Description
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.)
8 间牢房排成一排，每间牢房不是有人住就是空着。
每天，无论牢房是被占用或空置，都会根据以下规则进行更改：
如果一间牢房的两个相邻的房间都被占用或都是空的，那么该牢房就会被占用。
否则，它就会被空置。
（请注意，由于监狱中的牢房排成一行，所以行中的第一个和最后一个房间无法有两个相邻的房间。）
我们用以下方式描述监狱的当前状态：如果第 i 间牢房被占用，则 cell[i]==1，否则 cell[i]==0。
根据监狱的初始状态，在 N 天后返回监狱的状况（和上述 N 种变化）。
题目链接：https://leetcode.com/problems/prison-cells-after-n-days/
Difficulty: medium
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
分析
- updating（Solution）
参考代码
class Solution(object):
def prisonAfterNDays(self, cells, N):
def nextday(cells):
return [int(i > 0 and i < 7 and cells[i-1] == cells[i+1])
for i in xrange(8)]
seen = {}
while N > 0:
c = tuple(cells)
if c in seen:
N %= seen[c] - N
seen[c] = N
if N >= 1:
N -= 1
cells = nextday(cells)
return cells