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Given an integer n, your task is to count how many strings of length n can be formed under the following rules:
- Each character is a lower case vowel (
'a','e','i','o','u') - Each vowel
'a'may only be followed by an'e'. - Each vowel
'e'may only be followed by an'a'or an'i'. - Each vowel
'i'may not be followed by another'i'. - Each vowel
'o'may only be followed by an'i'or a'u'. - Each vowel
'u'may only be followed by an'a'.
Since the answer may be too large, return it modulo 10^9 + 7.
Example 1:
Input: n = 1 Output: 5 Explanation: All possible strings are: "a", "e", "i" , "o" and "u".
Example 2:
Input: n = 2 Output: 10 Explanation: All possible strings are: "ae", "ea", "ei", "ia", "ie", "io", "iu", "oi", "ou" and "ua".
Example 3:
Input: n = 5 Output: 68
Constraints:
1 <= n <= 2 * 10^4
给你一个整数 n，请你帮忙统计一下我们可以按下述规则形成多少个长度为 n 的字符串：
- 字符串中的每个字符都应当是小写元音字母（
'a','e','i','o','u'） - 每个元音
'a'后面都只能跟着'e' - 每个元音
'e'后面只能跟着'a'或者是'i' - 每个元音
'i'后面 不能 再跟着另一个'i' - 每个元音
'o'后面只能跟着'i'或者是'u' - 每个元音
'u'后面只能跟着'a'
由于答案可能会很大，所以请你返回 模 10^9 + 7 之后的结果。
示例 1：
输入：n = 1 输出：5 解释：所有可能的字符串分别是："a", "e", "i" , "o" 和 "u"。
示例 2：
输入：n = 2 输出：10 解释：所有可能的字符串分别是："ae", "ea", "ei", "ia", "ie", "io", "iu", "oi", "ou" 和 "ua"。
示例 3：
输入：n = 5 输出：68
提示：
1 <= n <= 2 * 10^4
Runtime: 100 ms
Memory Usage: 21.2 MB
1 class Solution { 2 func countVowelPermutation(_ n: Int) -> Int { 3 var dp:[[Int]] = [[Int]](repeating: [Int](repeating: 0, count: 5), count: n + 1) 4 let MOD:Int = 1000000007 5 for i in 0..<5 6 { 7 dp[1][i] = 1 8 } 9 for i in 1..<n 10 { 11 dp[i+1][0] = (dp[i][1] + dp[i][2] + dp[i][4]) % MOD 12 dp[i+1][1] = (dp[i][0] + dp[i][2]) % MOD 13 dp[i+1][2] = (dp[i][1] + dp[i][3]) % MOD 14 dp[i+1][3] = dp[i][2] 15 dp[i+1][4] = (dp[i][2] + dp[i][3]) % MOD 16 } 17 var res:Int = 0 18 for i in 0..<5 19 { 20 res = (res + dp[n][i]) % MOD 21 } 22 return res 23 } 24 }