Combination Sum

Combination Sum

Given an array of distinct integers candidates and a target integer target, return a list of all unique combinations of candidates where the chosen numbers sum to target. You may return the combinations in any order.

The same number may be chosen from candidates an unlimited number of times. Two combinations are unique if the frequency of at least one of the chosen numbers is different.

The test cases are generated such that the number of unique combinations that sum up to target is less than 150 combinations for the given input.

Examples

Example 1:

Input: candidates = [2, 3, 6, 7], target = 7
Output: [[2, 2, 3], [7]]
Explanation:
  2 + 2 + 3 = 7 (2 is used twice)
  7 = 7
These are the only two combinations.

Example 2:

Input: candidates = [2, 3, 5], target = 8
Output: [[2, 2, 2, 2], [2, 3, 3], [3, 5]]

Example 3:

Input: candidates = [2], target = 1
Output: []
Explanation: No combination sums to 1.

Constraints

• 1 <= candidates.length <= 30
• 2 <= candidates[i] <= 40
• All elements of candidates are distinct
• 1 <= target <= 40

Expected Complexity

• Time: O(n^(t/m)) where t is the target and m is the minimum candidate value. in the worst case we branch n ways at each of t/m levels
• Space: O(t/m). recursion depth (excluding the output)