1220. Count Vowels Permutation

Problem Link

Description

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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

Solution

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Python3

class Solution:
    def countVowelPermutation(self, n: int) -> int:
        a = e = i = o = u = 1
        MOD = 10 ** 9 + 7
 
        for _ in range(n - 1):
            a, e, i, o, u = e, a + i, a + e + o + u, i + u, a
            a %= MOD
            e %= MOD
            i %= MOD
            o %= MOD
            u %= MOD
        
        return (a + e + i + o + u) % MOD