Count number of pairs in array having sum divisible by K | SET 2

Given an array A[] and positive integer K, the task is to count the total number of pairs in the array whose sum is divisible by K.

Examples:

Input : A[] = {2, 2, 1, 7, 5, 3}, K = 4
Output : 5
There are five pairs possible whose sum
is divisible by ‘4’ i.e., (2, 2),
(1, 7), (7, 5), (1, 3) and (5, 3)

Input : A[] = {5, 9, 36, 74, 52, 31, 42}, K = 3
Output : 7

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

Approach: In the previous post, an approach using hashing is discussed. In this article, another approach using hashing is discussed.

The idea is to traverse the array, find (arr[i] % k) and keep track of these values in the hash.

The stepwise algorithm is:

1. Find x = arr[i]%k.
2. This array element can be paired with array elements having mod value k-x. This count of array elements is stored in hash. So add that count to answer.
3. Increment count for x in hash.
4. In case value of x is zero, then it can be paired only with elements having 0 mod value.

Below is the implementation of the above approach:

 `// C++ Program to count pairs ` `// whose sum divisible by 'K' ` `#include ` `using` `namespace` `std; ` ` `  `// Program to count pairs whose sum divisible ` `// by 'K' ` `int` `countKdivPairs(``int` `A[], ``int` `n, ``int` `K) ` `{ ` `    ``// Create a frequency array to count ` `    ``// occurrences of all remainders when ` `    ``// divided by K ` `    ``int` `freq[K] = { 0 }; ` ` `  `    ``// To store count of pairs. ` `    ``int` `ans = 0; ` ` `  `    ``// Traverse the array, compute the remainder ` `    ``// and add k-remainder value hash count to ans ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``int` `rem = A[i] % K; ` `        ``if` `(rem != 0) ` `            ``ans += freq[K - rem]; ` `        ``else` `            ``ans += freq[0]; ` ` `  `        ``// Increment count of remainder in hash map ` `        ``freq[rem]++; ` `    ``} ` ` `  `    ``return` `ans; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` ` `  `    ``int` `A[] = { 2, 2, 1, 7, 5, 3 }; ` `    ``int` `n = ``sizeof``(A) / ``sizeof``(A[0]); ` `    ``int` `K = 4; ` `    ``cout << countKdivPairs(A, n, K); ` ` `  `    ``return` `0; ` `} `

 `// Java Program to count pairs ` `// whose sum divisible by 'K' ` `class` `GFG  ` `{ ` ` `  `// Program to count pairs whose sum divisible ` `// by 'K' ` `static` `int` `countKdivPairs(``int` `A[], ``int` `n, ``int` `K) ` `{ ` `    ``// Create a frequency array to count ` `    ``// occurrences of all remainders when ` `    ``// divided by K ` `    ``int` `[]freq = ``new` `int``[K]; ` ` `  `    ``// To store count of pairs. ` `    ``int` `ans = ``0``; ` ` `  `    ``// Traverse the array, compute the remainder ` `    ``// and add k-remainder value hash count to ans ` `    ``for` `(``int` `i = ``0``; i < n; i++) ` `    ``{ ` `        ``int` `rem = A[i] % K; ` `        ``if` `(rem != ``0``) ` `            ``ans += freq[K - rem]; ` `        ``else` `            ``ans += freq[``0``]; ` ` `  `        ``// Increment count of remainder in hash map ` `        ``freq[rem]++; ` `    ``} ` ` `  `    ``return` `ans; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args)  ` `{ ` `    ``int` `A[] = { ``2``, ``2``, ``1``, ``7``, ``5``, ``3` `}; ` `    ``int` `n = A.length; ` `    ``int` `K = ``4``; ` `    ``System.out.println(countKdivPairs(A, n, K)); ` `} ` `} ` ` `  `// This code is contributed by Princi Singh `

 `# Python 3 Program to count pairs ` `# whose sum divisible by 'K' ` ` `  `# Program to count pairs whose sum divisible ` `# by 'K' ` `def` `countKdivPairs(A, n, K): ` `     `  `    ``# Create a frequency array to count ` `    ``# occurrences of all remainders when ` `    ``# divided by K ` `    ``freq ``=` `[``0` `for` `i ``in` `range``(K)] ` ` `  `    ``# To store count of pairs. ` `    ``ans ``=` `0` ` `  `    ``# Traverse the array, compute the remainder ` `    ``# and add k-remainder value hash count to ans ` `    ``for` `i ``in` `range``(n): ` `        ``rem ``=` `A[i] ``%` `K ` `        ``if` `(rem !``=` `0``): ` `            ``ans ``+``=` `freq[K ``-` `rem] ` `        ``else``: ` `            ``ans ``+``=` `freq[``0``] ` ` `  `        ``# Increment count of remainder in hash map ` `        ``freq[rem] ``+``=` `1` ` `  `    ``return` `ans ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``A ``=` `[``2``, ``2``, ``1``, ``7``, ``5``, ``3``] ` `    ``n ``=` `len``(A) ` `    ``K ``=` `4` `    ``print``(countKdivPairs(A, n, K)) ` ` `  `# This code is contributed by ` `# Surendra_Gangwar `

 `// C# Program to count pairs ` `// whose sum divisible by 'K' ` `using` `System; ` ` `  `class` `GFG  ` `{ ` ` `  `// Program to count pairs whose sum divisible ` `// by 'K' ` `static` `int` `countKdivPairs(``int` `[]A, ``int` `n, ``int` `K) ` `{ ` `    ``// Create a frequency array to count ` `    ``// occurrences of all remainders when ` `    ``// divided by K ` `    ``int` `[]freq = ``new` `int``[K]; ` ` `  `    ``// To store count of pairs. ` `    ``int` `ans = 0; ` ` `  `    ``// Traverse the array, compute the remainder ` `    ``// and add k-remainder value hash count to ans ` `    ``for` `(``int` `i = 0; i < n; i++) ` `    ``{ ` `        ``int` `rem = A[i] % K; ` `        ``if` `(rem != 0) ` `            ``ans += freq[K - rem]; ` `        ``else` `            ``ans += freq[0]; ` ` `  `        ``// Increment count of remainder in hash map ` `        ``freq[rem]++; ` `    ``} ` ` `  `    ``return` `ans; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args)  ` `{ ` `    ``int` `[]A = { 2, 2, 1, 7, 5, 3 }; ` `    ``int` `n = A.Length; ` `    ``int` `K = 4; ` `    ``Console.WriteLine(countKdivPairs(A, n, K)); ` `} ` `} ` ` `  `// This code contributed by Rajput-Ji `

Output:
```5
```

Time Complexity: O(N)
Auxiliary Space: O(1)

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