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跳表实现原理 php

2026-03-13 05:51:51PHP

跳表（Skip List）简介

跳表是一种概率性的数据结构，允许快速查询、插入和删除操作，时间复杂度为O(log n)。它通过多层链表实现，每一层都是下一层的子集，类似于二叉搜索树的层级结构。

跳表的核心原理

跳表通过随机化层级分配来平衡性能。每个节点包含多个指向后续节点的指针，数量由随机算法决定。高层指针跨越更多元素，加快搜索速度。

PHP实现跳表的基本结构

class SkipListNode {
    public $value;
    public $forward = array(); // 多层指针数组

    public function __construct($value, $level) {
        $this->value = $value;
        $this->forward = array_fill(0, $level + 1, null);
    }
}

class SkipList {
    private $maxLevel;    // 最大层数
    private $level;       // 当前层数
    private $header;      // 头节点
    private $probability; // 层级增长概率

    public function __construct($maxLevel, $probability = 0.5) {
        $this->maxLevel = $maxLevel;
        $this->level = 0;
        $this->probability = $probability;
        $this->header = new SkipListNode(null, $maxLevel);
    }
}

随机层级生成方法

跳表通过随机算法决定新节点的层级，保证高层节点数量逐渐减少：

跳表实现原理 php

private function randomLevel() {
    $level = 0;
    while (mt_rand() / mt_getrandmax() < $this->probability && 
           $level < $this->maxLevel) {
        $level++;
    }
    return $level;
}

插入操作实现

插入时需要找到每层的插入位置并更新指针：

public function insert($value) {
    $update = array_fill(0, $this->maxLevel + 1, null);
    $current = $this->header;

    for ($i = $this->level; $i >= 0; $i--) {
        while ($current->forward[$i] != null && 
               $current->forward[$i]->value < $value) {
            $current = $current->forward[$i];
        }
        $update[$i] = $current;
    }

    $newLevel = $this->randomLevel();
    if ($newLevel > $this->level) {
        for ($i = $this->level + 1; $i <= $newLevel; $i++) {
            $update[$i] = $this->header;
        }
        $this->level = $newLevel;
    }

    $newNode = new SkipListNode($value, $newLevel);
    for ($i = 0; $i <= $newLevel; $i++) {
        $newNode->forward[$i] = $update[$i]->forward[$i];
        $update[$i]->forward[$i] = $newNode;
    }
}

查找操作实现

从最高层开始搜索，逐步降低层级：

跳表实现原理 php

public function search($value) {
    $current = $this->header;
    for ($i = $this->level; $i >= 0; $i--) {
        while ($current->forward[$i] != null && 
               $current->forward[$i]->value < $value) {
            $current = $current->forward[$i];
        }
    }
    $current = $current->forward[0];
    return ($current != null && $current->value == $value) ? $current : null;
}

删除操作实现

删除时需要更新所有相关层的指针：

public function delete($value) {
    $update = array_fill(0, $this->maxLevel + 1, null);
    $current = $this->header;

    for ($i = $this->level; $i >= 0; $i--) {
        while ($current->forward[$i] != null && 
               $current->forward[$i]->value < $value) {
            $current = $current->forward[$i];
        }
        $update[$i] = $current;
    }

    $current = $current->forward[0];
    if ($current != null && $current->value == $value) {
        for ($i = 0; $i <= $this->level; $i++) {
            if ($update[$i]->forward[$i] != $current) break;
            $update[$i]->forward[$i] = $current->forward[$i];
        }
        while ($this->level > 0 && 
               $this->header->forward[$this->level] == null) {
            $this->level--;
        }
        return true;
    }
    return false;
}