Count of Pairs in given Array having both even or both odd or sum as K

Given an array arr[] of distinct integers of size N and an integer K, The task is to find the total no of possible pairs in the array such that, either both are even or both are odd or the sum of the pair is K

Note: No element is part of more than one pair.

Examples:

Input: N = 6, K = 7, arr[] = {1, 2, 3, 4, 5, 6}
Output: 3
Explanation: Possible pairs are: (5, 2), (1, 3), (4, 6)

Input: N = 4, K = 22, arr[] = {1, 3, 12, 9}
Output: 1
Explanation: Only one pair is possible. 
The pair can be either (1, 3) or (1, 9) or (3, 9).

Approach: The task can be solved using observations, one can observe that maximum pairing is possible if grouping of both odds together & both evens together are done initially and then, consider the involvement of K. 
Follow the below steps to solve the problem:

• Let ‘odds‘ and ‘evens‘ store the count of the number of odds & even elements respectively in the array.
• If both ‘odds’ and ‘evens’ are odd then after pairing odds & evens together, 1 odd & 1 even element will be left. To make maximum possible pairs, see whether there exists a pair with different parities & sum equal to K, If such a pair exists, increment the count of possible pairs.
• Otherwise, the total possible pairs would be the sum of odds/2 & evens/2

Below is the implementation of the above approach:

C++

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

// Function to find the total possible pairs
void go(int ar[], int N, int K)
{
    // Stores the count of odd & even
    // elements in the array
    int odds = 0, evens = 0;
    for (int i = 0; i < N; i++) {
        if (ar[i] & 1)
            odds++;
        else
            evens++;
    }

    // Total pairs
    int ans = odds / 2 + evens / 2;

    // If number of both odds & even
    // elements are odd
    if ((odds & 1) && (evens & 1)) {
        unordered_map<int, int> occ;
        for (int i = 0; i < N; i++)
            occ[ar[i]]++;

        // Check if there exists a pair
        // with different parity &
        // sum equals to K
        for (int i = 0; i < N; i++) {
            if (occ.find(K - ar[i])
                != occ.end()) {
                if (((ar[i] & 1) && !((K - ar[i]) & 1))
                    || (!(ar[i] & 1)
                        && ((K - ar[i])
                            & 1))) {
                    ans++;
                    break;
                }
            }
        }
    }

    cout << ans << endl;
}

// Driver Code
int main()
{
    int N = 6, K = 7;
    int arr[N] = { 1, 2, 3, 4, 5, 6 };
    go(arr, N, K);
    return 0;
}

Java

// Java code to implement above approach
import java.util.HashMap;
class GFG {

  // Function to find the total possible pairs
  static void go(int[] ar, int N, int K) {

    // Stores the count of odd & even
    // elements in the array
    int odds = 0, evens = 0;
    for (int i = 0; i < N; i++) {
      if ((ar[i] & 1) > 0)
        odds++;
      else
        evens++;
    }

    // Total pairs
    int ans = odds / 2 + evens / 2;

    // If number of both odds & even
    // elements are odd
    if ((odds & 1) > 0 && (evens & 1) > 0) {
      HashMap<Integer, Integer> occ = new HashMap<Integer, Integer>();
      for (int i = 0; i < N; i++) {
        if (occ.containsKey(ar[i]))
          occ.put(ar[i], occ.get(ar[i]) + 1);
        else
          occ.put(ar[i], 1);
      }

      // Check if there exists a pair
      // with different parity &
      // sum equals to K
      for (int i = 0; i < N; i++) {
        if (occ.containsKey(K - ar[i])) {
          if (((ar[i] & 1) > 0
               && ((K - ar[i]) & 1) < 1)
              || ((ar[i] & 1) < 1
                  && ((K - ar[i]) & 1) > 0)) {
            ans++;
            break;
          }
        }
      }
    }

    System.out.println(ans);
  }

  // Driver Code
  public static void main(String args[]) {
    int N = 6, K = 7;
    int[] arr = { 1, 2, 3, 4, 5, 6 };
    go(arr, N, K);
  }
}

