# All unique combinations whose sum equals to K

Given an array arr[] of size N and an integer K. The task is to find all the unique combinations from the given array such that sum of the elements in each combiantion is equal to K.

Examples:

Input: arr[] = {1, 2, 3}, K = 3
Output:
{1, 2}
{3}
These are the combinations whose sum equals to 3.

Input: arr[] = {2, 2, 2}, K = 4
Output:
{2, 2}

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

Approach: Some elements can be repeated in the given array. Make sure to iterate over the number of occurrences of those elements to avoid repeated combinations. Once you do that, things are fairly straightforward. Call a recursive function with the remaining sum and make the indices to move forward. When the sum reaches K, print all the elements which were selected to get this sum.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find all unique combination of ` `// given elements such that their sum is K ` `void` `unique_combination(``int` `l, ``int` `sum, ``int` `K, ` `                        ``vector<``int``>& local, vector<``int``>& A) ` `{ ` `    ``// If a unique combination is found ` `    ``if` `(sum == K) { ` `        ``cout << ``"{"``; ` `        ``for` `(``int` `i = 0; i < local.size(); i++) { ` `            ``if` `(i != 0) ` `                ``cout << ``" "``; ` `            ``cout << local[i]; ` `            ``if` `(i != local.size() - 1) ` `                ``cout << ``", "``; ` `        ``} ` `        ``cout << ``"}"` `<< endl; ` `        ``return``; ` `    ``} ` ` `  `    ``// For all other combinations ` `    ``for` `(``int` `i = l; i < A.size(); i++) { ` ` `  `        ``// Check if the sum exceeds K ` `        ``if` `(sum + A[i] > K) ` `            ``continue``; ` ` `  `        ``// Check if it is repeated or not ` `        ``if` `(i and A[i] == A[i - 1] and i > l) ` `            ``continue``; ` ` `  `        ``// Take the element into the combination ` `        ``local.push_back(A[i]); ` ` `  `        ``// Recursive call ` `        ``unique_combination(i + 1, sum + A[i], ` `                           ``K, local, A); ` ` `  `        ``// Remove element from the combination ` `        ``local.pop_back(); ` `    ``} ` `} ` ` `  `// Function to find all combination ` `// of the given elements ` `void` `Combination(vector<``int``> A, ``int` `K) ` `{ ` `    ``// Sort the given elements ` `    ``sort(A.begin(), A.end()); ` ` `  `    ``// To store combination ` `    ``vector<``int``> local; ` ` `  `    ``unique_combination(0, 0, K, local, A); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``vector<``int``> A = { 10, 1, 2, 7, 6, 1, 5 }; ` ` `  `    ``int` `K = 8; ` ` `  `    ``// Function call ` `    ``Combination(A, K); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.util.*; ` ` `  `class` `GFG  ` `{ ` ` `  `// Function to find all unique combination of ` `// given elements such that their sum is K ` `static` `void` `unique_combination(``int` `l, ``int` `sum, ``int` `K,  ` `                               ``Vector local,  ` `                               ``Vector A) ` `{ ` `    ``// If a unique combination is found ` `    ``if` `(sum == K)  ` `    ``{ ` `        ``System.out.print(``"{"``); ` `        ``for` `(``int` `i = ``0``; i < local.size(); i++) ` `        ``{ ` `            ``if` `(i != ``0``) ` `                ``System.out.print(``" "``); ` `            ``System.out.print(local.get(i)); ` `            ``if` `(i != local.size() - ``1``) ` `                ``System.out.print(``", "``); ` `        ``} ` `        ``System.out.println(``"}"``); ` `        ``return``; ` `    ``} ` ` `  `    ``// For all other combinations ` `    ``for` `(``int` `i = l; i < A.size(); i++) ` `    ``{ ` ` `  `        ``// Check if the sum exceeds K ` `        ``if` `(sum + A.get(i) > K) ` `            ``continue``; ` ` `  `        ``// Check if it is repeated or not ` `        ``if` `(i == ``1` `&& ` `            ``A.get(i) == A.get(i - ``1``) &&  ` `            ``i > l) ` `            ``continue``; ` ` `  `        ``// Take the element into the combination ` `        ``local.add(A.get(i)); ` ` `  `        ``// Recursive call ` `        ``unique_combination(i + ``1``, sum + A.get(i), ` `                           ``K, local, A); ` ` `  `        ``// Remove element from the combination ` `        ``local.remove(local.size() - ``1``); ` `    ``} ` `} ` ` `  `// Function to find all combination ` `// of the given elements ` `static` `void` `Combination(Vector A, ``int` `K) ` `{ ` `    ``// Sort the given elements ` `    ``Collections.sort(A); ` ` `  `    ``// To store combination ` `    ``Vector local = ``new` `Vector(); ` ` `  `    ``unique_combination(``0``, ``0``, K, local, A); ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args)  ` `{ ` `    ``Integer []arr = { ``10``, ``1``, ``2``, ``7``, ``6``, ``1``, ``5` `}; ` `    ``Vector A = ``new` `Vector<>(Arrays.asList(arr)); ` ` `  `    ``int` `K = ``8``; ` ` `  `    ``// Function call ` `    ``Combination(A, K); ` `} ` `} ` ` `  `// This code is contributed by PrinciRaj1992  `

