1220. Count Vowels Permutation

Hard

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:

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

Example 2:

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

Example 3:

Input: n = 5
Output:
 68

Constraints:

• 1 <= n <= 2 * 10^4

class Solution:
    def countVowelPermutation(self, n: int) -> int:
        MOD = 10**9 + 7
        # From Question find mapping
        """
        a -> e,i,u
        e -> a,i
        i -> e,o
        o -> i
        u -> o,i
        """
        a,e,i,o,u = [1]*5
        for _ in range(n-1):
            a,e,i,o,u = e+i+u, a+i, e+o, i, o+i
        return (a+e+i+o+u) % MOD