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

## Analysis

## Solution

Backtracking

这里技巧在于每次candidates的搜索空间要减小一些，但是又因为candidates\[]元素可以重复利用，因此进入下一层递归时，用startIdx = i，而不是 startIdx = i + 1。

```java
class Solution {
    public List<List<Integer>> combinationSum(int[] candidates, int target) {
        List<List<Integer>> ans = new ArrayList<>();

        Arrays.sort(candidates);

        helper(target, 0, 0, candidates, new ArrayList<>(), ans);

        return ans;
    }

    private void helper(int target, int sum, int startIdx, int[] candidates, 
                        List<Integer> combo, List<List<Integer>> ans) {
        if (sum == target) {
            ans.add(new ArrayList<Integer>(combo));
            return;
        }
        if (sum > target) {
            return;
        }

        for (int i = startIdx; i < candidates.length; i++) {
            combo.add(candidates[i]);
            // the startIdx is not i + 1 since we can reuse same elements
            helper(target, sum + candidates[i], i, candidates, combo, ans);
            combo.remove(combo.size() - 1);
        }
    }
}
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://aaronice.gitbook.io/lintcode/backtracking/combination-sum.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.