Count Vowels Permutation — LeetCode 1220 Python Solution

The problem

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'.

Example

Input

n = 1

Output

5

Explanation

All possible strings are: "a", "e", "i" , "o" and "u".

Python solution

class Solution:
    def countVowelPermutation(self, n: int) -> int:
        f = [1] * 5
        mod = 10**9 + 7
        for _ in range(n - 1):
            g = [0] * 5
            g[0] = (f[1] + f[2] + f[4]) % mod
            g[1] = (f[0] + f[2]) % mod
            g[2] = (f[1] + f[3]) % mod
            g[3] = f[2]
            g[4] = (f[2] + f[3]) % mod
            f = g
        return sum(f) % mod

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1220. Count Vowels Permutation is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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