count-sorted-vowel-strings

< Previous 　　　　　　　　　　　　　　　　 Next >

1641. Count Sorted Vowel Strings (Medium)

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 

Related Topics

[Math] [Dynamic Programming] [Backtracking]

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).