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This article follows up on Insertion Sort (Concepts) and presents the implementation steps and code for direct insertion sort. Since the Concepts section already has a large number of illustrations, it would be a bit long-winded to provide further illustrations in this article, so the steps and code are listed directly here.

Implementation steps:

1. Treat the first element of the first sequence to be sorted as an ordered sequence, and the second element to the last element as an unsorted sequence.
2. Scan the unsorted sequence from beginning to end once, and insert each scanned element into the appropriate position of the ordered sequence (one thing to note here is that if there is an element in the ordered sequence that is equal to the element to be inserted, the element to be inserted will be found after this element. This insertion sort is stable. If it is inserted in front of this element, then this insertion sort is unstable.

Implementation code (PHP code):

The first implementation code is to traverse backwards from the first element, find the corresponding position, and then move and insert the element. The code is as follows

$arr1 = array(
15,77,23,43,90,87,68,32,11,22,33,99,88,66,44,113,
224,765,980,159,456,7,998,451,96,0,673,82,91,100
);
for($i=1;$i<count($arr1);$i++){
    $p = $arr1[$i];
    for($j=0;$j<$i;$j++){
        if($arr1[$j]>$p){
            break;
        }
    }
    for($k=$i-1;$k>=$j;$k--){
        $arr1[$k+1] = $arr1[$k];
    }
    $arr1[$j] = $p;
}

The second implementation code is to traverse forward from the previous element of the current element to be sorted (that is, the last element of the ordered sequence), find the corresponding position, and then move and insert the element. The code is as follows

$arr2 = array(
15,77,23,43,90,87,68,32,11,22,33,99,88,66,44,113,
224,765,980,159,456,7,998,451,96,0,673,82,91,100
);
for($i=1;$i<count($arr2);$i++){
    $p = $arr2[$i];
    for($j=$i-1;$j>=0;$j--){
        if($arr2[$j]>$p){
            $arr2[$j+1] = $arr2[$j];
        }else{
            break;
        }
    }
    $arr2[$j+1] = $p;
}

The above two codes can both implement insertion sorting. However, after writing the codes, we tested the two codes and found that the second method runs faster than the first method by printing the running time. The following are the running times of each method after running 5 times (Note: the above is the first case, and the following is the second case)

The above time comparison actually means that the same algorithm will take different time if implemented in different ways. The test data above are just simple numbers, and the speed is only in microseconds. There is no obvious difference for us, but when applied to projects, for complex and large data, a good implementation can save us a lot of time. So even in the stage of learning principles, we should optimize the code as much as possible.

For direct insertion sort, whether it is the first implementation or the second implementation, their time complexity is the same, both are O(n²)