How to implement an efficient solution to the least coin change problem in PHP using the greedy algorithm?

How to implement an efficient solution to the minimum coin change problem in PHP using the greedy algorithm?

Introduction:
In daily life, we often need to make change, especially when shopping or trading. To use as few coins as possible, the change amount should be combined using as few coins as possible. In computer programming, we can use a greedy algorithm to solve this problem to get an efficient solution. This article describes how to implement an efficient solution to the minimum coin change problem using the greedy algorithm in PHP and provides corresponding code examples.

1. Principle of Greedy Algorithm
   The greedy algorithm is an idea of ​​​​solving problems. It selects the current optimal solution at each step and finally obtains the global optimal solution. In the minimum coin change problem, the idea of ​​the greedy algorithm is to select coins with the largest denomination less than or equal to the target amount to make change each time until all coins are found.
2. Solution to the minimum coin change problem
   The following are the steps to solve the minimum coin change problem using the greedy algorithm in PHP:

Step 1: Create a function, Named minimumCoins, it accepts two parameters: amount (amount) and coin denomination array (coins).
Step 2: Define an empty result array (result) to store the coin combination for change.
Step 3: Sort the coin denomination array in descending order to select coins with larger denominations from large to small.
Step 4: Traverse the coin denomination array, and each time select coins whose current denomination is less than or equal to the target amount to make change.
Step 5: During the change process, update the target amount, add the selected coin denomination to the result array, and subtract the selected coin denomination from the target amount.
Step 6: Repeat steps 4 and 5 until the target amount is 0.
Step 7: Return the result array.

The following is a specific PHP code example:

function minimumCoins($amount, $coins) {
    $result = []; // 存储找零的硬币组合
    rsort($coins); // 降序排列硬币面额数组
    
    foreach ($coins as $coin) {
        while ($coin <= $amount) {
            $result[] = $coin; // 将当前硬币面额添加到结果数组中
            $amount -= $coin; // 更新目标金额
        }
    }
    
    return $result;
}

$amount = 47; // 目标金额
$coins = [25, 10, 5, 1]; // 硬币面额数组
$result = minimumCoins($amount, $coins);

echo "找零组合：";
foreach ($result as $coin) {
    echo $coin . " ";
}

The above code will output: "Change combination: 25 10 10 1 1", that is, 5 coins are needed to find change of 47 yuan.

3. Time complexity and space complexity
   The time complexity of using the greedy algorithm to solve the minimum coin change problem is O(n), where n is the number of denominations of coins. The space complexity is O(1) because only constant extra space is required to store the result.

Conclusion:
By using the greedy algorithm, we can efficiently solve the minimum coin change problem in PHP. This problem is very practical in daily life, and the greedy algorithm provides a simple and efficient solution. I hope the code examples and solution ideas provided in this article will be helpful to you.

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