// This code is contributed by gfgking

Python3

# Python code for the above approach

# Function to find the total possible pairs
def go(ar, N, K):

    # Stores the count of odd & even
    # elements in the array
    odds = 0
    evens = 0
    for i in range(N):
        if (ar[i] & 1):
            odds += 1
        else:
            evens += 1

    # Total pairs
    ans = odds // 2 + evens // 2;

    # If number of both odds & even
    # elements are odd
    if ((odds & 1) and (evens & 1)):
        occ = {};
        for i in range(N):
            if (arr[i] in occ):
                occ[ar[i]] += 1
            else:
                occ[arr[i]] = 1


        # Check if there exists a pair
        # with different parity &
        # sum equals to K
        for i in range(N):
            if ((K - ar[i]) in occ):
                if (((ar[i] & 1) and not ((K - ar[i]) & 1)) or (not (ar[i] & 1) and ((K - ar[i]) & 1))):
                    ans += 1
                    break;

    print(int(ans))

# Driver Code
N = 6
K = 7;
arr = [1, 2, 3, 4, 5, 6];
go(arr, N, K);

# This code is contributed by Saurabh Jaiswal

C#

// C# code to implement above approach
using System;
using System.Collections.Generic;
class GFG {

    // Function to find the total possible pairs
    static void go(int[] ar, int N, int K)
    {

        // Stores the count of odd & even
        // elements in the array
        int odds = 0, evens = 0;
        for (int i = 0; i < N; i++) {
            if ((ar[i] & 1) > 0)
                odds++;
            else
                evens++;
        }

        // Total pairs
        int ans = odds / 2 + evens / 2;

        // If number of both odds & even
        // elements are odd
        if ((odds & 1) > 0 && (evens & 1) > 0) {
            Dictionary<int, int> occ
                = new Dictionary<int, int>();
            for (int i = 0; i < N; i++) {
                if (occ.ContainsKey(ar[i]))
                    occ[ar[i]]++;
                else
                    occ[ar[i]] = 1;
            }
            // Check if there exists a pair
            // with different parity &
            // sum equals to K
            for (int i = 0; i < N; i++) {
                if (occ.ContainsKey(K - ar[i])) {
                    if (((ar[i] & 1) > 0
                         && ((K - ar[i]) & 1) < 1)
                        || ((ar[i] & 1) < 1
                            && ((K - ar[i]) & 1) > 0)) {
                        ans++;
                        break;
                    }
                }
            }
        }

        Console.WriteLine(ans);
    }

    // Driver Code
    public static void Main()
    {
        int N = 6, K = 7;
        int[] arr = { 1, 2, 3, 4, 5, 6 };
        go(arr, N, K);
    }
}

// This code is contributed by ukasp.

Javascript

<script>
       // JavaScript code for the above approach

       // Function to find the total possible pairs
       function go(ar, N, K)
       {

           // Stores the count of odd & even
           // elements in the array
           let odds = 0, evens = 0;
           for (let i = 0; i < N; i++) {
               if (ar[i] & 1)
                   odds++;
               else
                   evens++;
           }

           // Total pairs
           let ans = odds / 2 + evens / 2;

           // If number of both odds & even
           // elements are odd
           if ((odds & 1) && (evens & 1)) {
               let occ = new Map();
               for (let i = 0; i < N; i++) {
                   if (occ.has(arr[i]))
                       occ.set(ar[i], occ.get(arr[i]) + 1);
                   else
                       occ.set(arr[i], 1)
               }

               // Check if there exists a pair
               // with different parity &
               // sum equals to K
               for (let i = 0; i < N; i++) {
                   if (occ.has(K - ar[i])
                   ) {
                       if (((ar[i] & 1) && !((K - ar[i]) & 1))
                           || (!(ar[i] & 1)
                               && ((K - ar[i])
                                   & 1))) {
                           ans++;
                           break;
                       }
                   }
               }
           }

           document.write(ans + "<br")
       }

       // Driver Code

       let N = 6, K = 7;
       let arr = [1, 2, 3, 4, 5, 6];
       go(arr, N, K);

 // This code is contributed by Potta Lokesh
   </script>

Output

3

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