How to implement line segment tree in PHP

The line segment tree is a binary search tree, similar to the interval tree. It divides an interval into some unit intervals, and each unit interval corresponds to a leaf node in the line segment tree. Below, the editor will share with you how to implement line segment trees in PHP. You can refer to it if you need it.

1. Features

• is not necessarily a complete binary tree

• must be peaceful Binary tree

• Leaf nodes store actual values, and non-leaf nodes store customized content

2. Time complexity Degree

Operation	Time complexity
Query	O(logn)

3. Diagram of line segment tree

4. Code

<?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 $max)
    {
        // 如果线段区间的最小值和最小值相同，则表示为叶子结点
        if ($min == $max) {
            $this->tree[$treeIndex] = $this->array->get($max);
            return;
        }

        // 四舍五入取中间值  最大值减最小值然后除以2拿到中间值，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下面所有结点的相加值, 这里可以改为它下面结点的总和值
        $this->tree[$treeIndex] = $this->tree[$leftIndex] . &#39;+&#39; . $this->tree[$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(&#39;父结点的索引不能小于0&#39;);
        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(&#39;父结点的索引不能小于0&#39;);
        return $parentIndex * 2 + 2;
    }
}

5.Example

<?php
require_once __DIR__ . &#39;/../../vendor/autoload.php&#39;;
$array = new ArrayBundleBaseArray();
for ($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
)

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