"""
LC957 - Prison cell after N days

There are 8 prison cells in a row, and each cell is either occupied or vacant.

Each day, whether the cell is occupied or vacant changes according to the following rules:

    If a cell has two adjacent neighbors that are both occupied or both vacant, then the cell becomes occupied.
    Otherwise, it becomes vacant.

(Note that because the prison is a row, the first and the last cells in the row can't have two adjacent neighbors.)

We describe the current state of the prison in the following way: cells[i] == 1 if the i-th cell is occupied, else
cells[i] == 0.

Given the initial state of the prison, return the state of the prison after N days (and N such changes described above.)

Example 1:

Input: cells = [0,1,0,1,1,0,0,1], N = 7
Output: [0,0,1,1,0,0,0,0]
Explanation:
The following table summarizes the state of the prison on each day:
Day 0: [0, 1, 0, 1, 1, 0, 0, 1]
Day 1: [0, 1, 1, 0, 0, 0, 0, 0]
Day 2: [0, 0, 0, 0, 1, 1, 1, 0]
Day 3: [0, 1, 1, 0, 0, 1, 0, 0]
Day 4: [0, 0, 0, 0, 0, 1, 0, 0]
Day 5: [0, 1, 1, 1, 0, 1, 0, 0]
Day 6: [0, 0, 1, 0, 1, 1, 0, 0]
Day 7: [0, 0, 1, 1, 0, 0, 0, 0]

Example 2:

Input: cells = [1,0,0,1,0,0,1,0], N = 1000000000
Output: [0,0,1,1,1,1,1,0]

Note:

    cells.length == 8
    cells[i] is in {0, 1}
    1 <= N <= 10^9
"""


class Solution(object):
    def transition(self, cells):
        """
        Make a single transition
        """
        return [0] + [1 if cells[i - 1] == cells[i + 1] else 0 for i in range(1, 7)] + [0]

    def prisonAfterNDays(self, cells, N):
        """
        :type cells: List[int]
        :type N: int
        :rtype: List[int]
        """
        # the blind approach to this problem is to record all past cells in a dictionary. Once a loop is found, we
        # just take the modulus of N with the loop count, and do that many iterations (hopefully much fewer than N)
        #
        # however, the loop has been empirically shown to be a max of 14, so we just mod N by 14 and do that many
        # transitions

        N %= 14
        if N == 0:
            N = 14

        for i in range(N):
            cells = self.transition(cells)

        return cells