# Print combinations of distinct numbers which add up to give sum N

Given a positive integer N, the task is to find out all the combinations of positive integers that add upto the given integer N. The program should print only combinations, not permutations and all the integers in a combination must be distinct. For example, for input 3, either 1, 2 or 2, 1 should be printed and 1, 1, 1 must not be printed as the integers are not distinct.
Examples:

Input: N = 3
Output:
1 2
3
Input: N = 7
Output:
1 2 4
1 6
2 5
3 4

Approach: The approach is an extension of the approach discussed here. The idea used to get all the distinct element is that first we find all the elements that add up to give sum N. Then we iterate over each of the elements and store the elements into the set. Storing the elements into set would remove all the duplicate elements, and after that we add up the sum of the elements of the set and check whether it is equal to N or not.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach` `#include ` `using` `namespace` `std;`   `/* arr[] to store all the distinct elements` `    ``index - next location in array ` `    ``num - given number ` `    ``reducedNum - reduced number */` `void` `findCombinationsUtil(``int` `arr[], ``int` `index,` `                          ``int` `n, ``int` `red_num)` `{`   `    ``// Set to store all the` `    ``// distinct elements` `    ``set<``int``> s;` `    ``int` `sum = 0;`   `    ``// Base condition` `    ``if` `(red_num < 0) {` `        ``return``;` `    ``}`   `    ``if` `(red_num == 0) {`   `        ``// Iterate over all the elements` `        ``// and store it into the set` `        ``for` `(``int` `i = 0; i < index; i++) {` `            ``s.insert(arr[i]);` `        ``}`   `        ``// Calculate the sum of all` `        ``// the elements of the set` `        ``for` `(``auto` `itr = s.begin();` `             ``itr != s.end(); itr++) {` `            ``sum = sum + (*itr);` `        ``}`   `        ``// Compare whether the sum is equal to n or not,` `        ``// if it is equal to n print the numbers` `        ``if` `(sum == n) {` `            ``for` `(``auto` `i = s.begin();` `                 ``i != s.end(); i++) {` `                ``cout << *i << ``" "``;` `            ``}` `            ``cout << endl;` `            ``return``;` `        ``}` `    ``}`   `    ``// Find previous number stored in the array` `    ``int` `prev = (index == 0) ? 1 : arr[index - 1];`   `    ``for` `(``int` `k = prev; k <= n; k++) {`   `        ``// Store all the numbers recursively` `        ``// into the arr[]` `        ``arr[index] = k;` `        ``findCombinationsUtil(arr, index + 1,` `                             ``n, red_num - k);` `    ``}` `}`   `// Function to find all the` `// distinct combinations of n` `void` `findCombinations(``int` `n)` `{` `    ``int` `a[n];` `    ``findCombinationsUtil(a, 0, n, n);` `}`   `// Driver code` `int` `main()` `{` `    ``int` `n = 7;` `    ``findCombinations(n);`   `    ``return` `0;` `}`

## Java

 `// Java implementation of the approach` `import` `java.util.*;` `class` `GFG ` `{`   `/* arr[] to store all the distinct elements` `    ``index - next location in array ` `    ``num - given number ` `    ``reducedNum - reduced number */` `static` `void` `findCombinationsUtil(``int` `arr[], ``int` `index,` `                        ``int` `n, ``int` `red_num)` `{`   `    ``// Set to store all the` `    ``// distinct elements` `    ``HashSet s = ``new` `HashSet<>();` `    ``int` `sum = ``0``;`   `    ``// Base condition` `    ``if` `(red_num < ``0``) ` `    ``{` `        ``return``;` `    ``}`   `    ``if` `(red_num == ``0``) ` `    ``{`   `        ``// Iterate over all the elements` `        ``// and store it into the set` `        ``for` `(``int` `i = ``0``; i < index; i++)` `        ``{` `            ``s.add(arr[i]);` `        ``}`   `        ``// Calculate the sum of all` `        ``// the elements of the set` `        ``for` `(Integer itr : s)` `        ``{`   `            ``sum = sum + itr;` `        ``}`   `        ``// Compare whether the sum is equal to n or not,` `        ``// if it is equal to n print the numbers` `        ``if` `(sum == n) ` `        ``{` `            ``for` `(Integer i : s) ` `            ``{` `                ``System.out.print(i+``" "``);` `            ``}` `            ``System.out.println();` `            ``return``;` `        ``}` `    ``}`   `    ``// Find previous number stored in the array` `    ``int` `prev = (index == ``0``) ? ``1` `: arr[index - ``1``];`   `    ``for` `(``int` `k = prev; k <= n; k++) ` `    ``{`   `        ``// Store all the numbers recursively` `        ``// into the arr[]` `        ``if``(index < n)` `        ``{` `            ``arr[index] = k;` `            ``findCombinationsUtil(arr, index + ``1``,` `                            ``n, red_num - k);` `            `  `        ``}` `    ``}` `}`   `// Function to find all the` `// distinct combinations of n` `static` `void` `findCombinations(``int` `n)` `{` `    ``int` `[]a = ``new` `int``[n];` `    ``findCombinationsUtil(a, ``0``, n, n);` `}`   `// Driver code` `public` `static` `void` `main(String arr[]) ` `{` `    ``int` `n = ``7``;` `    ``findCombinations(n);` `}` `}`   `/* This code contributed by PrinciRaj1992 */`

