# Count valid pairs in the array satisfying given conditions

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)

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `using` `namespace` `std; ` ` `  `// Function to return total valid pairs ` `int` `ValidPairs(``int` `arr[],``int` `n) ` `{ ` `  `  `    ``// Initialize count of all the elements ` `    ``int` `count={0}; ` `  `  `    ``// frequency count of all the elements ` `    ``for``(``int` `i=0;i

## 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

## 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``;  ` ` `  `    ``// frequency count of all the elements  ` `    ``for``(``int` `i=0;i

## PHP

 ` `

Output:

```1
```

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