Find the maximum sum pair in an Array with even parity

Given an array arr[] of N integers, the task is to find a pair with even parity and maximum sum.

Examples:

Input: arr[] = {18, 15, 8, 9, 14}
Output: 18 15
Explanation:
Binary Representation of elements –
18 => 10010, Parity = 2
15 => 1111, Parity = 4
8 => 1000, Parity = 1
9 => 1001, Parity = 2
14 => 1110, Parity = 3
Here, parity for elements 18, 15 and 9 are even
Hence, pair with maximum sum will be 18 and 15

Input: arr[] = {5, 3, 4, 2, 9}
Output: 9 5
Explanation:
The array contains three even parity values 5, 3 and 9.
Hence, pair with maximum sum will be 9 and 5.

Approach: The key observation in the problem is if we choose two maximum numbers with even parity, then it will be the desired answer.



Traverse the array and check if the current element is having even parity. Then, update the two maximum numbers with even parity.

if (findParity(arr[i]) % 2 == 0)
    if (arr[i] >= firstMaximum)
         secondMaximum = firstMaximum
         firstMaximum  = arr[i]
    elif (arr[i] >= secondMaximum)
         secondMaximum = arr[i]

Below is the implementation of the above approach:

C++

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// C++ implementation to find 
// a pair with even parity and
// maximum sum
  
#include <bits/stdc++.h>
using namespace std;
  
const int sz = 1e3;
  
// Function that returns true 
// if count of set bits 
// in given number is even
bool isEvenParity(int x)
{
    // Parity will store the
    // count of set bits
    int parity = 0;
    while (x != 0) {
        if (x & 1)
            parity++;
        x = x >> 1;
    }
  
    if (parity % 2 == 0)
        return true;
    else
        return false;
}
  
// Function to print the 
// elements of the array
void printArray(int arr[], int len)
{
    for (int i = 0; i < len; i++) {
        cout << arr[i] << ' ';
    }
}
  
// Function to remove all the 
// even parity elements from 
// the given array
void findPairEvenParity(
            int arr[], int len)
{
    int firstMaximum = INT_MIN;
    int secondMaximum = INT_MIN;
      
    // Traverse the array
    for (int i = 0; i < len; i++) {
  
        // If the current element 
        // has even parity
        if (isEvenParity(arr[i])) {
  
            if (arr[i] >= firstMaximum){
                secondMaximum = firstMaximum;
                firstMaximum = arr[i];
            }
            else if (arr[i] >= secondMaximum){
                secondMaximum = arr[i];
            }
        }
    }
      
    cout << firstMaximum 
         << " " << secondMaximum;
}
  
// Driver Code
int main()
{
    int arr[] = { 18, 15, 8, 9, 14 };
    int len = sizeof(arr) / sizeof(int);
      
    // Function Call
    findPairEvenParity(arr, len);
  
    return 0;
}

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Java

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// Java implementation to find 
// a pair with even parity and
// maximum sum
import java.util.*;
  
class GFG{
  
static int sz = (int) 1e3;
  
// Function that returns true 
// if count of set bits 
// in given number is even
static boolean isEvenParity(int x)
{
      
    // Parity will store the
    // count of set bits
    int parity = 0;
      
    while (x != 0
    {
        if (x % 2 == 1)
            parity++;
        x = x >> 1;
    }
  
    if (parity % 2 == 0)
        return true;
    else
        return false;
}
  
// Function to print the 
// elements of the array
static void printArray(int arr[],
                       int len)
{
    for(int i = 0; i < len; i++)
    {
       System.out.print(arr[i] + " ");
    }
}
  
// Function to remove all the 
// even parity elements from 
// the given array
static void findPairEvenParity(int arr[],
                               int len)
{
    int firstMaximum = Integer.MIN_VALUE;
    int secondMaximum = Integer.MIN_VALUE;
      
    // Traverse the array
    for(int i = 0; i < len; i++)
    {
         
       // If the current element 
       // has even parity
       if (isEvenParity(arr[i]))
       {
           if (arr[i] >= firstMaximum)
           {
               secondMaximum = firstMaximum;
               firstMaximum = arr[i];
           }
           else if (arr[i] >= secondMaximum)
           {
               secondMaximum = arr[i];
           }
       }
    }
    System.out.print(firstMaximum + " " +
                     secondMaximum);
}
  
// Driver Code
public static void main(String[] args)
{
    int arr[] = { 18, 15, 8, 9, 14 };
    int len = arr.length;
      
    // Function Call
    findPairEvenParity(arr, len);
}
}
  
// This code is contributed by amal kumar choubey

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C#

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// C# implementation to find 
// a pair with even parity and
// maximum sum
using System;
class GFG{
  
static int sz = (int) 1e3;
  
// Function that returns true 
// if count of set bits 
// in given number is even
static bool isEvenParity(int x)
{
      
    // Parity will store the
    // count of set bits
    int parity = 0;
      
    while (x != 0) 
    {
        if (x % 2 == 1)
            parity++;
        x = x >> 1;
    }
  
    if (parity % 2 == 0)
        return true;
    else
        return false;
}
  
// Function to print the 
// elements of the array
static void printArray(int []arr,
                       int len)
{
    for(int i = 0; i < len; i++)
    {
        Console.Write(arr[i] + " ");
    }
}
  
// Function to remove all the 
// even parity elements from 
// the given array
static void findPairEvenParity(int []arr,
                               int len)
{
    int firstMaximum = Int32.MinValue;
    int secondMaximum = Int32.MinValue;
      
    // Traverse the array
    for(int i = 0; i < len; i++)
    {
          
        // If the current element 
        // has even parity
        if (isEvenParity(arr[i]))
        {
            if (arr[i] >= firstMaximum)
            {
                secondMaximum = firstMaximum;
                firstMaximum = arr[i];
            }
            else if (arr[i] >= secondMaximum)
            {
                secondMaximum = arr[i];
            }
        }
    }
    Console.Write(firstMaximum + " " +
                  secondMaximum);
}
  
// Driver Code
public static void Main()
{
    int []arr = { 18, 15, 8, 9, 14 };
    int len = arr.Length;
      
    // Function Call
    findPairEvenParity(arr, len);
}
}
  
// This code is contributed by Code_Mech

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Output:

18 15

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