leetcode - 1641. Count Sorted Vowel Strings

Description

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 

Solution

For every iteration,
combinations that end with a => combinations that end with a
combinations that end with e => combinations that end with a + combinations that end with e
combinations that end with i => combinations that end with a + combinations that end with e + combinations that end with i
…

so keep records of the number of combinations that end with a,e,i,o,u and iterate.

Time complexity: $o(n)$
Space complexity: $o(1)$

Code

class Solution:
    def countVowelStrings(self, n: int) -> int:
        dp = [1,1,1,1,1]
        while n > 1:
            dp[1] += dp[0]
            dp[2] += dp[1]
            dp[3] += dp[2]
            dp[4] += dp[3]
            n -= 1
        return sum(dp)