cpp-flashcards/org/study_deck_02/dsa/2-d-dynamic-programming/1220-count-vowels-permutation.org

#+PROPERTY: STUDY_DECK_02
* TODO 1220. Count Vowels Permutation :hard:
:PROPERTIES:
:NEETCODE: [[file:../../roadmap.org::*1220. Count Vowels Permutation][1220. Count Vowels Permutation]]
:END:

Given an integer ~n~, your task is to count how many strings of length ~n~ can be formed under the following rules:

 - Each character is a lower case vowel (~'a'~, ~'e'~, ~'i'~, ~'o'~, ~'u'~)

 - Each vowel ~'a'~ may only be followed by an ~'e'~.

 - Each vowel ~'e'~ may only be followed by an ~'a'~ or an ~'i'~.

 - Each vowel ~'i'~ *may not* be followed by another ~'i'~.

 - Each vowel ~'o'~ may only be followed by an ~'i'~ or a ~'u'~.

 - Each vowel ~'u'~ may only be followed by an ~'a'~.

Since the answer may be too large, return it modulo ~10^9 + 7~.

*Example 1:*


#+begin_src
Input: n = 1
Output: 5
Explanation: All possible strings are: "a", "e", "i" , "o" and "u".
#+end_src


*Example 2:*


#+begin_src
Input: n = 2
Output: 10
Explanation: All possible strings are: "ae", "ea", "ei", "ia", "ie", "io", "iu", "oi", "ou" and "ua".
#+end_src


*Example 3: *


#+begin_src
Input: n = 5
Output: 68
#+end_src


*Constraints:*

 - ~1 <= n <= 2 * 10^4~

** TODO Approach
Write your approach here.

** TODO Python
#+begin_src python
class Solution:
    def countVowelPermutation(self, n: int) -> int:
#+end_src

** TODO C++
#+begin_src cpp
class Solution {
public:
    int countVowelPermutation(int n) {
        
    }
};
#+end_src