# Count number of ordered pairs with Even and Odd Product

Given an array of n positive numbers, the task is to count number of ordered pairs with even and odd product. Ordered pairs means (a, b) and (b,a) will be considered as different.

Examples:

Input: n = 3, arr[] = {1, 2, 7}
Output: Even product Pairs = 4, Odd product Pairs = 2
The ordered pairs are (1, 2), (1, 7), (2, 1), (7, 1), (2, 7), (7, 2)
Pairs with Odd product: (1, 7), (7, 1)
Pairs with Even product: (1, 2), (2, 7), (2, 1), (7, 2)

Input: n = 6, arr[] = {2, 4, 5, 9, 1, 8}
Output: Even product Pairs = 24, Odd product Pairs = 6

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

Approach:

The product of two numbers is odd only if both are numbers are odd. Therefore:

Number of odd product pairs = (count of odd numbers) * (count of odd numbers – 1)

And the number of even product pairs will be an inversion of number of odd product pairs. Therefore:

Number of even product pairs = Total Number of pairs – Number of odd product pairs

Below is the implementation of above approach:

## C++

 `// C++ implementation of the above approach ` `#include ` `using` `namespace` `std; ` ` `  `// function to count odd product pair ` `int` `count_odd_pair(``int` `n, ``int` `a[]) ` `{ ` `    ``int` `odd = 0, even = 0; ` ` `  `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// if number is even ` `        ``if` `(a[i] % 2 == 0) ` `            ``even++; ` ` `  `        ``// if number is odd ` `        ``else` `            ``odd++; ` `    ``} ` ` `  `    ``// count of ordered pairs ` `    ``int` `ans = odd * (odd - 1); ` ` `  `    ``return` `ans; ` `} ` ` `  `// function to count even product pair ` `int` `count_even_pair(``int` `odd_product_pairs, ``int` `n) ` `{ ` `    ``int` `total_pairs = (n * (n - 1)); ` `    ``int` `ans = total_pairs - odd_product_pairs; ` `    ``return` `ans ; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` ` `  `    ``int` `n = 6; ` `    ``int` `a[] = { 2, 4, 5, 9, 1, 8 }; ` ` `  `    ``int` `odd_product_pairs = count_odd_pair(n, a); ` ` `  `    ``int` `even_product_pairs = count_even_pair( ` `        ``odd_product_pairs, n); ` ` `  `    ``cout << ``"Even Product Pairs = "` `         ``<< even_product_pairs ` `         ``<< endl; ` `    ``cout << ``"Odd Product Pairs= "` `         ``<< odd_product_pairs ` `         ``<< endl; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java  implementation of the above approach  ` `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `     `  `// function to count odd product pair  ` `static` `int` `count_odd_pair(``int` `n, ``int` `a[])  ` `{  ` `    ``int` `odd = ``0``, even = ``0``;  ` ` `  `    ``for` `(``int` `i = ``0``; i < n; i++) {  ` ` `  `        ``// if number is even  ` `        ``if` `(a[i] % ``2` `== ``0``)  ` `            ``even++;  ` ` `  `        ``// if number is odd  ` `        ``else` `            ``odd++;  ` `    ``}  ` ` `  `    ``// count of ordered pairs  ` `    ``int` `ans = odd * (odd - ``1``);  ` ` `  `    ``return` `ans;  ` `}  ` ` `  `// function to count even product pair  ` `static` `int` `count_even_pair(``int` `odd_product_pairs, ``int` `n)  ` `{  ` `    ``int` `total_pairs = (n * (n - ``1``));  ` `    ``int` `ans = total_pairs - odd_product_pairs;  ` `    ``return` `ans; ` `}  ` ` `  `// Driver code  ` `    ``public` `static` `void` `main (String[] args) { ` ` `  `        ``int` `n = ``6``;  ` `        ``int` `[]a = { ``2``, ``4``, ``5``, ``9``, ``1``, ``8` `};  ` ` `  `        ``int` `odd_product_pairs = count_odd_pair(n, a);  ` ` `  `        ``int` `even_product_pairs = count_even_pair(  ` `            ``odd_product_pairs, n);  ` ` `  `        ``System.out.println( ``"Even Product Pairs = "``+ ` `            ``even_product_pairs ); ` `          `  `        ``System.out.println(``"Odd Product Pairs= "``+ ` `             ``odd_product_pairs ); ` `     `  `    ``} ` `} ` `//This Code is Contributed by ajit `

