> For the complete documentation index, see [llms.txt](https://shuati.gitbook.io/crack-lintcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://shuati.gitbook.io/crack-lintcode/linkedin/combination-sum.md).

# Combination Sum

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.

**Example 1:**

```
Input: candidates = [2,3,6,7], target = 7,
A solution set is:
[
  [7],
  [2,2,3]
]
```

**Example 2:**

```
Input: candidates = [2,3,5], target = 8,
A solution set is:
[
  [2,2,2,2],
  [2,3,3],
  [3,5]
]
```

```java
class Solution {
    public List<List<Integer>> combinationSum(int[] candidates, int target) {
        List<List<Integer>> res = new ArrayList<>();
        
        if(candidates == null || candidates.length == 0)
            return res;
        // Arrays.sort(candidates);
        backtracking(candidates,res,new ArrayList<>(),target,0);
        
        return res;
    }
    
    public void backtracking(int[] candidates, List<List<Integer>> res, List<Integer> list, int remain,int start){
        if(remain < 0)
            return;
        
        if(remain == 0){
            res.add(new ArrayList<>(list));
            return;
        }
        
        for(int i = start; i < candidates.length; i++){
            list.add(candidates[i]);
            backtracking(candidates,res,list,remain-candidates[i],i);
            
            list.remove(list.size()-1);
        }
            
    }
}
```

因为都是搜索题，所以搜索的时间复杂度是O(解的个数 \* 每个解生成的复杂度)\
combination sum 这个题目因为有target存在所以并不知道解的个数，但是解的个数最多是子集的个数2^n, 产生每个解的最坏复杂度n，所以我们可以粗略的估计时间复杂度是O(2^n \* n)

![](/files/-LO1FqRP1VrYHHBm-tzv)

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