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Find the maximum sum pair in an Array with even parity

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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++




// 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;
}


Java




// 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


Python3




# Python3 implementation to find
# a pair with even parity and
# maximum sum
import sys
 
sz = 1e3
 
# Function that returns true
# if count of set bits
# in given number is even
def isEvenParity(x):
     
    # Parity will store the
    # count of set bits
    parity = 0
     
    while x != 0:
        if (x & 1):
            parity = parity + 1;
         
        x = x >> 1
     
    if (parity % 2 == 0):
        return True
    else:
        return False
 
# Function to print the
# elements of the array
def printArray(arr, n):
     
    for i in range(0, n):
        print(arr[i], end = ' ')
     
# Function to remove all the
# even parity elements from
# the given array
def findPairEvenParity(arr, n):
     
    firstMaximum = -1
    secondMaximum = -1
     
    # Traverse the array
    for i in range(0, n):
         
        # If the current element
        # has even parity
        if isEvenParity(arr[i]) == True:
            if (arr[i] >= firstMaximum):
                secondMaximum = firstMaximum
                firstMaximum = arr[i]
             
            elif (arr[i] >= secondMaximum):
                secondMaximum = arr[i]
     
    print(firstMaximum, secondMaximum)
 
# Driver Code
if __name__ == "__main__":
     
    arr = [ 18, 15, 8, 9, 14 ]
    n = len(arr)
     
    # Function call
    findPairEvenParity(arr, n)
 
# This code is contributed by akhilsaini


C#




// 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


Javascript




<script>
// Javascript implementation to find
// a pair with even parity and
// maximum sum
 
let sz = 1e3;
  
// Function that returns true
// if count of set bits
// in given number is even
function isEvenParity(x)
{
      
    // Parity will store the
    // count of set bits
    let 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
function printArray(arr, len)
{
    for(let i = 0; i < len; i++)
    {
       document.write(arr[i] + " ");
    }
}
  
// Function to remove all the
// even parity elements from
// the given array
function findPairEvenParity(arr, len)
{
    let firstMaximum = Number.MIN_VALUE;
    let secondMaximum = Number.MIN_VALUE;
      
    // Traverse the array
    for(let 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];
           }
       }
    }
    document.write(firstMaximum + " " +
                     secondMaximum);
}
 
// Driver Code
     
      let arr = [ 18, 15, 8, 9, 14 ];
    let len = arr.length;
      
    // Function Call
    findPairEvenParity(arr, len);;
            
</script>


Output: 

18 15

 

Time Complexity: O(n*log10 n)
Auxiliary Space: O(1)



Last Updated : 05 Jan, 2023
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