C# Coding Test Course, Greedy Algorithm

Hello! In this lecture, we will cover greedy algorithms using C#. The greedy algorithm is a method of making the optimal choice at each moment, which is very useful for solving given problems. In this article, we will explain the concept of greedy algorithms and the process of solving a specific problem using them in detail.

Basic Concept of Greedy Algorithms

A greedy algorithm is a method of solving a problem by making the “best choice available at the moment”. This approach has the following characteristics:

  • Finding a local optimum leads to a global optimum.
  • It provides efficiency and simplicity for certain problems.
  • It does not require considering all possible cases.

However, greedy algorithms do not guarantee the optimal solution in every situation. Therefore, it is important to choose problems suitable for the algorithm. Generally, greedy algorithms are well applied in the following cases:

  • Minimum spanning tree problem
  • Shortest path problem
  • Fractional knapsack problem
  • Profit distribution and resource allocation problems

Problem Description

Problem: Coin Change Problem

The problem is to make a specific amount with the minimum number of coins. Given the types of coins and the target amount, the task is to find a way to create that amount using the least number of coins.

Input

  • Types of coins: {1 won, 5 won, 10 won, 50 won, 100 won, 500 won}
  • Target amount N (1 ≤ N ≤ 10000)

Output

  • Minimum number of coins needed to make the target amount N

Solution Process

To solve this problem, we will use the greedy algorithm approach. The steps are as follows:

  1. Start with the largest coin and choose coins to make the target amount.
  2. Use as many of the current coin as possible, then solve the remaining amount with the next largest coin.
  3. Repeat the above steps until the target amount is 0.

C# Code Implementation


using System;

class Program
{
    static void Main(string[] args)
    {
        int[] coins = { 500, 100, 50, 10, 5, 1 };
        int N = 1260;  // Target amount
        int coinCount = 0;

        for (int i = 0; i < coins.Length; i++)
        {
            if (N == 0)
                break;
            coinCount += N / coins[i];  // Add number of coins to use
            N %= coins[i];  // Update remaining amount
        }
        
        Console.WriteLine("Minimum number of coins: " + coinCount);
    }
}

The above code selects coins to make the target amount using the given types of coins and calculates the minimum number of coins. The target amount in this example is 1260 won, which is calculated as follows:

  • Use 2 of 500 won to make 1000 won
  • Use 2 of 100 won to make 1200 won
  • Use 1 of 50 won to make 1250 won
  • Use 1 of 10 won to make 1260 won

Ultimately, the minimum number of coins is 6.

Conclusion

In this lecture, we explored the concept of greedy algorithms using C# and the process of solving the coin change problem. Greedy algorithms can be powerful tools for problem-solving and can be applied to various problems. It is important to note that greedy choices may not always be the optimal choice. Therefore, it is essential to apply methods suitable for the nature of the problem.

We plan to share more algorithm problem-solving processes in the future, so please stay tuned!