PHP heap sort implementation code

The heap can be regarded as a complete binary tree. Except for the bottom layer, every level is full. This allows the heap to be represented by an array, and each node corresponds to an element in the array.
The relationship between arrays and heaps:
Binary heaps are generally divided into two types: maximum heap and minimum heap.
Max heap: The element value of each parent node in the heap is greater than or equal to its child node (if it exists);

Minimum heap: The element value of each parent node in the heap is less than or equal to its child Node (if it exists);

What is heap sort

Heap sort (assuming the maximum heap is used) is to take out the maximum number at the top of the heap, and continue to adjust the remaining heap to the maximum heap

Heap sorting algorithm

Building a heap: Building a heap is a process of constantly adjusting the heap, starting from len/2 and going to the first node, where len is the number of elements in the heap number. The process of building a heap is a linear process. The process of adjusting the heap is always called from len/2 to 0, which is equivalent to o(h1) + o(h2) ... + o(hlen/2) where h represents the depth of the node, len /2 represents the number of nodes. This is a summation process, and the result is linear O(n).

Adjustment heap: Adjustment heap will be used in the process of building the heap, and will also be used in the heap sorting process. The idea of ​​​​utilizing is to compare node i and its child nodes left(i), right(i), and select the largest (or smallest) of the three. If the largest (smallest)

value is not node i but One of its child nodes interacts with node i and then calls the heap adjustment process. This is a recursive process. The time complexity of the process of adjusting the heap is related to the depth of the heap. It is a logn operation, because

is adjusted along the depth direction.

Heap sort: Heap sort is performed using the above two processes. The first is to build a heap based on elements. Then take out the root node of the heap (usually exchange it with the last node), continue the heap adjustment process for the first len-1 nodes, and then take out the root node again, until all Remove all nodes. The time complexity of the heap sort process is O(nlogn). Because the time complexity of building a heap is O(n) (one call); the time complexity of adjusting the heap is logn, and it takes n-1 times to adjust the heap, so the time complexity of heap sorting is O( nlogn).

Example:

<?php
// PHP 堆排序算法实现、堆排序时间复杂度分析
/**
 * 堆排序
 * @param array $arr
 */
function heap_sort(array &$arr)
{
    $count = count($arr);
    // 建堆 (下标小于或等于floor($count/2)-1的节点都是要调整的节点)
    for($i = floor($count / 2) - 1; $i >= 0; $i --)
    {
        heap_adjust($arr, $i, $count);
    }
    // 调整堆
    for($i = $count - 1; $i >= 0; $i--)
    {
        //将堆顶元素与最后一个元素交换
        swap($arr,0,$i);
        heap_adjust($arr,0,$i - 1);
    }
}
/**
 * 交换2个值
 * @param array $arr
 * @param int $a 数组下标
 * @param int $b 数组下标
 */
function swap(array &$arr, $a, $b)
{
    $temp = $arr[$a];
    $arr[$a] = $arr[$b];
    $arr[$b] = $temp;
}
/**
 * 交换2个值
 * @param array $arr
 * @param int $start 数组下标
 * @param int $end 数组下标
 */
function heap_adjust(array &$arr, $start, $end)
{
    $temp = $arr[$start];
    //沿关键字较大的孩子节点向下筛选，这里数组开始下标识0
    for($j = 2 * $start + 1; $j <= $end; $j = 2 * $j + 1)
    {
        if($j != $end && $arr[$j] < $arr[$j + 1])
        {
            $j ++;
        }
        if($temp < $arr[$j])
        {
	        //将根节点设置为子节点的较大值
	        $arr[$start] = $arr[$j];
	        $start = $j;
        }
    }
    $arr[$start] = $temp;
}
// 使用
$arr = array(8,4,2,9,3,7,1,6,5);
heap_sort($arr);
print_r($arr);

Output:

Array ([0] => 1 [1] => 2 [2] => 3 [3] = > 4 [4] => 5 [5] => 6 [6] => 7 [7] => 8 [8] => 9 )

Time complexity analysis

In general, the time complexity of heap sort is O(nlogn). Since heap sort is not sensitive to the sorting state of the original records, its best, worst, and average time complexity is O(nlogn). This is obviously far better in performance than the O(n^2) time complexity of bubbling, simple selection, and direct insertion.

Heap sorting is an unstable sorting method (the order of the same elements before and after sorting may change).

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