LeetCode -- Combination Sum III

题目描述：

Find all possible combinations of k numbers that add up to a number n, given that only numbers from 1 to 9 can be used and each combination should be a unique set of numbers.

Ensure that numbers within the set are sorted in ascending order.

Example 1:

Input: k = 3, n = 7

Output:

[[1,2,4]]

Example 2:

Input: k = 3, n = 9

Output:

[[1,2,6], [1,3,5], [2,3,4]]

就是从1到9构成的数组{1,2,3,4,5,6,7,8,9}中，找到一种组合，包含K个元素，和为n。

思路：
是一个典型的回溯问题，也算是问题：从数组nums中找到所有和为n的组合情况的子问题。 
运用回溯模型直接解即可。 在遍历过程中，只需要收集只有k个元素的组合。

实现代码：

public class Solution {
public IList<IList<int>> CombinationSum3(int k, int n)
{
var result = new List<IList<int>>();
Find(1, n, k, new List<int>(), ref result);
return result;
}

private void Find(int start, int target, int k, IList<int> current, ref List<IList<int>> result)
{
if(current.Count > k || target < 0)
{
return;
}

if(target == 0)
{
if(current.Count == k){
result.Add(new List<int>(current));
}
//Console.WriteLine(current);
return;
}

for(var i = start; i < 10; i++)
{
current.Add(i);
Find(i + 1, target - i, k, current,ref result);
current.RemoveAt(current.Count-1);
}
}

}