Pass the pillow game – have you heard of this term? I assume you’ve played this game at least once in your life. Let’s explore the solution for the pass the pillow game using two algorithms: the first is simulating pillow passing, and the second is calculating pillow position.

In this tutorial, we’ll delve into the “Pass the Pillow” problem—a common exercise in intermediate-level interviews. The challenge revolves around passing a pillow among people standing in a line and determining the holder of the pillow after a given number of seconds. This problem tests one’s understanding of direction changes and efficient calculations. We’ll explore two distinct solutions in C# to address this problem.

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## Table of Contents

- Understand the Pass the Pillow Problem Statement
- Solution 1: Simulate Pillow Passing in C# or Simulation Approach
- Simulate Pillow Passing Explanation
- Solution 2: Calculate Pillow Position in C# or Mathematical Approach
- Mathematical Approach Explanation:
- Summarizing the Pillow Passing Solutions
- FAQs
- What is the best way to solve the “Pass the Pillow” problem in C#?
- Can I simulate pillow passing in C# for larger values of n and time?
- How does the mathematical approach handle direction changes?
- Is it possible to optimize the simulation approach further?
- Can these solutions handle edge cases where n or time are at their minimum or maximum values?

## Understand the Pass the Pillow Problem Statement

If you haven’t played this game, don’t worry. Let me explain how it works and the proper way to play it.

The problem is straightforward: there are n people standing in a line, and the first person holds a pillow. Every second, the pillow is passed to the next person. When the pillow reaches the end of the line, the direction changes, and the pillow is passed back. Given n (number of people) and time (seconds), determine who is holding the pillow after the given time.

If you’re still confused about how Pass The Pillow Game works, check out the two examples with image illustrations below.

### Example 1:

- Input: n = 4, time = 5
- Output: 2
- Explanation: Pillow passing sequence: 1 -> 2 -> 3 -> 4 -> 3 -> 2. After five seconds, person 2 holds the pillow.

### Example 2:

- Input: n = 3, time = 2
- Output: 3
- Explanation: Pillow passing sequence: 1 -> 2 -> 3. After two seconds, person 3 holds the pillow.

## Solution 1: Simulate Pillow Passing in C# or Simulation Approach

In this solution, I will use a straightforward method to write the program using a for loop. Since this solution works with linear time complexity, it is an effective way to address the pass the pillow problem.

Let’s delve into the code and see how it works.

```
public class Solution {
public int PassThePillow(int n, int time) {
int index = 1; // Initial position
int direction = 1; // 1 means forward, -1 means backward
for (int t = 0; t < time; t++) {
index += direction;
if (index == n || index == 1) {
direction *= -1; // Change direction
}
}
return index;
}
}
```

## Simulate Pillow Passing Explanation

- Initialize the pillow with the first person (index = 1).
- Use a loop to simulate each second.
- Change direction when the pillow reaches the end of the line.
- Return the index of the person holding the pillow after the given time.

By breaking down each step and providing examples, it becomes easier to understand how the simulation works and how the pillow’s position is determined after a given time.

## Solution 2: Calculate Pillow Position in C# or Mathematical Approach

This approach avoids simulating each second and instead uses arithmetic to find the solution efficiently. This method is particularly useful if you are interviewing for an advanced level position and encounter this question. By choosing this approach, you can demonstrate your strong mathematical skills in solving the pass the pillow game problem.

```
public class Solution {
public int PassThePillow(int n, int time) {
int count = time % (n - 1);
int rest = time / (n - 1);
if (rest % 2 == 0) {
return count + 1;
} else {
return n - count;
}
}
}
```

## Mathematical Approach Explanation:

- Calculate count as the remainder of time divided by (n – 1).
- Calculate rest as the quotient of time divided by (n – 1).
- Determine the direction based on whether rest is even or odd.
- Return the position based on the direction.

By breaking down each step and providing examples, it becomes easier to understand how the arithmetic works and how the pillow’s position is determined after a given time.

## Summarizing the Pillow Passing Solutions

In summary, the “Pass the Pillow Game” problem can be tackled using either a simulation approach or a mathematical approach in C#. The simulation approach involves iterating through each second, while the mathematical approach uses arithmetic to directly compute the result. Both methods are efficient given the constraints and provide a clear understanding of the problem-solving techniques in C#.

By understanding and implementing these solutions, you can confidently approach similar problems in C# programming interviews.

## FAQs

### What is the best way to solve the “Pass the Pillow” problem in C#?

The mathematical approach is more efficient as it avoids simulating each second and directly computes the result.

### Can I simulate pillow passing in C# for larger values of n and time?

Yes, but the mathematical approach is preferred for larger values due to its efficiency.

### How does the mathematical approach handle direction changes?

It calculates the direction based on the number of complete cycles of passing back and forth.

### Is it possible to optimize the simulation approach further?

The simulation approach is already straightforward, but using the mathematical approach is generally more optimal for larger inputs.

### Can these solutions handle edge cases where n or time are at their minimum or maximum values?

Yes, both solutions are designed to handle the full range of given constraints efficiently.