Solving the Pass The Pillow Problem in C# With 2 Easy Algorithms
Tags: programming, interview, career, algorithms
Published: 2024-07-12 03:53:57

Are you familiar with the Pass the Pillow game? It's a fun activity where a pillow is passed along a line of people, and we're here to solve it using C#! This article explores two efficient methods: simulating the passing sequence and using a mathematical approach. Whether you're preparing for an interview or just curious, dive into our detailed explanations and examples.




![This illustration shows the solution to the Pass the Pillow game, detailing the positions of the pillow after a specified number of seconds and how it changes direction when reaching the last player.](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/0qpz5jlwp102rvxo299x.jpg)



## Understanding the Pass the Pillow Problem

Imagine a line of n people, starting with the first person holding a pillow. Every second, the pillow moves to the next person. When it reaches the end, it reverses direction. Given n and time (seconds), our goal is to determine who holds the pillow after that time.


![Example of Pass the Pillow Game by wikipedia](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/qmyuthtlo7h41epoy1f4.png) image by wikipedia



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## Simulation Approach

In the simulation approach, we use a straightforward method involving a loop. Starting with the first person, we simulate each second's movement and handle direction changes at the line's ends. This method is effective for understanding the sequential passing and is suitable for practical applications.

```
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;
    }
}
```

## Mathematical Approach

For those with a knack for numbers, the mathematical approach offers a streamlined solution. By leveraging arithmetic operations, we compute the pillow's position without iterating through each second. This approach showcases efficiency and is ideal for advanced interview scenarios where optimization and mathematical thinking are valued.

```
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;
        }
    }
}
```

## 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.