All unique combinations whose sum equals to K - GeeksforGeeks

07 Sep, 2021
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 combination is equal to K.
Examples: 
Input: arr[] = {1, 2, 3}, K = 3 Output: {1, 2} {3} Explanation:These are the combinations whose sum equals to 3. 
Input: arr[] = {2, 2, 2}, K = 4 Output: {2, 2} 
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++
Java
Python3
C#
Javascript
// 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 Kvoid 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 elementsvoid 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 codeint 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 approachimport 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 codeif __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 approachusing 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 Kfunction 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 elementsfunction 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 callCombination(A, K); // This code is contributed by _saurabh_jaiswal </script>
{1,  1,  6}
{1,  2,  5}
{1,  7}
{2,  6}
princiraj1992
Rajput-Ji
SURENDRA_GANGWAR
richaranderia
_saurabh_jaiswal
shijo2895
khushboogoyal499
Arrays
Recursion
Sorting
Arrays
Recursion
Sorting
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