Print all distinct integers that can be formed by K numbers from a given array of N numbers

Given an array of N elements and an integer K, print all the distinct integers which can be formed by choosing K numbers from the given N numbers. A number from an array can be chosen any number of times.

Examples:

Input: k = 2, a[] = {3, 8, 17, 5}
Output: The 10 distinct integers are:
6 8 10 11 13 16 20 22 25 34
The 2 elements chosen are:
3+3 = 6, 5+3 = 8, 5+5 = 10, 8+3 = 11, 8+5 = 13
8+8 = 16, 17+3 = 20, 17+5 = 22, 17+8 = 25, 17+17 = 34.

Input: k = 3, a[] = {3, 8, 17}
Output: The 10 distinct integers are:
9 14 19 23 24 28 33 37 42 51

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

Approach: The problem will be solved using recursion. All combinations are to be tried, when the count of elements selected is equal to k, then we keep the num formed in the set so that the repetitive elements are not counted twice. The function generateNumber(int count, int a[], int n, int num, int k) is a recursive function, in which the base case is when the count becomes K which signifies that K elements from the array have been chosen. num in the parameter signifies the number formed by count number of numbers. In the function, iterate over the array and for every element, call the recursive function with count as count+1 and num as num+a[i].

Below is the implementation of the above approach:

C++

 // C++ program to print all distinct // integers that can be formed by K numbers // from a given array of N numbers. #include using namespace std;    // stores all the distinct integers formed set s;    // Function to generate all possible numbers void generateNumber(int count, int a[], int n,                     int num, int k) {        // Base case when K elements     // are chosen     if (k == count) {         // insert it in set         s.insert(num);         return;     }        // Choose every element and call the function     for (int i = 0; i < n; i++) {         generateNumber(count + 1, a, n, num + a[i], k);     } } // Function to print the distinct integers void printDistinctIntegers(int k, int a[], int n) {     generateNumber(0, a, n, 0, k);     cout << "The " << s.size()          << " distinct integers are:\n";        // prints all the elements in the set     while (!s.empty()) {         cout << *s.begin() << " ";            // erase the number after printing it         s.erase(*s.begin());     } } // Driver Code int main() {     int a[] = { 3, 8, 17, 5 };     int n = sizeof(a) / sizeof(a);     int k = 2;        // Calling Function     printDistinctIntegers(k, a, n);     return 0; }

Java

 // Java program to print all  // distinct integers that can  // be formed by K numbers from // a given array of N numbers. import java.util.*; import java.lang.*;    class GFG {     // stores all the distinct      // integers formed     static TreeSet set =                     new TreeSet();            // Function to generate      // all possible numbers     public static void generateNumber(int count, int a[],                                        int n, int num, int k)     {         // Base case when K          // elements are chosen         if(count == k)         {             set.add(num);             return;         }                    // Choose every element          // and call the function         for(int i = 0; i < n; i++)         generateNumber(count + 1, a, n,                        num + a[i], k);     }            // Function to print      // the distinct integers     public static void printDistinctIntegers(int k,                                               int a[], int n)     {         generateNumber(0, a, n, 0, k);         System.out.print("The" + " " + set.size() +                           " " + "distinct integers are: ");         System.out.println();         Iterator i = set.iterator();                    // prints all the         // elements in the set         while(set.isEmpty() == false)         {                            while(i.hasNext())             {                 System.out.print(i.next() + " ");                 //set.remove(i.next());             }            }     }            // Driver Code     public static void main (String[] args)      {         int arr[] = {3, 8, 17, 5};         int n = arr.length;         int k = 2;                    // Calling Function         printDistinctIntegers(k, arr, n);     } }

Python3

 # Python3 program to print all distinct  # integers that can be formed by K numbers  # from a given array of N numbers.     # stores all the distinct integers formed  s = set()    # Function to generate all possible numbers  def generateNumber(count, a, n, num, k):         # Base case when K elements are chosen      if k == count:                     # insert it in set          s.add(num)          return            # Choose every element and call the function      for i in range(0, n):          generateNumber(count + 1, a, n,                               num + a[i], k)     # Function to print the distinct integers  def printDistinctIntegers(k, a, n):        generateNumber(0, a, n, 0, k)      print("The", len(s),            "distinct integers are:")         # prints all the elements in the set      for i in sorted(s):          print(i, end = " ")        # Driver Code  if __name__ == "__main__":        a = [3, 8, 17, 5]      n, k = len(a), 2        # Calling Function      printDistinctIntegers(k, a, n)        # This code is contributed by Rituraj Jain

C#

 // C# program to print all  // distinct integers that can  // be formed by K numbers from // a given array of N numbers. using System; using System.Collections.Generic;    class GFG {     // stores all the distinct      // integers formed     static SortedSet set =                  new SortedSet();            // Function to generate      // all possible numbers     public static void generateNumber(int count, int []a,                                      int n, int num, int k)     {         // Base case when K          // elements are chosen         if(count == k)         {             set.Add(num);             return;         }                    // Choose every element          // and call the function         for(int i = 0; i < n; i++)         generateNumber(count + 1, a, n,                     num + a[i], k);     }            // Function to print      // the distinct integers     public static void printDistinctIntegers(int k,                                              int []a, int n)     {         generateNumber(0, a, n, 0, k);         Console.Write("The" + " " + set.Count +                          " " + "distinct integers are: ");         Console.WriteLine();                       // prints all the         // elements in the set         foreach(int sets in set)         {                 Console.Write(sets + " ");            }     }            // Driver Code     public static void Main (String[] args)      {         int []arr = {3, 8, 17, 5};         int n = arr.Length;         int k = 2;                    // Calling Function         printDistinctIntegers(k, arr, n);     } }    // This code has been contributed by 29AjayKumar

Output:

The 10 distinct integers are:
6 8 10 11 13 16 20 22 25 34

My Personal Notes arrow_drop_up The function of education is to teach one to think intensively and to think critically

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Improved By : rituraj_jain, 29AjayKumar

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