## Python3

 `# Python3 implementation of the approach`   `# arr[] to store all the distinct elements` `# index - next location in array ` `# num - given number ` `# reducedNum - reduced number` `def` `findCombinationsUtil(arr, index, n, red_num):` `    `  `    ``# Set to store all the` `    ``# distinct elements` `    ``s ``=` `set``()` `    ``sum` `=` `0`   `    ``# Base condition` `    ``if` `(red_num < ``0``):` `        ``return`   `    ``if` `(red_num ``=``=` `0``):` `        `  `        ``# Iterate over all the elements` `        ``# and store it into the set` `        ``for` `i ``in` `range``(index):` `            ``s.add(arr[i])`   `        ``# Calculate the sum of all` `        ``# the elements of the set` `        ``for` `itr ``in` `s:` `            ``sum` `=` `sum` `+` `(itr)`   `        ``# Compare whether the sum is equal to n or not,` `        ``# if it is equal to n print the numbers` `        ``if` `(``sum` `=``=` `n):` `            ``for` `i ``in` `s:` `                ``print``(i, end ``=` `" "``)` `            ``print``(``"\n"``, end ``=` `"")` `            ``return`   `    ``# Find previous number stored in the array` `    ``if` `(index ``=``=` `0``):` `        ``prev ``=` `1` `    ``else``:` `        ``prev ``=` `arr[index ``-` `1``]`   `    ``for` `k ``in` `range``(prev, n ``+` `1``, ``1``):` `        `  `        ``# Store all the numbers recursively` `        ``# into the arr[]` `        ``arr[index] ``=` `k` `        ``findCombinationsUtil(arr, index ``+` `1``, ` `                             ``n, red_num ``-` `k)`   `# Function to find all the` `# distinct combinations of n` `def` `findCombinations(n):` `    ``a ``=` `[``0` `for` `i ``in` `range``(n ``+` `1``)]` `    ``findCombinationsUtil(a, ``0``, n, n)`   `# Driver code` `if` `__name__ ``=``=` `'__main__'``:` `    ``n ``=` `7` `    ``findCombinations(n)`   `# This code is contributed by Surendra_Gangwar`

## C#

 `// C# implementation of the approach` `using` `System;` `using` `System.Collections.Generic; `   `class` `GFG ` `{`   `/* arr[] to store all the distinct elements` `    ``index - next location in array ` `    ``num - given number ` `    ``reducedNum - reduced number */` `static` `void` `findCombinationsUtil(``int` `[]arr, ``int` `index,` `                        ``int` `n, ``int` `red_num)` `{`   `    ``// Set to store all the` `    ``// distinct elements` `    ``HashSet<``int``> s = ``new` `HashSet<``int``>();` `    ``int` `sum = 0;`   `    ``// Base condition` `    ``if` `(red_num < 0) ` `    ``{` `        ``return``;` `    ``}`   `    ``if` `(red_num == 0) ` `    ``{`   `        ``// Iterate over all the elements` `        ``// and store it into the set` `        ``for` `(``int` `i = 0; i < index; i++)` `        ``{` `            ``s.Add(arr[i]);` `        ``}`   `        ``// Calculate the sum of all` `        ``// the elements of the set` `        ``foreach` `(``int` `itr ``in` `s)` `        ``{`   `            ``sum = sum + itr;` `        ``}`   `        ``// Compare whether the sum is equal to n or not,` `        ``// if it is equal to n print the numbers` `        ``if` `(sum == n) ` `        ``{` `            ``foreach` `(``int` `i ``in` `s)` `            ``{` `                ``Console.Write(i+``" "``);` `            ``}` `            ``Console.WriteLine();` `            ``return``;` `        ``}` `    ``}`   `    ``// Find previous number stored in the array` `    ``int` `prev = (index == 0) ? 1 : arr[index - 1];`   `    ``for` `(``int` `k = prev; k <= n; k++) ` `    ``{`   `        ``// Store all the numbers recursively` `        ``// into the arr[]` `        ``if``(index < n)` `        ``{` `            ``arr[index] = k;` `            ``findCombinationsUtil(arr, index + 1,` `                            ``n, red_num - k);` `            `  `        ``}` `    ``}` `}`   `// Function to find all the` `// distinct combinations of n` `static` `void` `findCombinations(``int` `n)` `{` `    ``int` `[]a = ``new` `int``[n];` `    ``findCombinationsUtil(a, 0, n, n);` `}`   `// Driver code` `public` `static` `void` `Main(String []arr) ` `{` `    ``int` `n = 7;` `    ``findCombinations(n);` `}` `}`   `// This code contributed by Rajput-Ji`

## Javascript

 ``

Output:

```1 2 4
1 6
2 5
3 4
7```

Time Complexity: O(nlogn)

Auxiliary Space: O(n)

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