What is the time complexity of Pass the Pillow?

The optimal solution has a time complexity of O(t).

What data structures are used to solve Pass the Pillow?

This problem uses Math, Simulation. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Pass the Pillow?

Insight 1: Recognizing the cyclical nature of the pillow passing. After the pillow reaches the end of the line and changes direction, the pattern repeats. Insight 2: Understanding that the efficient solution involves calculating the remainder after accounting for full cycles of passing the pillow.

Which companies ask LeetCode 2582. Pass the Pillow in interviews?

This problem is frequently asked at MathWorks.

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Pass the Pillow - LeetCode 2582 Solution

Pass the Pillow - Complete Solution Guide

Pass the Pillow is LeetCode problem 2582, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

There are n people standing in a line labeled from 1 to n . The first person in the line is holding a pillow initially. Every second, the person holding the pillow passes it to the next person standing in the line. Once the pillow reaches the end of the line, the direction changes, and people continue passing the pillow in the opposite direction. For example, once the pillow reaches the n th person they pass it to the n - 1 th person, then to the n - 2 th person and so on. Given the two positive

Detailed Explanation

The problem simulates passing a pillow among `n` people standing in a line. Initially, person 1 holds the pillow. Every second, the pillow is passed to the next person. When the pillow reaches either end of the line, the direction reverses. The goal is to find the index of the person holding the pillow after a given `time` (in seconds).

Solution Approach

The Python and C solutions use a simulation approach, iteratively moving the pillow according to the rules. The Java and C++ solutions leverage mathematical insight to efficiently calculate the final position without explicit simulation. They identify the length of a complete cycle and use the modulo operator to find the position after a certain number of cycles.

Step-by-Step Algorithm

Step 1: (Simulation Approach) Initialize the person holding the pillow to 1 and the direction of passing to 1 (forward).
Step 2: (Simulation Approach) Iterate `time` times, updating the person's index and reversing the direction when the pillow reaches the line's ends.
Step 3: (Simulation Approach) Return the final index of the person holding the pillow.
Step 1: (Mathematical Approach) Check if `time` is less than or equal to `n`. If so, the pillow is still within the initial forward pass, and the result is simply `time`.
Step 2: (Mathematical Approach) Calculate the length of a full cycle (forward and backward pass): `2 * (n - 1)`.
Step 3: (Mathematical Approach) Calculate the remaining time after completing full cycles: `time % cycle_length`.
Step 4: (Mathematical Approach) Determine the person's index based on the remaining time: If it's within the forward pass, the index is `n - rem`; otherwise (backward pass), it's `rem - (n - 1) + 1`.

Key Insights

Insight 1: Recognizing the cyclical nature of the pillow passing. After the pillow reaches the end of the line and changes direction, the pattern repeats.
Insight 2: Understanding that the efficient solution involves calculating the remainder after accounting for full cycles of passing the pillow.
Insight 3: Handling edge cases where `time` is less than or equal to `n` (meaning the pillow hasn't changed direction yet).

Complexity Analysis

Time Complexity: O(t)

Space Complexity: O(1)

Topics

This problem involves: Math, Simulation.

Companies

Asked at: MathWorks.

Pass the Pillow | LeetCode 2582

Easy

Math Simulation

Time: O(t)Space: O(1)

Solution Code

Available in:

class Solution {
    public int passThePillow(int n, int time) {
        if (time <= n) {
            return time;
        }
        time -= n;
        int cycle = (n - 1) * 2;
        int rem = time % cycle;
        if (rem == 0) {
            return n;
        }
        if (rem <= n - 1) {
            return n - rem;
        } else {
            return rem - (n - 1);
        }
    }
}

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Problem Info

Description

Problem 2582: Pass the Pillow - Detailed explanation and solution approaches.

Topics

Math Simulation

Companies

MathWorks

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:2582

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

7 steps

1
Step 1: (Simulation Approach) Initialize the person holding the pillow to 1 and the direction of passing to 1 (forward).
2
Step 2: (Simulation Approach) Iterate `time` times, updating the person's index and reversing the direction when the pillow reaches the line's ends.
3
Step 3: (Simulation Approach) Return the final index of the person holding the pillow.
4
Step 1: (Mathematical Approach) Check if `time` is less than or equal to `n`. If so, the pillow is still within the initial forward pass, and the result is simply `time`.
5
Step 2: (Mathematical Approach) Calculate the length of a full cycle (forward and backward pass): `2 * (n - 1)`.
6
Step 3: (Mathematical Approach) Calculate the remaining time after completing full cycles: `time % cycle_length`.
7
Step 4: (Mathematical Approach) Determine the person's index based on the remaining time: If it's within the forward pass, the index is `n - rem`; otherwise (backward pass), it's `rem - (n - 1) + 1`.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(t)

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The simulation approach takes O(t) time in the worst case. The mathematical approach takes O(1) time as it performs a constant number of arithmetic operations regardless of `n` or `time`. Both solutions use only a constant amount of extra space.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

✨

Key Insights

1Insight 1: Recognizing the cyclical nature of the pillow passing. After the pillow reaches the end of the line and changes direction, the pattern repeats.
2Insight 2: Understanding that the efficient solution involves calculating the remainder after accounting for full cycles of passing the pillow.
3Insight 3: Handling edge cases where `time` is less than or equal to `n` (meaning the pillow hasn't changed direction yet).

📚

Key Terms Explained

For Students

Edge Cases

Edge case 1: `time` is less than or equal to `n`. The mathematical solution handles this directly, while the simulation solution handles it naturally through its loop condition.
Edge case 2: `n` is 2. This is properly handled by both approaches. The simulation method will reverse direction quickly, while the mathematical method correctly accounts for the shorter cycle length.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly handling the direction change. Failing to adjust the person index or direction correctly when the pillow reaches either end of the line leads to incorrect results.

✗Common mistake 2: Off-by-one errors. These are common when calculating indices and managing array bounds, particularly when dealing with the reversal of direction.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Simulating tasks that are passed between multiple workers or processors in a cyclical pattern. This could be in a distributed system or parallel processing scenario.

🏦Real-world scenario 2: Modeling a relay race where the baton is passed between runners. The problem can be adapted to find the runner holding the baton after a specific time.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ Watch Out

Always test your solution with edge cases: empty input, single element, and boundary values.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: August 2, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 14

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 7

❓

Frequently Asked Questions

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Pass the Pillow"?

For this easy-level Math problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether simulation techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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