How to implement the reverse order algorithm using PHP

How to use PHP to implement the reverse-order pair algorithm

In computer science, the reverse-order pair is in a sequence. For any two elements ai and aj, if i < j and ai > aj, It is called a reverse order pair. Solving the reverse order problem is of great practical significance and has applications in fields such as optimization of sorting problems and data analysis.

In this article, we will introduce how to use the PHP programming language to implement the reverse pair algorithm in order to better understand and master this common problem.

First, we need to think about how to calculate reverse-order pairs. A simple approach is to use two nested loops, comparing all pairs of elements each time. If the condition ai > aj is met, then increment the counter of the reverse-order pair. However, the time complexity of this method is O(n^2) and is not suitable for large data sets.

Another more efficient method is to use the merge sort algorithm. The basic idea of ​​this algorithm is to decompose a sequence into smaller subsequences and then merge them into a larger sorted sequence. During the merging process, we can easily count the number of pairs in reverse order.

The following is an example code for us to use the PHP programming language to implement the reverse order algorithm:

function mergeSortCount(&$arr) {
    $temp = array();
    $count = 0;
    $length = count($arr);
    $temp = array_fill(0, $length, 0); // 创建一个临时数组用于存储合并过程中的结果

    $count = mergeSort($arr, $temp, 0, $length - 1); // 调用真正的归并排序函数

    return $count;
}

function mergeSort(&$arr, &$temp, $left, $right) {
    $count = 0;
    if ($left < $right) {
        $mid = floor(($left + $right) / 2); // 找到中间位置
        $count += mergeSort($arr, $temp, $left, $mid); // 递归地对左子数组进行排序
        $count += mergeSort($arr, $temp, $mid + 1, $right); // 递归地对右子数组进行排序
        $count += merge($arr, $temp, $left, $mid + 1, $right); // 合并左右子数组，并计算逆序对数量
    }
    return $count;
}

function merge(&$arr, &$temp, $left, $mid, $right) {
    $count = 0;
    $i = $left; // 左子数组起始位置
    $j = $mid; // 右子数组起始位置
    $k = $left; // 合并后的数组起始位置

    while ($i <= $mid - 1 && $j <= $right) {
        if ($arr[$i] <= $arr[$j]) {
            $temp[$k++] = $arr[$i++];
        } else {
            $temp[$k++] = $arr[$j++];
            $count += $mid - $i;
        }
    }

    while ($i <= $mid - 1) {
        $temp[$k++] = $arr[$i++];
    }

    while ($j <= $right) {
        $temp[$k++] = $arr[$j++];
    }

    for ($i = $left; $i <= $right; $i++) {
        $arr[$i] = $temp[$i];
    }

    return $count;
}

// 测试示例
$arr = array(3, 1, 2, 4, 5);
$count = mergeSortCount($arr);
echo "逆序对的数量：" . $count;

The above code first defines a mergeSortCount function, which accepts an array as a parameter , and returns the number of pairs in reverse order. In this function, we create a temporary array temp, initialize a counter count, and record the length of the array length.

Next, we call the mergeSort function to perform the actual merge sort. mergeSort The function accepts a left closed interval $left and a right closed interval $right as parameters. In each recursive call, it will split the array and recurse Sort the subarrays and then call the merge function to merge the subarrays and count the number of reversed pairs.

In the merge function, we use three pointers $i, $j and $k, for the left , the right subarray and the merged array are traversed. If the current element of the left subarray is less than or equal to the current element of the right subarray, put the current element of the left subarray into a temporary array, and $i and $k The pointer moves backward one position. If the current element of the right subarray is smaller than the current element of the left subarray, put the current element of the right subarray into the temporary array and move the $j and $k pointers backward Move one position. In this process, if the current element of the right subarray is smaller than the current element of the left subarray, the counter $count is added to the number of elements from the current position of the left subarray to the middle position (because the left subarray already in order).

Finally, we copy the elements in the temporary array $temp back to the original array $arr, and then return the counter $count.

In the final test example, we defined an array containing 5 integers and called the mergeSortCount function to count the number of reverse-order pairs. In this example, the number of reversed pairs is 2.

Through the above code examples, we can see that it is not difficult to implement the reverse pair algorithm using the PHP programming language. The core idea of ​​the merge sort algorithm is to decompose the sequence into smaller subsequences, implement sorting through merging operations, and calculate the number of reverse-order pairs at the same time. This is an efficient and commonly used sorting algorithm that can be applied to various practical problems.

The above is the detailed content of How to implement the reverse order algorithm using PHP. For more information, please follow other related articles on the PHP Chinese website!