# 39 Combination Sum

## 39. [Combination Sum](https://leetcode.com/problems/combination-sum/description/)

## 1. Question

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

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

**Note:**

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

For example, given candidate set`[2, 3, 6, 7]`and target`7`,\
A solution set is:

```
[
  [7],
  [2, 2, 3]
]
```

## 2. Implementation

**(1) Backtracking**

```java
class Solution {
    public List<List<Integer>> combinationSum(int[] candidates, int target) {
        List<List<Integer>> res = new ArrayList<>();
        List<Integer> combinations = new ArrayList<>();
        getCombinations(candidates, 0, 0, target, combinations, res);
        return res;
    }

    public void getCombinations(int[] candidates, int index, int sum, int target, List<Integer> combinations, List<List<Integer>> res) {
        if (sum > target) {
            return;
        }

        if (sum == target) {
            res.add(new ArrayList<>(combinations));
            return;
        }

        for (int i = index; i < candidates.length; i++) {
            combinations.add(candidates[i]);
            getCombinations(candidates, i, sum + candidates[i], target, combinations, res);
            combinations.remove(combinations.size() - 1);
        }
    }
}
```

## 3. Time & Space Complexity

**Backtracking: 时间复杂度O(2^n), 空间复杂度O(2^n)**