README.md

1220. Count Vowels Permutation

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

Solutions (Rust)

1. Dynamic Programming

impl Solution {
    pub fn count_vowel_permutation(n: i32) -> i32 {
        let mut end = vec![1 as u32; 5];

        for _ in 1..n {
            let mut tmp = Vec::new();
            tmp.push((end[1] + end[2] + end[4]) % 1_000_000_007);
            tmp.push((end[0] + end[2]) % 1_000_000_007);
            tmp.push((end[1] + end[3]) % 1_000_000_007);
            tmp.push((end[2]) % 1_000_000_007);
            tmp.push((end[2] + end[3]) % 1_000_000_007);
            end = tmp;
        }

        (end.iter().sum::<u32>() % 1_000_000_007) as i32
    }
}