1641. Count Sorted Vowel Strings

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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

Solution

    public int countVowelStrings(int n) {
        int[][] dp = new int[n+1][6];
        for(int i = 1; i <= n; i++){
            for(int k = 1; k < 6; k++){
                //dp[i][k-1], length i and not include vowels[k]
                dp[i][k] = dp[i][k-1] + ( i > 1 ? dp[i-1][k] : 1); 
                                                  //dp[i-1][k] : combination count of s[0....i], 
                                                  //where we fixed the s[i] is the lacking vowels[k]    
                                                  // so dp[i-1][k] will be the count of including voewls[k] 
            }
            
        }
        return dp[n][5];
    }