1641. Count Sorted Vowel Strings

问题：

用a,e,i,o,u构成字符串，前面的字符一定是后面字符的字母序之前。

构成长度为n的字符串，有多少种方法。

Example 1:
Input: n = 1
Output: 5
Explanation: The 5 sorted strings that consist of vowels only are ["a","e","i","o","u"].

Example 2:
Input: n = 2
Output: 15
Explanation: The 15 sorted strings that consist of vowels only are
["aa","ae","ai","ao","au","ee","ei","eo","eu","ii","io","iu","oo","ou","uu"].
Note that "ea" is not a valid string since 'e' comes after 'a' in the alphabet.

Example 3:
Input: n = 33
Output: 66045
 
Constraints:
1 <= n <= 50 

　　

解法：Backtracking（回溯算法）

状态：第pos位上可选择的字符。到目前为止选择的结果为path。

选择：path最后一位之后的字符。

递归退出条件：pos==n

 

代码参考：

class Solution {
public:
    void backtrack(int& res, int n, vector<int>& path) {
        if(path.size()==n) {
            res++;
            return;
        }
        for(int i=(path.size()!=0?path.back():0); i<5; i++) {
            path.push_back(i);
            backtrack(res, n, path);
            path.pop_back();
        }
        return;
    }
    int countVowelStrings(int n) {
        int res=0;
        vector<int> path;
        backtrack(res, n, path);
        return res;
    }
};