python coding test course, finding the minimum number of coins

Hello! Today we will cover one of the frequently asked questions in Python coding tests, which is the problem of finding the minimum number of coins. This problem is particularly helpful in understanding algorithms and greedy problems and can be applied in various situations.

Problem Description

You have various coins, each with a finite quantity. You need to use the minimum number of coins to provide change for a given amount. Given the types of coins and the target amount as input, write a program that outputs the minimum number of coins needed.

Input Format

  • In the first line, the number of coin types n (1 ≤ n ≤ 100) and the target amount k (1 ≤ k ≤ 10000) are given.
  • In the second line, the values of n coins are given, separated by spaces. Each coin value is different and between 1 and 10,000.

Output Format

Output the minimum number of coins needed to make the target amount.

Example Input

    3 11
    1 2 5

Example Output

    3

Solution Approach

This problem can be solved using a greedy algorithm. A greedy algorithm is a method of solving a problem by choosing the option that seems best at the moment, aiming to find an optimal solution overall. In this case, we can start by using the highest value coins as much as possible.

Step-by-Step Approach

  1. Start from the highest coin value and calculate the maximum number of that coin that can be used.
  2. Subtract the value of the used coins from the remaining amount and move to the next highest coin.
  3. Repeat this process until the target amount is reduced to 0.

Code Implementation

Now, let’s implement the Python code based on the above approach. We will write code to count the number of coins based on the given input.

    def min_coins(n, k, coins):
        # Sort coins in descending order.
        coins.sort(reverse=True)
        
        count = 0
        for coin in coins:
            # Calculate the maximum number of current coins that can be used.
            if k == 0:
                break
            count += k // coin  # How many of this coin can be used
            k %= coin  # Update the remaining amount
        
        return count

    # Input
    n, k = map(int, input().split())
    coins = list(map(int, input().split()))

    # Output result
    print(min_coins(n, k, coins))

Execution Result Analysis

The above code demonstrates the process of using the minimum number of coins based on the entered coin values and target amount. For example, if the coin types are [1, 2, 5] and the target amount is 11, the balance is reduced through the following process:

  • Use 2 coins of 5: remaining 1 (count = 2)
  • Use 1 coin of 1: remaining 0 (count = 3)

Time Complexity

The time complexity of this algorithm is O(n). Here, n is the number of given coins, and sorting the coin list takes O(n log n). Therefore, the overall time complexity can be considered O(n log n).

Precautions

One thing to be cautious of when finding the minimum number of coins is when there is no guarantee that coins will always exist. For example, if it is not possible to create the target amount, appropriate messages can be output through exception handling.

Conclusion

I hope this problem has helped enhance your understanding of greedy algorithms. Practice the algorithm by trying various combinations of coins and target amounts. Since this is a common problem in coding tests, it will be very beneficial to be familiar with it.

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