Count valid pairs in the array satisfying given conditions

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Given an array of integers arr[], the task is to count the number of valid pairs of elements from arr. A pair (arr[x], arr[y]) is said to be invalid if

arr[x] < arr[y]
abs(arr[x] – arr[y]) is odd

Note: Pairs (arr[x], arr[y]) and (arr[y], arr[x]) are two different pairs when x != y and the value of arr[i] for all possible values of i is ? 120.

Examples:

Input: arr[] = {16, 17, 18}
Output: 2
Only valid pair is (18, 16)

Input: arr[] = {16, 16}
Output: 2
Valid pairs are (16, 16) and (16, 16)

Approach: Instead of processing all the elements, we can process pairs of (arr[i], count) representing the count of element arr[i] in the array. Since there are only 120 possible values, we make a frequency count of each element group which reduces the overall complexity.

For each pair (arr[x], countX) and (arr[y], countY), if the conditions are satisfied, then total valid pairs will be countX * countY.

If arr[x] = arr[y], then we over-counted some pairs. In that case, valid pairs will be countA * (countA – 1) as no element can make a pair with itself.

Below is the implementation of the above approach:

C++

//C++ implementation of the approach
#include<bits/stdc++.h>
using namespace std;
 
// Function to return total valid pairs
int ValidPairs(int arr[],int n)
{
  
    // Initialize count of all the elements
    int count[121]={0};
  
    // frequency count of all the elements
    for(int i=0;i<n;i++)
        count[arr[i]] += 1;
  
    int ans = 0;
    for(int i=0;i<n;i++)
        for(int j=0;j<n;j++)
        {
            if( arr[i] < arr[j])
                continue;
            if (abs(arr[i] - arr[j]) % 2 == 1)
                continue;
  
            // Add total valid pairs
            ans += count[arr[i]]* count[arr[j]];
            if (arr[i] == arr[j])
  
                // Exclude pairs made with a single element 
                // i.e. (x, x)
                ans -= count[arr[i]];
        }
    return ans;
}
  
// Driver Code
int main()
{
int arr[] = {16, 17, 18};
int n= sizeof(arr)/sizeof(int);
  
// Function call to print required answer
cout<<(ValidPairs(arr,n));
return 0;
}
//contributed by Arnab Kundu

Java

//Java implementation of the approach 
 
class GFG{
// Function to return total valid pairs 
static int ValidPairs(int arr[],int n) 
{ 
 
    // Initialize count of all the elements 
    int[] count=new int[121]; 
 
    // frequency count of all the elements 
    for(int i=0;i<n;i++) 
        count[arr[i]] += 1; 
 
    int ans = 0; 
    for(int i=0;i<n;i++) 
        for(int j=0;j<n;j++) 
        { 
            if( arr[i] < arr[j]) 
                continue; 
            if (Math.abs(arr[i] - arr[j]) % 2 == 1) 
                continue; 
 
            // Add total valid pairs 
            ans += count[arr[i]]* count[arr[j]]; 
            if (arr[i] == arr[j]) 
 
                // Exclude pairs made with a single element 
                // i.e. (x, x) 
                ans -= count[arr[i]]; 
        } 
    return ans; 
} 
 
// Driver Code 
public static void main(String[] args) 
{ 
int arr[] = {16, 17, 18}; 
int n= arr.length; 
 
// Function call to print required answer 
System.out.println(ValidPairs(arr,n)); 
}
}
// This code contributed by mits

Python3

# Python3 implementation of the approach
 
# Function to return total valid pairs
def ValidPairs(arr):
 
    # Initialize count of all the elements
    count = [0] * 121
 
    # frequency count of all the elements
    for ele in arr:
        count[ele] += 1
 
    ans = 0
    for eleX, countX in enumerate(count):
        for eleY, countY in enumerate(count):
            if eleX < eleY:
                continue
            if (abs(eleX - eleY) % 2 == 1):
                continue
 
            # Add total valid pairs
            ans += countX * countY
            if eleX == eleY:
 
                # Exclude pairs made with a single element 
                # i.e. (x, x)
                ans -= countX
 
    return ans
 
# Driver Code
arr = [16, 17, 18]
 
# Function call to print required answer
print(ValidPairs(arr))

C#

//C# implementation of the approach 
using System;
 
class GFG{
// Function to return total valid pairs 
static int ValidPairs(int[] arr,int n) 
{ 
 
    // Initialize count of all the elements 
    int[] count=new int[121]; 
 
    // frequency count of all the elements 
    for(int i=0;i<n;i++) 
        count[arr[i]] += 1; 
 
    int ans = 0; 
    for(int i=0;i<n;i++) 
        for(int j=0;j<n;j++) 
        { 
            if( arr[i] < arr[j]) 
                continue; 
            if (Math.Abs(arr[i] - arr[j]) % 2 == 1) 
                continue; 
 
            // Add total valid pairs 
            ans += count[arr[i]]* count[arr[j]]; 
            if (arr[i] == arr[j]) 
 
                // Exclude pairs made with a single element 
                // i.e. (x, x) 
                ans -= count[arr[i]]; 
        } 
    return ans; 
} 
 
// Driver Code 
public static void Main() 
{ 
int[] arr =new int[]{16, 17, 18}; 
int n= arr.Length; 
 
// Function call to print required answer 
Console.WriteLine(ValidPairs(arr,n)); 
}
}
// This code contributed by mits

PHP

<?php
//PHP implementation of the approach
 
// Function to return total valid pairs
function ValidPairs($arr,$n)
{
 
    // Initialize count of all the elements
    $count=array_fill(0,121,0);
 
    // frequency count of all the elements
    for($i=0;$i<$n;$i++)
        $count[$arr[$i]] += 1;
 
    $ans = 0;
    for($i=0;$i<$n;$i++)
        for($j=0;$j<$n;$j++)
        {
            if( $arr[$i] < $arr[$j])
                continue;
            if (abs($arr[$i] - $arr[$j]) % 2 == 1)
                continue;
 
            // Add total valid pairs
            $ans += $count[$arr[$i]]* $count[$arr[$j]];
            if ($arr[$i] == $arr[$j])
 
                // Exclude pairs made with a single element 
                // i.e. (x, x)
                $ans -= $count[$arr[$i]];
        }
    return $ans;
}
 
// Driver Code
 
$arr = array(16, 17, 18);
$n= count($arr);
 
// Function call to print required answer
echo (ValidPairs($arr,$n));
 
//This code is contributed by mits
?>

Javascript

<script>
// javascript implementation of the approach     
// Function to return total valid pairs
    function ValidPairs(arr , n) 
    {
 
        // Initialize count of all the elements
        var count = Array(121).fill(0);
 
        // frequency count of all the elements
        for (i = 0; i < n; i++)
            count[arr[i]] += 1;
 
        var ans = 0;
        for (i = 0; i < n; i++)
            for (j = 0; j < n; j++) {
                if (arr[i] < arr[j])
                    continue;
                if (Math.abs(arr[i] - arr[j]) % 2 == 1)
                    continue;
 
                // Add total valid pairs
                ans += count[arr[i]] * count[arr[j]];
                if (arr[i] == arr[j])
 
                    // Exclude pairs made with a single element
                    // i.e. (x, x)
                    ans -= count[arr[i]];
            }
        return ans;
    }
 
    // Driver Code
     
        var arr = [ 16, 17, 18 ];
        var n = arr.length;
 
        // Function call to print required answer
        document.write(ValidPairs(arr, n));
 
// This code is contributed by umadevi9616
</script>

Output

Complexity Analysis:

Time Complexity: O(n^2)
Auxiliary Space: O(1)

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