# Find all possible combinations with sum K from a given number N(1 to N) with the repetition of numbers is allowed

Objective: Given two integers N and K, Write an algorithm to find possible combinations that add to K, from the numbers 1 to N.

Condition: An integer from 1 to N can be repeated any number of times in combination.

Example:

N = 5
K = 3
Output:
[1, 1, 1]
[1, 2]
[3]

N = 6
K = 5
Output:
[1, 1, 1, 1, 1]
[1, 1, 1, 2]
[1, 1, 3]
[1, 2, 2]
[1, 4]
[2, 3]
[5]

Approach: Use Recursion

1. Given N and required sum K.
3. Iterate through i = startNumber to N.
2. Put i to combinationList.
3. Make a recursive call with startNumber (to process next elements) and combinationList.
4. In tail recursion, backtrack and remove i from the combinationList to find more solutions
5. Base case: if currSum=K,  Print combinationList.

Complete Code:

Output:

Given Number: 6, required sum K: 5
[1, 1, 1, 1, 1]
[1, 1, 1, 2]
[1, 1, 3]
[1, 2, 2]
[1, 4]
[2, 3]
[5]

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