[LeetCode 216] Combination Sum III

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本文介绍了一个经典的回溯算法问题——组合总和III。该问题要求找出所有可能的k个数的组合，使得这些数的和等于给定的目标值n，并且只能使用1到9之间的整数，每个组合中的数字互不相同且按升序排列。文章提供了详细的解决方案及示例。

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]]

Solution:

DFS, two conditions for basic case, one is sum , second is k number

public List<List<Integer>> combinationSum3(int k, int n) {
        List<List<Integer>> result = new ArrayList<>();
        List<Integer> cur = new ArrayList<>();
        if(k<1 || n<1 || k>n) return result;
        dfs(result, cur, 0, k, n, 1);
        return result;
    }
    public void dfs(List<List<Integer>> result, List<Integer> cur, int sum, int k, int n, int level) {
        if(sum == n && k==0) {
            result.add(new ArrayList(cur));
            return;
        } else if(sum> n || k<0) return;
        for(int i=level;i<=9;i++){
            cur.add(i);
            dfs(result, cur, sum+i, k-1, n, i+1);
            cur.remove(cur.size()-1);
        }
    }