Count Sorted Vowel Strings

给 (a, e, i, o, u) 5个元音, 求满足字典序下n个字母的组合.

dp[i][j] = 前i个字符自称的j个元音的总数.

dp[1][i] = [1...5]

dp[i][1] = 1 (a, e, i, o, u)

dp[i][j] = dp[i][j - 1] + dp[i - 1][j]

class Solution {
    public int countVowelStrings(int n) {
        int[][] dp = new int[n + 1][6];
        for(int i = 1; i <= 5; i++) {
            dp[1][i] = i;
        }
        for(int i = 1; i <= n; i++) {
            dp[i][1] = 1;
        }
        for(int i = 2; i <= n; i++) {
            for(int j = 2; j <= 5; j++) {
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
            }
        }
        return dp[n][5];
    }
}