1641. Count Sorted Vowel Strings

Given an integer n, return the number of strings of length n that consist only of vowels (a, e, i, o, u) and are lexicographically sorted.

A string s is lexicographically sorted if for all valid i, s[i] is the same as or comes before s[i+1] in the alphabet.

 

Example 1:

Input: n = 1
Output: 5
Explanation: The 5 sorted strings that consist of vowels only are ["a","e","i","o","u"].

Example 2:

Input: n = 2
Output: 15
Explanation: The 15 sorted strings that consist of vowels only are
["aa","ae","ai","ao","au","ee","ei","eo","eu","ii","io","iu","oo","ou","uu"].
Note that "ea" is not a valid string since 'e' comes after 'a' in the alphabet.

Example 3:

Input: n = 33
Output: 66045

 

Constraints:

  • 1 <= n <= 50 

Rust Solution

struct Solution;

impl Solution {
    fn count_vowel_strings(n: i32) -> i32 {
        let n = n as usize;
        let mut res = 0;
        for i in 0..5 {
            res += Self::dp(i, n);
        }
        res
    }

    fn dp(i: i32, n: usize) -> i32 {
        if n == 1 {
            1
        } else {
            let mut res = 0;
            for j in 0..=i {
                res += Self::dp(j, n - 1);
            }
            res
        }
    }
}

#[test]
fn test() {
    let n = 1;
    let res = 5;
    assert_eq!(Solution::count_vowel_strings(n), res);
    let n = 2;
    let res = 15;
    assert_eq!(Solution::count_vowel_strings(n), res);
    let n = 33;
    let res = 66045;
    assert_eq!(Solution::count_vowel_strings(n), res);
}

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