Java Coding Test Course, Finding the Minimum Number of Coins

Many developers encounter various algorithm problems while preparing for coding tests. Among them, the “Minimum Coin Count Problem” is one of the frequently appearing problems. Today, we will take a detailed look at the theory, algorithms, and how to implement them in Java to solve this problem.

Problem Description

The problem is to minimize the number of coins needed to form a target amount given the types of coins and a target amount. You need to find a way to minimize the count of each coin used to form a specific amount.

For example, let’s assume the following situation:

• Types of coins: {1, 5, 10, 25}
• Target amount: 63

In this case, you can create 63 using two 25-cent coins, one 10-cent coin, one 5-cent coin, and three 1-cent coins, totaling 4 coins.

Input and Output

Input:

• n: Number of types of coins
• coins[n]: List of coins
• amount: Target amount

Output: Minimum number of coins required to make the target amount

If it is impossible to form the target amount with the coins, return -1.

Problem Solving Approach

This problem is a typical dynamic programming problem where we calculate the minimum number of coins for each amount and use that to calculate the next amounts.

Step-by-step Approach

1. Initialization: Prepare an array to store the results and set the initial values.
2. Using a bottom-up approach, process the types of coins through a loop.
3. When forming an amount based on each coin, calculate the minimum number of coins that can form that amount.
4. Return the minimum value for the target amount from the result array.

Java Code Implementation

Now, let’s write the Java code based on the approach mentioned above.

import java.util.Arrays;

public class CoinChange {
    public static int minCoins(int[] coins, int amount) {
        // Initialize the array to store the minimum number of coins
        int[] dp = new int[amount + 1];
        Arrays.fill(dp, amount + 1);
        dp[0] = 0; // The number of coins needed to make 0 is 0
        
        // Iterate through the coin types
        for (int coin : coins) {
            for (int x = coin; x <= amount; x++) {
                dp[x] = Math.min(dp[x], dp[x - coin] + 1);
            }
        }
        
        // Determine if it is possible and return the result
        return dp[amount] > amount ? -1 : dp[amount];
    }
    
    public static void main(String[] args) {
        int[] coins = {1, 5, 10, 25};
        int amount = 63;
        int result = minCoins(coins, amount);
        if (result != -1) {
            System.out.println("Minimum number of coins to make the target amount " + amount + ": " + result);
        } else {
            System.out.println("It's not possible to make the target amount.");
        }
    }
}
    

Algorithm Analysis

The above code uses dynamic programming to calculate the minimum number of coins needed to make the target amount. This code has the following characteristics:

• Time Complexity: O(n * m), where n is the number of types of coins and m is the target amount.
• Space Complexity: O(m), which is the space used for the array storing the number of coins.

Conclusion

As such, the problem of finding the minimum number of coins can be efficiently solved using a dynamic programming approach. In real coding tests, it is crucial to accurately understand and implement the given input types and edge cases. Additionally, adding clear comments during the coding process and clarifying the roles of each function to enhance readability is essential.

In this lecture, we have thoroughly explored how to solve the minimum coin count problem. I hope this will help you as you prepare for coding tests while tackling various algorithm problems.