Mastering the Waiter Problem in C# : Interviews Preparation

In the realm of coding interviews, problem-solving with arrays and stacks is a frequent challenge. One intriguing problem that often surfaces is the “Waiter” problem. This problem tests your understanding of prime numbers, stacks, and iterative processing. Today, we will delve into solving this problem using C# and discuss how it can be a strong component of your interview preparation toolkit.

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Waiter Problem Description

The Waiter problem involves managing a stack of numbered plates and processing them based on prime number divisibility. The goal is to perform a series of operations to reorder the plates and return the final arrangement.

Waiter Problem Breakdown

You start with a stack of plates, each marked with a number. You will use a sequence of prime numbers to determine how to divide and reorder the plates. For each prime number, you check whether each plate’s number is divisible by the prime. Plates that are divisible are moved to a new stack, while those that are not remain in the original stack. After processing with the required number of primes, you collect and return the reordered plates.

Input Format

1. An integer n, the number of plates.
2. An integer q, the number of iterations or primes to use.
3. A list of n integers representing the initial numbers on the plates.

Output Format

A sequence of numbers representing the final order of the plates after all iterations.

Constraints

1. The number of iterations q is less than or equal to the number of plates n.
2. Each plate number and prime number are positive integers.

Waiter Problem Example

Given the following input:

5 1
3 4 7 6 5

After processing with the first prime (2), the output should be:

4
6
3
7
5

Waiter Problem Solution Approach in C#

Let’s break down the Waiter Problem Solution using C#:

1. Initialize Structures: Use two stacks to manage the plates during each iteration.
2. Process Plates: For each prime number, iterate through the stack, check divisibility, and move plates accordingly.
3. Output Results: After processing all primes, output the remaining plates in the order they appear.

C# Code Implementation of Waiter Problem

Here’s a step-by-step implementation of the solution in C#:

using System;
using System.Collections.Generic;
using System.Linq;

class Waiter
{
    // Function to perform the waiter problem solution
    static List<int> ProcessPlates(List<int> plates, List<int> primes)
    {
        List<int> result = new List<int>();
        Stack<int> stack = new Stack<int>(plates);

        foreach (int prime in primes)
        {
            Stack<int> divisible = new Stack<int>();
            Stack<int> notDivisible = new Stack<int>();

            while (stack.Count > 0)
            {
                int plate = stack.Pop();
                if (plate % prime == 0)
                {
                    divisible.Push(plate);
                }
                else
                {
                    notDivisible.Push(plate);
                }
            }

            // Push divisible plates to result stack
            while (divisible.Count > 0)
            {
                result.Add(divisible.Pop());
            }

            // Update stack with not divisible plates
            stack = new Stack<int>(notDivisible);
        }

        // Add any remaining plates to result
        while (stack.Count > 0)
        {
            result.Add(stack.Pop());
        }

        return result;
    }

    static void Main(string[] args)
    {
        // Read input
        var input = Console.ReadLine().Split();
        int n = int.Parse(input[0]);
        int q = int.Parse(input[1]);

        var plates = Console.ReadLine().Split().Select(int.Parse).ToList();

        // Sample prime numbers for demonstration purposes
        List<int> primes = new List<int> { 2, 3, 5, 7 }; // Adjust based on q and actual prime list

        // Call the process function
        var result = ProcessPlates(plates, primes.Take(q).ToList());

        // Output the result
        foreach (var plate in result)
        {
            Console.WriteLine(plate);
        }
    }
}

Explanation of the Waiter Problem C# Code

1. Stack Initialization: We use a Stack to manage the plates. This structure helps in efficiently processing plates in LIFO (Last In, First Out) order.
2. Processing Loop: For each prime number, we create two stacks: divisible and notDivisible. We then process the original stack and distribute plates into these two stacks based on divisibility.
3. Result Construction: After processing each prime, the plates divisible by the prime are added to the result list. Finally, the remaining plates in the stack are also added to the result list.

Summarizing Waiter Problem Solution

Mastering the Waiter problem not only sharpens your problem-solving skills but also prepares you for similar challenges in technical interviews. Understanding how to manipulate stacks and iterate efficiently through a series of operations is key to solving such problems. With practice, you’ll be able to tackle these challenges with confidence.

Happy coding and best of luck with your interviews!