Combination Sum Problem

Given a set of candidate numbers (candidates) (without duplicates) and a target number (target), find all unique combinations in candidates where the candidate numbers sums to target.

The same repeated number may be chosen from candidates unlimited number of times.

Note:

  • All numbers (including target) will be positive integers.
  • The solution set must not contain duplicate combinations.

Examples

  1. Input: candidates = [2,3,6,7], target = 7,
  3. A solution set is:
  4. [
  5.   [7],
  6.   [2,2,3]
  7. ]
  1. Input: candidates = [2,3,5], target = 8,
  3. A solution set is:
  4. [
  5.   [2,2,2,2],
  6.   [2,3,3],
  7.   [3,5]
  8. ]

Explanations

Since the problem is to get all the possible results, not the best or the number of result, thus we don’t need to consider DP (dynamic programming), backtracking approach using recursion is needed to handle it.

Here is an example of decision tree for the situation when candidates = [2, 3] and target = 6:

  1.                 0
  2.               /   \
  3.            +2      +3
  4.           /   \      \
  5.        +2       +3    +3
  6.       /  \     /  \     \
  7.     +2    ✘   ✘   ✘     ✓
  8.    /  \
  9.   ✓    ✘

References