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Hill sort is named after the designer of the algorithm, Hill. It is an improvement of Hill on the basis of insertion sort and can be said to be a special insertion sort.

Here are the properties of insertion sort:

First of all, the insertion sort algorithm is very efficient when operating on already ordered data, and can achieve the efficiency of linear sorting.

Secondly, when inserting sort, only one data can be moved in each sorting, so this sorting method is relatively inefficient.

Based on this property, the designer of Hill sort invented the Hill sort algorithm, whose basic idea is:

First, the entire sequence of records to be sorted is divided into several subsequences and sorted by direct insertion. The method of dividing the subsequence is to set an increment. When each subsequence is in order, the increment is reduced by half (divided by 2, rounded up), and the subsequence is sorted again. This is done in sequence. When the records in the entire sequence are basically in order, all records are sorted by direct insertion in sequence. At this time, the increment is reduced to 1, because direct insertion sort is very efficient when the elements are basically in order (according to the first point above, close to the best case).

Therefore, to sum up, Shell sort is a group insertion method. Because an increment is set and the increment is reduced by 1 in sequence, Shell sort is also called a descending incremental sorting algorithm.

The algorithm steps of Hill sort can be represented by the following figure:

It should be mentioned here that Shell sort is a stable sort. We can set a set of data to be sorted in the above way, and we can find that it is a stable sort.

After Hill sort is grouped by increments, insertion sort can be used to sort within the group. Of course, bubble sort, selection sort, etc. can also be used.

Here is the PHP implementation code of Hill sort

$arr = array(10,6,20,50,30,7,23,35,40,1,17);
/*
 * 首先初始化 增量  数组长度/2 取整 floor() 函数向下取整  对于增量每次循环都由 当前增量/2
 */
for($dl=floor(count($arr)/2);$dl>=1;$dl=floor($dl/2)){
    /*
     * 每次从 增量的位置开始，直到数组递增变量达到数组的长度
     */
    for($j=$dl;$j<count($arr);$j++){
        for($i=$j-$dl;$i>=0;$i-=$dl){
            if($arr[$i+$dl]<$arr[$i]){
                $temp = $arr[$i+$dl];
                $arr[$i+$dl]=$arr[$i];
                $arr[$i]=$temp;
            }
        }
    }
}

The above code is just one of the implementation methods. There are many ways to implement it. There are many ways to sort within a group. If you have any good method, please leave a message below so that we can discuss and improve together.