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]
]

The below algorithm beats 100% of all the leetcode answers in C#.

 1 public class Solution {
 2     public IList<IList<int>> CombinationSum(int[] candidates, int target) {
 3         //
 
 idea 1: brute force, generate all possible combination which has 2^N possibilities and check whether 
 4         // each combination‘s sum equals target. This doesn‘t work though as one element can be used multi times.
 5         
 6         // idea 2: backtracking, potential optimazition, sort the candidates first. Memorization probably will help
 
 7         // but it‘s a little bit hard to check dup output
 8         var result = new List<IList<int>>();
 9         
10         Array.Sort(candidates);
11         if (candidates.Length == 0 || target < candidates[0]) return result;
12         
13         DFS(candidates, target, 0, new List<int>(), result);
14         
15         return result;
16     }
17     
18     private void DFS(int[] candidates, int target, int sum, IList<int> res, IList<IList<int>> result)
19     {
20         if (target < sum) return;
21         if (target == sum)
22         {
23             result.Add(new List<int>(res));
24             return;
25         }
26         
27         for (int i = 0; i < candidates.Length; i++)
28         {
29             if (sum + candidates[i] > target)
30             {
31                 break;
32             }
33             
34             // to make sure the output result is always sorted to avoid duplicate
35             if (res.Count > 0 && candidates[i] < res[res.Count - 1]) continue;
36             
37             res.Add(candidates[i]);
38             DFS(candidates, target, sum + candidates[i], res, result);
39             res.RemoveAt(res.Count - 1);
40         }
41     }
42 }

Leetcode 39: Combination Sum