统计字典序元音字符串的数目

/* 
 * Problem: Given an integer n, return the number of strings of length n that can be formed using only vowels (a, e, i, o, u) and are lexicographically sorted. 
 * 
 * Approach: 
 * This problem can be solved using dynamic programming and Java streams. We maintain a 2D array dp where dp[i][j] represents the number of valid strings of length i that end with the j-th vowel. 
 * Transition: For each length i and each vowel j, dp[i][j] is the sum of all dp[i-1][k] where k <= j. This is because if a string ends with the j-th vowel, the previous character must be a vowel less than or equal to the j-th vowel to maintain lexicographical order. 
 * Base case: For strings of length 1, dp[1][j] is 1 for all j because each vowel is a valid string of length 1. 
 */ 
 
import java.util.stream.IntStream; 
 
public class VowelStringCountStream { 
    public int countVowelStrings(int n) { 
        int[][] dp = new int[n + 1][5]; 
        IntStream.range(0, 5).forEach(j -> dp[1][j] = 1); // Base case: strings of length 1 
        IntStream.range(2, n + 1).forEach(i -> 
            IntStream.range(0, 5).forEach(j -> 
                dp[i][j] = IntStream.rangeClosed(0, j).map(k -> dp[i-1][k]).sum() 
            ) 
        ); 
        return IntStream.range(0, 5).map(j -> dp[n][j]).sum(); 
    } 
}