr[] whose sum of elements is equal to K(=5), the required output is 2.

Approach: The problem can be solved using the two-pointer technique. Follow the steps below to solve this problem:

• Sort the array in ascending order.
• Initialize two variables, say left = 0 and right = N – 1 to store the index of left and right pointers respectively.
• Initialize a variable, say cntPairs, to store the minimum count of pairs required to be removed such that no pair exists in the array whose sum is equal to K.
• Traverse the array and check the following conditions. 
  • If arr[left] + arr[right] == K, then increment the value of cntPairs by 1 and update left += 1 and right -= 1.
  • If arr[left] + arr[right] < K, then update left += 1.
  • If arr[left] + arr[right] < K, then update right -= 1.
• Finally, print the value of cntPairs.

Below is the implementation of the above approach:

C++14

// C++14 program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find the maximum count of pairs
// required to be removed such that no pairs
// exist whose sum equal to K
int maxcntPairsSumKRemoved(vector<int> arr, int k)
{

    // Stores maximum count of pairs required
    // to be removed such that no pairs
    // exist whose sum equal to K
    int cntPairs = 0;

    // Base Case
    if (arr.size() <= 1)
        return cntPairs;

    // Sort the array
    sort(arr.begin(), arr.end());

    // Stores index of
    // left pointer
    int left = 0;

    // Stores index of
    // right pointer
    int right = arr.size() - 1;

    while (left < right)
    {

        // Stores sum of left
        // and right pointer
        int s = arr[left] + arr[right];

        // If s equal to k
        if (s == k)
        {

            // Update cntPairs
            cntPairs += 1;

            // Update left
            left += 1;

            // Update right
            right -= 1;
        }

        // If s > k
        else if (s > k)

            // Update right
            right -= 1;
        else

            // Update left
            left += 1;
    }

    // Return the cntPairs
    return cntPairs;
}

// Driver Code
int main()
{
    vector<int> arr = { 1, 2, 3, 4 };
    int K = 5;

    // Function call
    cout << (maxcntPairsSumKRemoved(arr, K));

    return 0;
}

// This code is contributed by mohit kumar 29

Java

// Java program for the above approach
import java.util.*;

class GFG{

// Function to find the maximum count of pairs
// required to be removed such that no pairs
// exist whose sum equal to K
static int maxcntPairsSumKRemoved(int[] arr, int k)
{

    // Stores maximum count of pairs required
    // to be removed such that no pairs
    // exist whose sum equal to K
    int cntPairs = 0;

    // Base Case
    if (arr.length <= 1)
        return cntPairs;

    // Sort the array
    Arrays.sort(arr);

    // Stores index of
    // left pointer
    int left = 0;

    // Stores index of
    // right pointer
    int right = arr.length - 1;

    while (left < right)
    {

        // Stores sum of left
        // and right pointer
        int s = arr[left] + arr[right];

        // If s equal to k
        if (s == k)
        {

            // Update cntPairs
            cntPairs += 1;

            // Update left
            left += 1;

            // Update right
            right -= 1;
        }

        // If s > k
        else if (s > k)

            // Update right
            right -= 1;
        else

            // Update left
            left += 1;
    }

    // Return the cntPairs
    return cntPairs;
}

// Driver Code
public static void main (String[] args)
{
    int[] arr = { 1, 2, 3, 4 };
    int K = 5;

    // Function call
    System.out.println (maxcntPairsSumKRemoved(arr, K));
}
}

Python3

# Python3 program to implement
# the above approach

# Function to find the maximum count of pairs
# required to be removed such that no pairs
# exist whose sum equal to K
def maxcntPairsSumKRemoved(arr, k):

    # Stores maximum count of pairs required
    # to be removed such that no pairs
    # exist whose sum equal to K
    cntPairs = 0

    # Base Case
    if not arr or len(arr) == 1:
        return cntPairs

    # Sort the array
    arr.sort()

    # Stores index of
    # left pointer
    left = 0

    # Stores index of
    # right pointer
    right = len(arr) - 1

    while left < right:

        # Stores sum of left
        # and right pointer
        s = arr[left] + arr[right]

        # If s equal to k
        if s == k:

            # Update cntPairs
            cntPairs += 1

            # Update left
            left += 1

            # Update right
            right-= 1

        # If s > k
        elif s > k:

            # Update right
            right-= 1
        else:

            # Update left
            left+= 1

    # Return the cntPairs
    return cntPairs

# Driver Code
if __name__ == "__main__":
    arr =[1, 2, 3, 4]
    K = 5

    # Function call
    print(maxcntPairsSumKRemoved(arr, K))

C#

// C# program for the above approach
using System;
class GFG{

// Function to find the maximum count of pairs
// required to be removed such that no pairs
// exist whose sum equal to K
static int maxcntPairsSumKRemoved(int[] arr, int k)
{

    // Stores maximum count of pairs required
    // to be removed such that no pairs
    // exist whose sum equal to K
    int cntPairs = 0;

    // Base Case
    if (arr.Length <= 1)
        return cntPairs;

    // Sort the array
    Array.Sort(arr);

    // Stores index of
    // left pointer
    int left = 0;

    // Stores index of
    // right pointer
    int right = arr.Length - 1;

    while (left < right)
    {

        // Stores sum of left
        // and right pointer
        int s = arr[left] + arr[right];

        // If s equal to k
        if (s == k)
        {

            // Update cntPairs
            cntPairs += 1;

            // Update left
            left += 1;

            // Update right
            right -= 1;
        }

        // If s > k
        else if (s > k)

            // Update right
            right -= 1;
        else

            // Update left
            left += 1;
    }

    // Return the cntPairs
    return cntPairs;
}

// Driver Code
public static void Main(String[] args)
{
    int[] arr = { 1, 2, 3, 4 };
    int K = 5;

    // Function call
    Console.WriteLine (maxcntPairsSumKRemoved(arr, K));
}
}

// This code is contributed by 29AjayKumar

Javascript

<script>
//Javascript program to implement
// the above approach

// Function to find the maximum count of pairs
// required to be removed such that no pairs
// exist whose sum equal to K
function maxcntPairsSumKRemoved( arr, k)
{

    // Stores maximum count of pairs required
    // to be removed such that no pairs
    // exist whose sum equal to K
    var cntPairs = 0;

    // Base Case
    if (arr.length <= 1)
        return cntPairs;

    // Sort the array
    arr.sort();

    // Stores index of
    // left pointer
    var left = 0;

    // Stores index of
    // right pointer
    var right = arr.length - 1;

    while (left < right)
    {

        // Stores sum of left
        // and right pointer
        var s = arr[left] + arr[right];

        // If s equal to k
        if (s == k)
        {

            // Update cntPairs
            cntPairs += 1;

            // Update left
            left += 1;

            // Update right
            right -= 1;
        }

        // If s > k
        else if (s > k)

            // Update right
            right -= 1;
        else

            // Update left
            left += 1;
    }

    // Return the cntPairs
    return cntPairs;
}

var arr = [ 1,2,3,4];
var K = 5;

// Function call
document.write(maxcntPairsSumKRemoved(arr, K));

//This code is contributed by SoumikMondal
</script>

Output:

2

Time Complexity: O(N*logN) as it sorts the given array
Auxiliary Space: O(1)