Todas las combinaciones únicas cuya suma es igual a K

Dada una array arr[] de tamaño N y un entero K . La tarea es encontrar todas las combinaciones únicas de la array dada de modo que la suma de los elementos en cada combinación sea igual a K .

Ejemplos: 

Entrada: arr[] = {1, 2, 3}, K = 3 
Salida: 
{1, 2} 
{3} 
Explicación:
Estas son las combinaciones cuya suma es igual a 3. 

Entrada: arr[] = {2, 2, 2}, K = 4 
Salida: 
{2, 2} 

Enfoque: algunos elementos se pueden repetir en la array dada. Asegúrese de iterar sobre el número de ocurrencias de esos elementos para evitar combinaciones repetidas. Una vez que haces eso, las cosas son bastante sencillas. Llame a una función recursiva con la suma restante y haga que los índices avancen. Cuando la suma llegue a K, imprima todos los elementos que fueron seleccionados para obtener esta suma.

A continuación se muestra la implementación del enfoque anterior: 

// C++ implementation of the approach
#include <bits/stdc++.h>
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 > l and A[i] == A[i - 1])
            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 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<Integer> local,
                                   Vector<Integer> 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 > l && A.get(i) == A.get(i - 1) )
                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<Integer> A, int K)
    {
        // Sort the given elements
        Collections.sort(A);
 
        // To store combination
        Vector<Integer> local = new Vector<Integer>();
 
        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<Integer> A
            = new Vector<>(Arrays.asList(arr));
 
        int K = 8;
 
        // Function call
        Combination(A, K);
    }
}
 
// This code is contributed by PrinciRaj1992

# 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 > l and
                A[i] == A[i - 1]):
            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# 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 >l && A[i] == A[i - 1])
                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

<script>
 
// JavaScript implementation of the approach
 
// Function to find all unique combination of
// given elements such that their sum is K
function unique_combination(l, sum, K, local, A) {
    // If a unique combination is found
    if (sum == K) {
        document.write("{");
        for (let i = 0; i < local.length; i++) {
            if (i != 0)
                document.write(" ");
            document.write(local[i]);
            if (i != local.length - 1)
                document.write(", ");
        }
        document.write("}" + "<br>");
        return;
    }
 
    // For all other combinations
    for (let i = l; i < A.length; i++) {
 
        // Check if the sum exceeds K
        if (sum + A[i] > K)
            continue;
 
        // Check if it is repeated or not
        if (i > l && A[i] == A[i - 1])
            continue;
 
        // Take the element into the combination
        local.push(A[i]);
 
        // Recursive call
        unique_combination(i + 1, sum + A[i], K, local, A);
 
        // Remove element from the combination
        local.pop();
    }
}
 
// Function to find all combination
// of the given elements
function Combination(A, K) {
    // Sort the given elements
    A.sort((a, b) => a - b);
 
    // To store combination
    let local = [];
 
    unique_combination(0, 0, K, local, A);
}
 
// Driver code
 
let A = [10, 1, 2, 7, 6, 1, 5];
 
let K = 8;
 
// Function call
Combination(A, K);
 
// This code is contributed by _saurabh_jaiswal
 
</script>

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