1. 特色
不肯定是齐全二叉树
肯定是温和二叉树
叶子结点存储的是理论的值，非叶子结点存的是自定义的内容
2. 工夫复杂度
3. 线段树的图解
4. 代码
<?php/** * content: 线段树（区间树） * create: 2020-11-12 */namespace HeapBundle;use ArrayBundle\BaseArray;class SegmentTreeHeap{ /** * 传入的数组对象 * @var BaseArray */ protected $array; /** * 数组 * @var array */ protected $tree = []; public function __construct(BaseArray $array) { $this->array = $array; $this->build(0, 0, $this->array->getSize() - 1); } /** * 构建线段树 * @param int $treeIndex * @param int $min * @param int $max * @throws \Exception */ public function build(int $treeIndex, int $min, int $max) { // 如果线段区间的最小值和最小值雷同，则示意为叶子结点 if ($min == $max) { $this->tree[$treeIndex] = $this->array->get($max); return; } // 四舍五入取两头值 最大值减最小值而后除以2拿到两头值，并加上最小值 $mid = floor(($max - $min) / 2) + $min; // 获取左儿子的索引值，并递归往下构建 $leftIndex = $this->leftChildIndex($treeIndex); $this->build($leftIndex, $min, $mid); // 获取右儿子的索引值，并递归往下构建 $rightIndex = $this->rightChildIndex($treeIndex); $this->build($rightIndex, $mid + 1, $max); // 非叶子结点的值保留的是它上面所有结点的相加值, 这里能够改为它上面结点的总和值 $this->tree[$treeIndex] = $this->tree[$leftIndex] . '+' . $this->tree[$rightIndex]; } /** * 打印线段树 */ public function varDump() { ksort($this->tree); print_r($this->tree); } /** * 获取线段树的长度 * @return int */ public function getSize(): int { return count($this->tree); } /** * 获取左儿子索引 * @param int $parentIndex * @return int * @throws \Exception */ public function leftChildIndex(int $parentIndex): int { if ($parentIndex < 0) throw new \Exception('父结点的索引不能小于0'); return $parentIndex * 2 + 1; } /** * 获取右儿子索引 * @param int $parentIndex * @return int * @throws \Exception */ public function rightChildIndex(int $parentIndex): int { if ($parentIndex < 0) throw new \Exception('父结点的索引不能小于0'); return $parentIndex * 2 + 2; }}
5.示例
<?phprequire_once __DIR__ . '/../../vendor/autoload.php';$array = new ArrayBundleBaseArray();for ($i = 0; $i < 10; $i++) { $array->addLast($i + 10);}$heap = new HeapBundleSegmentTreeHeap($array);$heap->varDump();
Array( [0] => 10+11+12+13+14+15+16+17+18+19 [1] => 10+11+12+13+14 [2] => 15+16+17+18+19 [3] => 10+11+12 [4] => 13+14 [5] => 15+16+17 [6] => 18+19 [7] => 10+11 [8] => 12 [9] => 13 [10] => 14 [11] => 15+16 [12] => 17 [13] => 18 [14] => 19 [15] => 10 [16] => 11 [23] => 15 [24] => 16)