Examples to explain how to use php to implement Hill sorting

1. What is Hill sorting

Hill sorting, also called reduced incremental sorting, is a high-efficiency implementation of insertion sorting. Since insertion sorting is inefficient when processing large-scale data, Hill sorting expands the interval of insertion sorting by dividing the sequence and performing insertion sorting separately, thereby reducing the number of moving elements and improving sorting efficiency.

2. The basic idea of ​​Hill sorting

The sorting idea used by Hill sorting can be understood as inserting and sorting multiple subsequences separated by h. Each time a smaller h is used to divide, and after each subsequence is inserted and sorted, the value of h is changed and the sequence is re-divided until finally h=1, and the sorting is completed.

3. PHP implements Hill sorting

The following is the PHP code implementation of Hill sorting:

function shellSort($arr) {
    $length = count($arr);
    // 初始时gap最大，按照插入排序的方式进行排序
    for ($gap = floor($length / 2); $gap > 0; $gap = floor($gap / 2)) {
        for ($i = $gap; $i < $length; $i++) {
            $j = $i;
            while ($j - $gap >= 0 && $arr[$j] < $arr[$j - $gap]) {
                // 插入排序
                $tmp = $arr[$j];
                $arr[$j] = $arr[$j - $gap];
                $arr[$j - $gap] = $tmp;
                $j -= $gap;
            }
        }
    }
    return $arr;
}

The above code uses two layers of loops, the first layer of loops Use the $gap variable to divide and sort the array, and the second level loop compares and moves elements. The time complexity of the two-level loop is $O(n^2)$.

4. Time complexity of Hill sorting

Under different sequences, the time complexity of Hill sorting is also different. The time complexity of Hill sorting is $O(n logn)$ in the best case, $O(n^2)$ in the worst case, and $O(n log^2n)$ in the average case. .

5. Advantages and disadvantages of Hill sorting

Advantages:

• Hill sorting is a highly efficient sorting algorithm. Compared with selection sorting and risk sorting, Bubble sort is faster.
• The exchange distance in Hill sorting is shorter, which reduces the number of element comparisons and the number of element movements.

Disadvantages:

• The time complexity of Hill sorting is difficult to analyze accurately.
• The code implementation of Hill sorting is more complicated than other sorting algorithms.

6. Summary

Hill sorting is an efficient version of insertion sorting. By introducing the concept of interval, it reduces the number of element comparisons and moves, thereby improving sorting efficiency. The time complexity of Hill sorting is affected by the sequence, and it is difficult to conduct precise analysis. Therefore, in actual encoding, it is necessary to select an appropriate interval sequence according to the size and characteristics of the data to achieve the optimal sorting effect.

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