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 

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 <bits/stdc++.h>
using namespace std;

// stores all the distinct integers formed
set<int> 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[0]);
    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<Integer> set =
                   new TreeSet<Integer>();

    // 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<Integer> 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<int> set =
                new SortedSet<int>();

    // 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

Javascript

<script>

// Javascript 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
var s = new Set();

// Function to generate all possible numbers
function 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(var i = 0; i < n; i++)
    {
        generateNumber(count + 1, a, n,
                         num + a[i], k);
    }
}

// Function to print the distinct integers
function printDistinctIntegers(k, a, n)
{
    generateNumber(0, a, n, 0, k);
    document.write("The " + s.size +
                   " distinct integers are:<br>");

    // prints all the elements in the set
    while (s.size != 0)
    {
        var tmp = [...s].sort((a, b) => a - b)[0]
        document.write(tmp + " ");

        // Erase the number after printing it
        s.delete(tmp);
    }
}

// Driver Code
var a = [ 3, 8, 17, 5 ];
var n = a.length;
var k = 2;

// Calling Function
printDistinctIntegers(k, a, n);

// This code is contributed by itsok

</script>

Output

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