2022-08-07 Daily-Challenge

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In: DailyChallenge

Today I have done leetcode's August LeetCoding Challenge with cpp.

August LeetCoding Challenge 7

Description

Count Vowels Permutation

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

Solution

auto speedup = [](){
  cin.tie(nullptr);
  cout.tie(nullptr);
  ios::sync_with_stdio(false);
  return 0;
}();
int dp[2][5];
const int MOD = 1e9 + 7;
class Solution {
public:
  int countVowelPermutation(int n) {
    for(int i = 0; i < 5; ++i) dp[1][i] = 1;
    for(int l = 2; l <= n; ++l) {
      int parity = l & 1;
      dp[parity][3] = dp[!parity][2];
      dp[parity][4] = (dp[!parity][2] + dp[!parity][3]) % MOD;
      dp[parity][1] = (dp[!parity][2] + dp[!parity][0]) % MOD;
      dp[parity][0] = (dp[!parity][1] + dp[!parity][4]) % MOD;
      dp[parity][0] = (dp[parity][0] + dp[!parity][2]) % MOD;
      dp[parity][2] = (dp[!parity][3] + dp[!parity][1]) % MOD;
    }

    int answer = 0;
    for(int v = 0; v < 5; ++v) {
      answer += dp[n & 1][v];
      answer %= MOD;
    }
    return answer;
  }
};

// Accepted
// 43/43 cases passed (0 ms)
// Your runtime beats 100 % of cpp submissions
// Your memory usage beats 93.61 % of cpp submissions (5.9 MB)
Algorithm