Detailed explanation of how to implement heap sorting in PHP

Definition of heap:

#n keyword sequences Kl, K2,...,Kn are called (Heap) if and only if This sequence satisfies the following properties (heap properties for short): (1) ki<=k(2i) and ki<=k(2i+1)(1≤i≤n/2). Of course, this is a small root heap, The big root heap is replaced with the >= sign. k(i) is equivalent to the non-leaf node of the binary tree, K(2i) is the left child node, and k(2i+1) is the right child node. If the vector R[1..n] stored in this sequence is regarded as the storage structure of a complete binary tree, then the heap is essentially a complete binary tree that satisfies the following properties: the key of any non-leaf node in the tree is A keyword that is not greater than (or not less than) its left and right child nodes (if they exist).

/**
 * 调整堆
 * @param array $arr	排序数组
 * @param int $i    	待调节元素的下标
 * @param int $size 	数组大小, 准确来说是数组最大索引值加1
 */
function heapAjust(& $arr, $i, $size)
{
	$key = $arr[$i];
	// 索引从0开始
	// 左孩子节点为 2i+1, 右孩子节点为 2i+2
	for($j = 2 * $i + 1; $j < $size; $j = 2 * $j + 1) {
		if($j + 1 < $size && $arr[$j] < $arr[$j + 1])
			$j++;
		if($key > $arr[$j])
			break ;
		$arr[$i] = $arr[$j]; //调换值
		$i = $j;
	}
	$arr[$i] = $key;
}

/**
 * 堆排序
 * 时间复杂度：O(nlogn)
 * 不稳定的排序算法
 */
function heapSort(& $arr)
{
	$len = count($arr);
	
	// 构建初始大根堆
	for($i = intval($len/2); $i >= 0; $i--) {
		heapAjust($arr, $i, $len);
	}

	// 调换堆顶元素和最后一个元素
	for($j = $len - 1; $j > 0; $j--) {
		$swap = $arr[0];
		$arr[0] = $arr[$j];
		$arr[$j] = $swap;
		heapAjust($arr, 0, $j); //继续调整剩余元素为大根堆
	}
}

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