## Python3

 `# Python 3 implementation of the approach ` ` `  `# Function to find all unique combination of ` `# given elements such that their sum is K ` `def` `unique_combination(l, ``sum``, K, local, A): ` `     `  `    ``# If a unique combination is found ` `    ``if` `(``sum` `=``=` `K): ` `        ``print``(``"{"``, end ``=` `"") ` `        ``for` `i ``in` `range``(``len``(local)): ` `            ``if` `(i !``=` `0``): ` `                ``print``(``" "``, end ``=``"") ` `            ``print``(local[i], end ``=` `"") ` `            ``if` `(i !``=` `len``(local) ``-` `1``): ` `                ``print``(``", "``, end ``=` `"") ` `        ``print``(``"}"``) ` `        ``return` ` `  `    ``# For all other combinations ` `    ``for` `i ``in` `range``(l, ``len``(A), ``1``): ` `         `  `        ``# Check if the sum exceeds K ` `        ``if` `(``sum` `+` `A[i] > K): ` `            ``continue` ` `  `        ``# Check if it is repeated or not ` `        ``if` `(i ``=``=` `1` `and`  `            ``A[i] ``=``=` `A[i ``-` `1``] ``and` `i > l): ` `            ``continue` ` `  `        ``# Take the element into the combination ` `        ``local.append(A[i]) ` ` `  `        ``# Recursive call ` `        ``unique_combination(i ``+` `1``, ``sum` `+` `A[i],  ` `                                ``K, local, A) ` ` `  `        ``# Remove element from the combination ` `        ``local.remove(local[``len``(local) ``-` `1``]) ` ` `  `# Function to find all combination ` `# of the given elements ` `def` `Combination(A, K): ` `     `  `    ``# Sort the given elements ` `    ``A.sort(reverse ``=` `False``) ` ` `  `    ``local ``=` `[] ` ` `  `    ``unique_combination(``0``, ``0``, K, local, A) ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``A ``=` `[``10``, ``1``, ``2``, ``7``, ``6``, ``1``, ``5``] ` ` `  `    ``K ``=` `8` ` `  `    ``# Function call ` `    ``Combination(A, K) ` `     `  `# This code is contributed by ` `# Surendra_Gangwar `

## C#

 `// C# implementation of the approach ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG  ` `{ ` ` `  `// Function to find all unique combination of ` `// given elements such that their sum is K ` `static` `void` `unique_combination(``int` `l, ``int` `sum, ``int` `K,  ` `                               ``List<``int``> local,  ` `                               ``List<``int``> A) ` `{ ` `    ``// If a unique combination is found ` `    ``if` `(sum == K)  ` `    ``{ ` `        ``Console.Write(``"{"``); ` `        ``for` `(``int` `i = 0; i < local.Count; i++) ` `        ``{ ` `            ``if` `(i != 0) ` `                ``Console.Write(``" "``); ` `            ``Console.Write(local[i]); ` `            ``if` `(i != local.Count - 1) ` `                ``Console.Write(``", "``); ` `        ``} ` `        ``Console.WriteLine(``"}"``); ` `        ``return``; ` `    ``} ` ` `  `    ``// For all other combinations ` `    ``for` `(``int` `i = l; i < A.Count; i++) ` `    ``{ ` ` `  `        ``// Check if the sum exceeds K ` `        ``if` `(sum + A[i] > K) ` `            ``continue``; ` ` `  `        ``// Check if it is repeated or not ` `        ``if` `(i == 1 && ` `            ``A[i] == A[i - 1] &&  ` `            ``i > l) ` `            ``continue``; ` ` `  `        ``// Take the element into the combination ` `        ``local.Add(A[i]); ` ` `  `        ``// Recursive call ` `        ``unique_combination(i + 1, sum + A[i], ` `                           ``K, local, A); ` ` `  `        ``// Remove element from the combination ` `        ``local.RemoveAt(local.Count - 1); ` `    ``} ` `} ` ` `  `// Function to find all combination ` `// of the given elements ` `static` `void` `Combination(List<``int``> A, ``int` `K) ` `{ ` `    ``// Sort the given elements ` `    ``A.Sort(); ` ` `  `    ``// To store combination ` `    ``List<``int``> local = ``new` `List<``int``>(); ` ` `  `    ``unique_combination(0, 0, K, local, A); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args)  ` `{ ` `    ``int` `[]arr = { 10, 1, 2, 7, 6, 1, 5 }; ` `    ``List<``int``> A = ``new` `List<``int``>(arr); ` ` `  `    ``int` `K = 8; ` ` `  `    ``// Function call ` `    ``Combination(A, K); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

Output:

```{1,  1,  6}
{1,  2,  5}
{1,  7}
{2,  6}
```

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