> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/recursion-and-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]
]
```

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

    public static void backTrack(List<List<Integer>> ans, ArrayList<Integer> temp, int[] candidates, int target,
            int start) {
        if (target <= 0) {
            if (target == 0) {
                ans.add(new ArrayList<>(temp));
            }
            return;
        }
        for (int i = start; i < candidates.length; i++) {
            temp.add(candidates[i]);
            backTrack(ans, temp, candidates, target - candidates[i], i);
            temp.remove(temp.size() - 1);
        }
    }
}
```