## Python3

 `# Python3 implementation of  ` `# above approach ` ` `  `# function to count odd product pair ` `def` `count_odd_pair(n, a): ` `    ``odd ``=` `0` `    ``even ``=` `0` `    ``for` `i ``in` `range``(``0``,n): ` `         `  `        ``# if number is even ` `        ``if` `a[i] ``%` `2``=``=``0``: ` `            ``even``=``even``+``1` `        ``# if number is odd ` `        ``else``: ` `            ``odd``=``odd``+``1` `     `  `    ``# count of ordered pairs ` `    ``ans ``=` `odd ``*` `(odd ``-` `1``) ` `    ``return` `ans ` ` `  `# function to count even product pair ` `def` `count_even_pair(odd_product_pairs, n): ` `    ``total_pairs ``=` `(n ``*` `(n ``-` `1``)) ` `    ``ans ``=` `total_pairs ``-` `odd_product_pairs ` `    ``return` `ans ` ` `  `#Driver code ` `if` `__name__``=``=``'__main__'``: ` `    ``n ``=` `6` `    ``a ``=` `[``2``, ``4``, ``5``, ``9``, ``1` `,``8``] ` ` `  `    ``odd_product_pairs ``=` `count_odd_pair(n, a) ` `    ``even_product_pairs ``=` `(count_even_pair ` `                       ``(odd_product_pairs, n)) ` ` `  `    ``print``(``"Even Product Pairs = "` `          ``,even_product_pairs) ` `    ``print``(``"Odd Product Pairs= "` `          ``,odd_product_pairs) ` ` `  `# This code is contributed by  ` `# Shashank_Sharma `

## C#

 `// C#  implementation of the above approach ` `using` `System; ` ` `  `public` `class` `GFG{ ` `     `  `         `  `// function to count odd product pair  ` `static` `int` `count_odd_pair(``int` `n, ``int` `[]a)  ` `{  ` `    ``int` `odd = 0, even = 0;  ` ` `  `    ``for` `(``int` `i = 0; i < n; i++) {  ` ` `  `        ``// if number is even  ` `        ``if` `(a[i] % 2 == 0)  ` `            ``even++;  ` ` `  `        ``// if number is odd  ` `        ``else` `            ``odd++;  ` `    ``}  ` ` `  `    ``// count of ordered pairs  ` `    ``int` `ans = odd * (odd - 1);  ` ` `  `    ``return` `ans;  ` `}  ` ` `  `// function to count even product pair  ` `static` `int` `count_even_pair(``int` `odd_product_pairs, ``int` `n)  ` `{  ` `    ``int` `total_pairs = (n * (n - 1));  ` `    ``int` `ans = total_pairs - odd_product_pairs;  ` `    ``return` `ans; ` `}  ` ` `  `// Driver code  ` `     `  `static` `public` `void` `Main (){ ` `        ``int` `n = 6;  ` `        ``int` `[]a = { 2, 4, 5, 9, 1, 8 };  ` ` `  `        ``int` `odd_product_pairs = count_odd_pair(n, a);  ` ` `  `        ``int` `even_product_pairs = count_even_pair(  ` `            ``odd_product_pairs, n);  ` ` `  `        ``Console.WriteLine( ``"Even Product Pairs = "``+ ` `            ``even_product_pairs ); ` `         `  `        ``Console.WriteLine(``"Odd Product Pairs= "``+ ` `            ``odd_product_pairs ); ` `    ``} ` `} `

## PHP

 ` `

Output:

```Even Product Pairs = 24
Odd Product Pairs= 6
```

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