# Count all distinct pairs with product equal to K

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: 1
Explanation:
There is only one pair (1, 3) with product = K = 3.

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

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

Naive Approach: The naive approach for this problem is to consider all pairs one by one and check the product between every pair. If the product is equal to K, then increment the count and finally print it. However, the limitation is that this approach doesn’t work if there are duplicates in the array because we only need to consider distinct pairs.

Below is the implementation of the above approach:

 `// C++ program to count the number of pairs ` `// whose product is equal to K ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to count the number of pairs ` `// whose product is equal to K ` `int` `countPairsWithProdK(``int` `arr[], ``int` `n, ``int` `k) ` `{ ` `    ``int` `count = 0; ` ` `  `    ``// Pick all elements one by one ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``for` `(``int` `j = i + 1; j < n; j++) ` ` `  `            ``// Check if the product of this pair ` `            ``// is equal to K ` `            ``if` `(arr[i] * arr[j] == k) ` `                ``count++; ` `    ``} ` ` `  `    ``return` `count; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 5, 3, 4, 2 }; ` `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr); ` `    ``int` `K = 3; ` ` `  `    ``cout << countPairsWithProdK(arr, N, K); ` `    ``return` `0; ` `} `

 `// Java program to count the number of pairs ` `// whose product is equal to K ` `class` `GFG { ` ` `  `     ``// Function to count the number of pairs ` `    ``// whose product is equal to K ` `    ``static` `int` `countPairsWithProdK(``int` `arr[], ``int` `n, ``int` `k) ` `    ``{ ` `        ``int` `count = ``0``; ` `     `  `        ``// Pick all elements one by one ` `        ``for` `(``int` `i = ``0``; i < n; i++) { ` `            ``for` `(``int` `j = i + ``1``; j < n; j++) ` `     `  `                ``// Check if the product of this pair ` `                ``// is equal to K ` `                ``if` `(arr[i] * arr[j] == k) ` `                    ``count++; ` `        ``} ` `     `  `        ``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.println(countPairsWithProdK(arr, N, K)); ` `    ``} ` `} ` ` `  `// This code is contributed by AnkitRai01 `

 `# Python3 program to count the number of pairs ` `# whose product is equal to K ` ` `  `# Function to count the number of pairs ` `# whose product is equal to K ` `def` `countPairsWithProdK(arr, n, k): ` `    ``count ``=` `0` ` `  `    ``# Pick all elements one by one ` `    ``for` `i ``in` `range``(n): ` `        ``for` `j ``in` `range``(i ``+` `1``, n): ` ` `  `            ``# Check if the product of this pair ` `            ``# is equal to K ` `            ``if` `(arr[i] ``*` `arr[j] ``=``=` `k): ` `                ``count ``+``=` `1` ` `  `    ``return` `count ` ` `  `# Driver code ` `arr ``=` `[``1``, ``5``, ``3``, ``4``, ``2``] ` `N ``=` `len``(arr) ` `K ``=` `3` ` `  `print``(countPairsWithProdK(arr, N, K)) ` ` `  `# This code is contributed by mohit kumar 29 `

 `// C# program to count the number of pairs ` `// whose product is equal to K ` `using` `System; ` ` `  `class` `GFG { ` ` `  `     ``// Function to count the number of pairs ` `    ``// whose product is equal to K ` `    ``static` `int` `countPairsWithProdK(``int` `[]arr, ``int` `n, ``int` `k) ` `    ``{ ` `        ``int` `count = 0; ` `     `  `        ``// Pick all elements one by one ` `        ``for` `(``int` `i = 0; i < n; i++) { ` `            ``for` `(``int` `j = i + 1; j < n; j++) ` `     `  `                ``// Check if the product of this pair ` `                ``// is equal to K ` `                ``if` `(arr[i] * arr[j] == k) ` `                    ``count++; ` `        ``} ` `     `  `        ``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.WriteLine(countPairsWithProdK(arr, N, K)); ` `    ``} ` `} ` ` `  `// This code is contributed by AnkitRai01 `

Output:
```1
```

Time Complexity: O(N2)

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++ 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); ` `    ``int` `K = 3; ` ` `  `    ``cout << countPairsWithProductK(arr, N, K); ` `    ``return` `0; ` `} `

 `// 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 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# 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 `

Output:
```1
```

Time Complexity: O(N * log(N))

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