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:
/**
* @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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