跳跃列表（Skip List）详解

news2024/10/1 17:17:22

什么是跳跃列表？

跳跃列表是一种概率性的数据结构，旨在提高链表的搜索、插入和删除效率。它通过在普通链表的基础上增加多个层次，以实现更快的访问速度。跳跃列表的设计灵感来源于跳跃图（Skip Graph）和多层索引的概念，适合需要频繁进行动态数据操作的场景。

跳跃列表的基本结构

跳跃列表由多个层次的链表组成。最底层的链表包含所有的元素，而上层的链表则通过指针跳过一些节点，从而加快搜索速度。每个节点不仅存储自己的值，还持有一个指针数组，指向同层的下一个节点。

结构示例

头节点：通常存储负无穷，方便搜索。
节点：每个节点包含一个值和多个指针，指向相同或更高层的节点。

操作实现

1. 节点类

首先定义节点类，包含节点的值和指针数组。

class Node:
    def __init__(self, value, level):
        self.value = value
        self.forward = [None] * (level + 1)  # 指针数组

2. 跳跃列表类

实现跳跃列表类，包含插入、删除和搜索的方法。

import random

class SkipList:
    def __init__(self, max_level):
        self.max_level = max_level
        self.header = Node(float('-inf'), max_level)  # 头节点
        self.level = 0  # 当前层数

    def random_level(self):
        level = 0
        while random.random() < 0.5 and level < self.max_level:
            level += 1
        return level

    def insert(self, value):
        update = [None] * (self.max_level + 1)  # 保存前驱节点
        current = self.header
        
        for i in range(self.level, -1, -1):
            while current.forward[i] and current.forward[i].value < value:
                current = current.forward[i]
            update[i] = current

        current = current.forward[0]  # 最底层的下一个节点
        
        if current is None or current.value != value:
            new_level = self.random_level()  # 随机层数
            if new_level > self.level:
                for i in range(self.level + 1, new_level + 1):
                    update[i] = self.header
                self.level = new_level

            new_node = Node(value, new_level)  # 新节点
            for i in range(new_level + 1):
                new_node.forward[i] = update[i].forward[i]
                update[i].forward[i] = new_node

    def delete(self, value):
        update = [None] * (self.max_level + 1)
        current = self.header
        
        for i in range(self.level, -1, -1):
            while current.forward[i] and current.forward[i].value < value:
                current = current.forward[i]
            update[i] = current

        current = current.forward[0]

        if current and current.value == value:
            for i in range(self.level + 1):
                if update[i].forward[i] != current:
                    break
                update[i].forward[i] = current.forward[i]

            while self.level > 0 and self.header.forward[self.level] is None:
                self.level -= 1

    def search(self, value):
        current = self.header
        for i in range(self.level, -1, -1):
            while current.forward[i] and current.forward[i].value < value:
                current = current.forward[i]
        current = current.forward[0]
        return current is not None and current.value == value

示例使用

skip_list = SkipList(max_level=4)
skip_list.insert(3)
skip_list.insert(6)
skip_list.insert(7)
skip_list.insert(9)
skip_list.insert(12)
skip_list.insert(19)

print(skip_list.search(7))  # True
print(skip_list.search(15))  # False

skip_list.delete(3)
print(skip_list.search(3))  # False