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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