php implements merge sort

1. Concept

Merge sort is an efficient sorting algorithm based on the merge operation, which is a typical application of divide and conquer. Merge the ordered subsequences to obtain a completely ordered sequence, that is, order each subsequence first, and then order the subsequences. If two sorted lists are merged into one sorted list, it is called two-way merge.

2. Diagram

As shown in the figure, from bottom to top, each step needs to merge two already ordered subsequences into a large ordered array

3. Code implementation

//Merge two sorted arrays
function merge(&$arr, $low, $mid, $high){
    $temp = $arr; //Generate a temporary array, exactly the same as the original array, for later comparison
    $i = $low;
    $j = $mid+1;
    while ($low<=$mid && $j<=$high) {
        if ($temp[$low]>$temp[$j]) {
            $arr[$i++] = $temp[$j++];
        }else {
            $arr[$i++] = $temp[$low++];
        }
    }
    //if one of the arrays is left
    while ($low<=$mid) {
        $arr[$i++] = $temp[$low++];
    }
    // the case where another array is left
    while ($j<=$high) {
        $arr[$i++] = $temp[$j++];
    }
    unset($temp); // release the temporary array
}
//recursive call
function merge_sort(&$arr,$low,$high) {
    if ($low>=$high) return; //end condition
    $mid = (int)(($low+$high)/2);
    merge_sort($arr,$low,$mid);
    merge_sort($arr,$mid+1,$high);
    merge($arr,$low,$mid,$high);
}
$arr = [12,56,98,32,16,34,2,9,1];
$len = count($arr);
merge_sort($arr, 0, $len-1);
dump($arr);

4. Effect display

5. Complexity Analysis

The time complexity of merge sort is O(nlogn) and the space complexity is O(n). But it is a stable sorting algorithm, because of the pairwise merge, they are based on the comparison between adjacent elements.