LeetCode 216. Combination Sum III

原题链接在这里：https://leetcode.com/problems/combination-sum-iii/

题目：

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]]

题解：

与Combination Sum II相似，不同的是中不是所有元素相加，只是k个元素相加。

所以在把item的copy 加到res前需要同时满足item.size() == k 和 target == 0两个条件. candidates里没有相同元素，所以res中不可能有duplicates. 因此没有检验去重的步骤。

Time Complexity: exponenetial.

Space: O(1). stack space最多9层.

AC Java:

class Solution {
    public List<List<Integer>> combinationSum3(int k, int n) {
        List<List<Integer>> res = new ArrayList<List<Integer>>();
        if(k<=0 || n<=0){
            return res;
        }
        
        dfs(k, n, 1, new ArrayList<Integer>(), res);
        return res;
    }
    
    private void dfs(int k, int target, int start, List<Integer> item, List<List<Integer>> res){
        if(target == 0 && item.size() == k){
            res.add(new ArrayList<Integer>(item));
            return;
        }
        
        if(target < 0 || item.size() > k){
            return;
        }
        
        for(int i = start; i<=9; i++){
            item.add(i);
            dfs(k, target-i, i+1, item, res);
            item.remove(item.size()-1);
        }
    }
}

AC Python:

class Solution:
    def combinationSum3(self, k: int, n: int) -> List[List[int]]:
        res = []
        self.dfs(k, n, 1, [], res)
        return res
    
    def dfs(self, k: int, n: int, start: int, item: List[int], res: List[List[int]]) -> None:
        if n == 0 and len(item) == k:
            res.append(item[:])
            return
        
        if(n < 0 or len(item) > k):
            return
        
        for i in range(start, 10):
            item.append(i)
            self.dfs(k, n - i, i + 1, item, res)
            item.pop()

跟上Combination Sum IV.