1641. Count Sorted Vowel Strings
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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
Hints
Hint 1
For each character, its possible values will depend on the value of its previous character, because it needs to be not smaller than it.
Hint 2
Think backtracking. Build a recursive function count(n, last_character) that counts the number of valid strings of length n and whose first characters are not less than last_character.
Hint 3
In this recursive function, iterate on the possible characters for the first character, which will be all the vowels not less than last_character, and for each possible value c, increase the answer by count(n-1, c).