Leetcode #957: Prison Cells After N Days

In this guide, we solve Leetcode #957 Prison Cells After N Days in Python and focus on the core idea that makes the solution efficient.

You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.

Problem Statement

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.

Quick Facts

• Difficulty: Medium
• Premium: No
• Tags: Bit Manipulation, Array, Hash Table, Math

Intuition

Fast membership checks and value lookups are the heart of this problem, which makes a hash map the natural choice.

By storing what we have already seen (or counts/indexes), we can answer the question in one pass without backtracking.

Approach

Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.

This keeps the solution linear while remaining easy to explain in an interview setting.

Steps:

• Initialize a hash map for seen items or counts.
• Iterate through the input, querying/updating the map.
• Return the first valid result or the final computed value.

Example

Python Solution

Complexity

The time complexity is O(n). The space complexity is O(n).

Edge Cases and Pitfalls

Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.

Summary

This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.