Leetcode 216. Combination Sum III

题目

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

**Level: ** Medium

Discription:
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.

Example 1:

Input: k = 3, n = 7
Output: [[1,2,4]]

Note:

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

代码1

class Solution {
public:
    vector<vector<int>> combinationSum3(int k, int n) {
        vector<vector<int>> ret;
        vector<int> temp;
        search(n, k, 1, ret, temp);
        return ret;
    }
    void search(int n, int k, int start, vector<vector<int>> &ret, vector<int> &temp)
    {
        if(n==0 && k==0)
        {
            ret.push_back(temp);
            return;
        }
        if(n<0 || k<0 || start==10)
            return;       
        for(int i = start; i <= 9 ; i++)
        {
            if(i>n)
                return;
            temp.push_back(i);
            search(n-i, k-1, i+1, ret, temp);  
            temp.pop_back();
        }
    }
};

思考

• 算法时间复杂度，对这题来说，只有9个数字，取k个数字即可。时间复杂度正比于\(C_9^k\)。若整数个数任意，时间复杂度就是O(n!)。
• 这题用的递归的思想，递归主要包含递归体和出口，不断地调用自身，在一定条件下返回。不是很熟悉，此外对这种算法的时间复杂度分析比较麻烦，继续刷题加深理解。