# Question

Formatted question description: https://leetcode.ca/all/1641.html

 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


# Algorithm

Use dynamic programming. Create a 2D array dp of n rows and 5 columns, where dp[i][j] represents the number of sorted vowel strings of length i + 1 with the first j + 1 vowel letters. Initially, dp[i] = i + 1 for 0 <= i < 5, and dp[i] = 1 for 0 <= i < n. For 1 <= i < n and 1 <= j < 5, there is dp[i][j] = dp[i - 1][j] + dp[i][j - 1]. Finally, return dp[n - 1].

Or, use math, the combination result.

# Code

Java

Java

class Solution {
public int countVowelStrings(int n) {
int[][] dp = new int[n];
for (int i = 0; i < 5; i++)
dp[i] = i + 1;
for (int i = 1; i < n; i++) {
dp[i] = 1;
for (int j = 1; j < 5; j++)
dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
}
return dp[n - 1];
}
}