LeetCode 216 Combination Sum III (DFS)

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本文解析了LeetCode上的组合总和III问题，利用深度优先搜索(DFS)算法寻找所有可能的k个数字组合，这些数字加起来等于给定的数字n。示例包括输入k=3,n=7的[[1,2,4]]输出和k=3,n=9的[[1,2,6],[1,3,5],[2,3,4]]输出。

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.

Note:

All numbers will be positive integers.
The solution set must not contain duplicate combinations.

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]]

题目链接: https://leetcode.com/problems/combination-sum-iii/

题目分析：水题，DFS的时候倒着求以减少参数个数

class Solution {
    
    public void DFS(int k, int n, int st, List<Integer> nums, List<List<Integer>> ans) {
        if (k == 0) {
            if (n == 0) {
                ans.add(new ArrayList<Integer>(nums));
            }
            return;
        }
        for (int i = st; i <= 9; i++) {
            if (n - i < 0) {
                return;
            }
            nums.add(i);
            DFS(k - 1, n - i, i + 1, nums, ans);
            nums.remove(nums.size() - 1);
        }
    }
    
    public List<List<Integer>> combinationSum3(int k, int n) {
        List<Integer> nums = new ArrayList<>();
        List<List<Integer>> ans = new ArrayList<>();
        DFS(k, n, 1, nums, ans);
        return ans;
    }
}