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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