# Count all distinct pairs with product equal to K

• Last Updated : 20 Aug, 2022

Given an integer array arr[] of size N and a positive integer K, the task is to count all the distinct pairs in the array with product equal to K.
Examples:

Input: arr[] = {1, 5, 3, 4, 2}, K = 3
Output:
Explanation:
There is only one pair (1, 3) with product = K = 3.
Input: arr[] = {1, 2, 16, 4, 4}, K = 16
Output:
Explanation:
There are two pairs (1, 16) and (4, 4) with product = K = 16.

Efficient Approach: The idea is to use hashing.

1. Initially, insert all the elements from the array into the hashmap. While inserting, ignore if a particular element is already present in the hashmap.
2. Now, we have all the unique elements in the hash. So, for every element in the array arr[i], we check if arr[i] / K is present in the hashmap or not.
3. If the value is present, then we increment the count and remove that particular element from the hash( To get the unique pairs).

Below is the implementation of the above approach:

## C++

 `// C++ program to count the number of pairs``// whose product is equal to K` `#include ``#include ``using` `namespace` `std;``#define MAX 100000` `// Function to count the number of pairs``// whose product is equal to K``int` `countPairsWithProductK(``int` `arr[], ``int` `n, ``int` `k)``{``    ``// Initialize the count``    ``int` `count = 0;` `    ``// Initialize empty hashmap.``    ``bool` `hashmap[MAX] = { ``false` `};` `    ``// Insert array elements to hashmap``    ``for` `(``int` `i = 0; i < n; i++)``        ``hashmap[arr[i]] = ``true``;` `    ``for` `(``int` `i = 0; i < n; i++) {``        ``int` `x = arr[i];` `        ``double` `index = 1.0 * k / arr[i];` `        ``// Checking if the index is a whole number``        ``// and present in the hashmap``        ``if` `(index >= 0``            ``&& ((index - (``int``)(index)) == 0)``            ``&& hashmap[k / x])` `            ``count++;``        ``hashmap[x] = ``false``;``    ``}``    ``return` `count;``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 1, 5, 3, 4, 2 };``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``int` `K = 3;` `    ``cout << countPairsWithProductK(arr, N, K);``    ``return` `0;``}`

## Java

 `// Java program to count the number of pairs``// whose product is equal to K``    ` `class` `GFG``{``    ``static` `int` `MAX = ``100000``;``    ` `    ``// Function to count the number of pairs``    ``// whose product is equal to K``    ``static` `int` `countPairsWithProductK(``int` `arr[], ``int` `n, ``int` `k)``    ``{``        ``// Initialize the count``        ``int` `count = ``0``;``        ``int` `i;` `        ``// Initialize empty hashmap.``        ``boolean` `hashmap[] = ``new` `boolean``[MAX];``        ` `        ``// Insert array elements to hashmap``        ``for` `(i = ``0``; i < n; i++)``            ``hashmap[arr[i]] = ``true``;``        ` `        ``for` `(i = ``0``; i < n; i++) {``            ``int` `x = arr[i];``        ` `            ``double` `index = ``1.0` `* k / arr[i];``        ` `            ``// Checking if the index is a whole number``            ``// and present in the hashmap``            ``if` `(index >= ``0``                ``&& ((index - (``int``)(index)) == ``0``)``                ``&& hashmap[k / x])``        ` `                ``count++;``            ``hashmap[x] = ``false``;``        ``}``        ``return` `count;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main(String []args)``    ``{``        ``int` `arr[] = { ``1``, ``5``, ``3``, ``4``, ``2` `};``        ``int` `N = arr.length;``        ``int` `K = ``3``;``        ` `        ``System.out.print(countPairsWithProductK(arr, N, K));``        ` `    ``}``}`

## Python3

 `# Python3 program to count the number of pairs``# whose product is equal to K``MAX` `=` `100000``;` `# Function to count the number of pairs``# whose product is equal to K``def` `countPairsWithProductK(arr, n, k) :` `    ``# Initialize the count``    ``count ``=` `0``;` `    ``# Initialize empty hashmap.``    ``hashmap ``=` `[``False``]``*``MAX` `;` `    ``# Insert array elements to hashmap``    ``for` `i ``in` `range``(n) :``        ``hashmap[arr[i]] ``=` `True``;` `    ``for` `i ``in` `range``(n) :``        ``x ``=` `arr[i];` `        ``index ``=` `1.0` `*` `k ``/` `arr[i];` `        ``# Checking if the index is a whole number``        ``# and present in the hashmap``        ``if` `(index >``=` `0``            ``and` `((index ``-` `int``(index)) ``=``=` `0``)``            ``and` `hashmap[k ``/``/` `x]) :` `                ``count ``+``=` `1``;``        ` `        ``hashmap[x] ``=` `False``;``    ` `    ``return` `count;` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:``    ``arr ``=` `[ ``1``, ``5``, ``3``, ``4``, ``2` `];``    ``N ``=` `len``(arr);``    ``K ``=` `3``;` `    ``print``(countPairsWithProductK(arr, N, K));` `# This code is contributed by AnkitRai01`

## C#

 `// C# program to count the number of pairs``// whose product is equal to K    ``using` `System;` `class` `GFG``{``    ``static` `int` `MAX = 100000;``     ` `    ``// Function to count the number of pairs``    ``// whose product is equal to K``    ``static` `int` `countPairsWithProductK(``int` `[]arr, ``int` `n, ``int` `k)``    ``{``        ``// Initialize the count``        ``int` `count = 0;``        ``int` `i;`` ` `        ``// Initialize empty hashmap.``        ``bool` `[]hashmap = ``new` `bool``[MAX];``         ` `        ``// Insert array elements to hashmap``        ``for` `(i = 0; i < n; i++)``            ``hashmap[arr[i]] = ``true``;``         ` `        ``for` `(i = 0; i < n; i++) {``            ``int` `x = arr[i];``         ` `            ``double` `index = 1.0 * k / arr[i];``         ` `            ``// Checking if the index is a whole number``            ``// and present in the hashmap``            ``if` `(index >= 0``                ``&& ((index - (``int``)(index)) == 0)``                ``&& hashmap[k / x])``         ` `                ``count++;``            ``hashmap[x] = ``false``;``        ``}``        ``return` `count;``    ``}``     ` `    ``// Driver code``    ``public` `static` `void` `Main(String []args)``    ``{``        ``int` `[]arr = { 1, 5, 3, 4, 2 };``        ``int` `N = arr.Length;``        ``int` `K = 3;``         ` `        ``Console.Write(countPairsWithProductK(arr, N, K));        ``    ``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``

Output:

`1`

Time Complexity: O(N)

Auxiliary Space: O(MAX), since MAX space has been taken.

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