【leetcode刷题笔记】Combination Sum

Given a set of candidate numbers (C) 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.
• Elements in a combination (a1, a2, … , ak) must be in non-descending order. (ie, a1 ≤ a2 ≤ … ≤ ak).
• 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] 

---

题解：类似八皇后问题。每次把candidates[i]加入到numbers列表中，然后递归的搜索target-candidates[i]的组成方法。

要注意的一点是，将candidates[i]加入到numbers列表后，i前面的元素就不能再往numbers里面加了，只能再加入i本身或者i后面的元素。所以在递归函数中要有一个参数start，表明只有start本身或者以后的元素可以加入numbers中。每当递归函数参数target等于0的时候，说明找到了一组答案在numbers中，把numbers加入到answer里面就可以了。

代码如下：

public class Solution {
    private void combiDfs(int[] candidates,int target,List<List<Integer>> answer,List<Integer> numbers,int start){
        if(target == 0){
            answer.add(new ArrayList<Integer>(numbers));
            return;
        }
        for(int i = start;i < candidates.length;i++){
            if(candidates[i] > target)
                break;
            numbers.add(candidates[i]);
            combiDfs(candidates, target-candidates[i], answer, numbers,i);
            numbers.remove(numbers.size()-1);
        }
    }
    public List<List<Integer>> combinationSum(int[] candidates, int target) {
        List<List<Integer>> answer = new ArrayList<List<Integer>>();
        List<Integer> numbers = new ArrayList<Integer>();
        Arrays.sort(candidates);
        combiDfs(candidates, target, answer, numbers,0);
        
        return answer;
        
    }
}