552. Student Attendance Record II

552. Student Attendance Record II

Hard

An attendance record for a student can be represented as a string where each character signifies whether the student was absent, late, or present on that day. The record only contains the following three characters:

• 
  'A': Absent.


• 
  'L': Late.


• 
  'P': Present.

Any student is eligible for an attendance award if they meet both of the following criteria:

• The student was absent ('A') for strictly fewer than 2 days total.


• The student was never late ('L') for 3 or more consecutive days.

Given an integer n, return the number of possible attendance records of length n that make a student eligible for an attendance award. The answer may be very large, so return it modulo 109 + 7.

Example 1:

• 
  Input: n = 2


• 
  Output: 8


• 
  Explanation: There are 8 records with length 2 that are eligible for an award:

"PP", "AP", "PA", "LP", "PL", "AL", "LA", "LL"

Only "AA" is not eligible because there are 2 absences (there need to be fewer than 2).

Example 2:

• 
  Input: n = 1


• 
  Output: 3

Example 3:

• 
  Input: n = 10101


• 
  Output: 183236316

Constraints:

• 1 <= n <= 109

Solution:

class Solution {



    /**

     * @param Integer $n

     * @return Integer

     */

    function checkRecord($n) {

        $kMod = 1000000007;

        $dp = array(array(0, 0, 0), array(0, 0, 0));

        $dp[0][0] = 1;



        while ($n-- > 0) {

            $prev = array_map(function($A) {

                return array_values($A);

            }, $dp);



            $dp[0][0] = ($prev[0][0] + $prev[0][1] + $prev[0][2]) % $kMod;



            $dp[0][1] = $prev[0][0];



            $dp[0][2] = $prev[0][1];



            $dp[1][0] = ($prev[0][0] + $prev[0][1] + $prev[0][2] + $prev[1][0] + $prev[1][1] + $prev[1][2]) % $kMod;



            $dp[1][1] = $prev[1][0];



            $dp[1][2] = $prev[1][1];

        }



        return (int)(($dp[0][0] + $dp[0][1] + $dp[0][2] + $dp[1][0] + $dp[1][1] + $dp[1][2]) % $kMod);



    }

}

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