关于数据结构:8-数据结构PHP实现-线段树的实现

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

<?php
require_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
)