What is the best approach for Prison Cells After N Days with very large N?

Use a hash map to detect repeating cell patterns and compute N modulo the cycle length to jump ahead efficiently.

Can bit manipulation really speed up cell updates?

Yes, representing the 8 cells as an 8-bit integer allows state updates with shifts and XOR, reducing computation and memory.

Why do the first and last cells always become vacant?

They have only one neighbor, so the transformation rule for two neighbors cannot apply; they are set to vacant by definition.

How do I detect cycles in cell configurations?

Store each day's configuration in a hash map; when a repeat occurs, the distance between repeats gives the cycle length.

Does this approach generalize to arrays longer than 8 cells?

Yes, the simulation and cycle detection methods work for longer arrays, but bit manipulation optimization will need larger integer representations.

#957

Medium

auto_awesome数组·哈希·扫描

LeetCode 题解工作台

N 天后的牢房

监狱中 8 间牢房排成一排，每间牢房可能被占用或空置。每天，无论牢房是被占用或空置，都会根据以下规则进行变更：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。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牢房不存在两个相邻的房间。给你…

数组哈希表数学位运算

题目描述

监狱中 8 间牢房排成一排，每间牢房可能被占用或空置。

每天，无论牢房是被占用或空置，都会根据以下规则进行变更：

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。

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牢房不存在两个相邻的房间。

给你一个整数数组 cells ，用于表示牢房的初始状态：如果第 i 间牢房被占用，则 cell[i]==1，否则 cell[i]==0 。另给你一个整数 n 。

请你返回 n 天后监狱的状况（即，按上文描述进行 n 次变更）。

示例 1：

输入：cells = [0,1,0,1,1,0,0,1], n = 7
输出：[0,0,1,1,0,0,0,0]
解释：下表总结了监狱每天的状况：
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]

示例 2：

输入：cells = [1,0,0,1,0,0,1,0], n = 1000000000
输出：[0,0,1,1,1,1,1,0]

提示：

cells.length == 8
cells[i] 为 0 或 1
1 <= n <= 10⁹

lightbulb

解题思路

方法一

1

2

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Will ask if the solution handles very large N efficiently without full simulation.
question_mark
May probe about how to detect repeating patterns and cycle lengths.
question_mark
Could question the bit manipulation optimization for faster state updates.

warning

常见陷阱

外企场景

error
Forgetting to treat the first and last cells as always vacant the next day.
error
Overwriting the current day's cell values before computing neighbors, causing incorrect results.
error
Failing to detect cycles, leading to excessive computation for large N values.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Prison cells of arbitrary length instead of 8, requiring generalized neighbor rules.
arrow_right_alt
Changing the state transition rule to different neighbor conditions, affecting cycle detection.
arrow_right_alt
Return the number of days until the cells first repeat instead of final state after N days.

help

常见问题

外企场景

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