# 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[0][i] = i + 1`

for `0 <= i < 5`

, and `dp[i][0] = 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][4]`

.

Or, use math, the combination result.

# Code

Java

Java

```
class Solution {
public int countVowelStrings(int n) {
int[][] dp = new int[n][5];
for (int i = 0; i < 5; i++)
dp[0][i] = i + 1;
for (int i = 1; i < n; i++) {
dp[i][0] = 1;
for (int j = 1; j < 5; j++)
dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
}
return dp[n - 1][4];
}
}
```