跳表的C语言实现

跳表（Skip List）是一种基于链表的动态数据结构，用于实现高效的查找、插入和删除操作。它通过引入多级索引来加速查找过程，类似于多级索引的有序链表。跳表的平均时间复杂度为 O(logn)，在某些场景下可以替代平衡树。

以下是跳表的基本实现思路和一个简单的 C 语言实现示例。

1. 跳表的基本概念

节点结构：每个节点包含一个值和多个指向不同层级的指针。
层级：每个节点的层级是随机的，通常通过抛硬币的方式决定。层级越高，索引的作用越强。
头节点：跳表的入口，包含指向各级索引的指针。
尾节点（可选）：用于快速判断是否到达链表末尾。

2. 跳表的关键操作

查找：从最高层开始，逐层向下查找，直到找到目标值或到达底层。
插入：找到插入位置后，随机生成节点的层级，并更新指针。
删除：找到目标节点后，更新相关指针，并释放节点。

3. C语言实现

以下是一个简单的跳表实现，支持查找、插入和删除操作：

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

#define MAX_LEVEL 16  // 最大层级
#define PROBABILITY 0.5  // 随机层级的概率

typedef struct SkipListNode {
    int value;
    struct SkipListNode* next[MAX_LEVEL];
} SkipListNode;

typedef struct SkipList {
    SkipListNode* head;
    int level;
} SkipList;

// 创建新节点
SkipListNode* createNode(int value, int level) {
    SkipListNode* node = (SkipListNode*)malloc(sizeof(SkipListNode));
    node->value = value;
    for (int i = 0; i < level; i++) {
        node->next[i] = NULL;
    }
    return node;
}

// 创建跳表
SkipList* createSkipList() {
    SkipList* list = (SkipList*)malloc(sizeof(SkipList));
    list->head = createNode(-1, MAX_LEVEL);  // 创建头节点
    list->level = 0;
    return list;
}

// 随机生成层级
int randomLevel() {
    int level = 1;
    while (rand() / (double)RAND_MAX < PROBABILITY && level < MAX_LEVEL) {
        level++;
    }
    return level;
}

// 查找操作
SkipListNode* search(SkipList* list, int value) {
    SkipListNode* current = list->head;
    for (int i = list->level - 1; i >= 0; i--) {
        while (current->next[i] != NULL && current->next[i]->value < value) {
            current = current->next[i];
        }
    }
    current = current->next[0];
    if (current != NULL && current->value == value) {
        return current;
    }
    return NULL;
}

// 插入操作
void insert(SkipList* list, int value) {
    int level = randomLevel();
    SkipListNode* newNode = createNode(value, level);
    SkipListNode* update[MAX_LEVEL] = {NULL};

    SkipListNode* current = list->head;
    for (int i = list->level - 1; i >= 0; i--) {
        while (current->next[i] != NULL && current->next[i]->value < value) {
            current = current->next[i];
        }
        update[i] = current;
    }

    for (int i = 0; i < level; i++) {
        newNode->next[i] = update[i]->next[i];
        update[i]->next[i] = newNode;
    }

    if (level > list->level) {
        for (int i = list->level; i < level; i++) {
            list->head->next[i] = newNode;
        }
        list->level = level;
    }
}

// 删除操作
void deleteNode(SkipList* list, int value) {
    SkipListNode* update[MAX_LEVEL] = {NULL};

    SkipListNode* current = list->head;
    for (int i = list->level - 1; i >= 0; i--) {
        while (current->next[i] != NULL && current->next[i]->value < value) {
            current = current->next[i];
        }
        update[i] = current;
    }

    current = current->next[0];
    if (current != NULL && current->value == value) {
        for (int i = 0; i < list->level; i++) {
            if (update[i]->next[i] != current) {
                break;
            }
            update[i]->next[i] = current->next[i];
        }
        free(current);

        while (list->level > 1 && list->head->next[list->level - 1] == NULL) {
            list->level--;
        }
    }
}

// 打印跳表
void printSkipList(SkipList* list) {
    for (int i = list->level - 1; i >= 0; i--) {
        SkipListNode* current = list->head->next[i];
        printf("Level %d: ", i);
        while (current != NULL) {
            printf("%d ", current->value);
            current = current->next[i];
        }
        printf("\n");
    }
}

int main() {
    srand(time(NULL));
    SkipList* list = createSkipList();
    insert(list, 3);
    insert(list, 6);
    insert(list, 7);
    insert(list, 9);
    insert(list, 12);
    insert(list, 19);
    insert(list, 17);
    insert(list, 26);
    insert(list, 21);
    insert(list, 25);

    printf("Skip List:\n");
    printSkipList(list);

    SkipListNode* result = search(list, 19);
    if (result != NULL) {
        printf("Found %d in the skip list.\n", result->value);
    } else {
        printf("Value not found.\n");
    }

    deleteNode(list, 19);
    printf("Skip List after deletion:\n");
    printSkipList(list);

    return 0;
}