# 1641. Count Sorted Vowel Strings

https://leetcode.com/problems/count-sorted-vowel-strings/

Given an integer n, return the number of strings of length n that consist only of vowels (a, e, i, o, u) and are lexicographically sorted. A string s is lexicographically sorted if for all valid i, s[i] is the same as or comes before s[i+1] in the alphabet.

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
``````

code

``````class Solution {
public int countVowelStrings(int n) {
return (n + 4) * (n + 3) * (n + 2) * (n + 1) / 24;
}
}
``````

code TLE

``````class Solution:
def countVowelStrings(self, n: int) -> int:
self.res = 0
def dfs(cur_start, path):
if len(path) == n:
self.res += 1
return
for i in range(cur_start, 5):
dfs(i, path + [i])
dfs(0, [])
return self.res
``````