浅析SkipList跳跃表原理及代码实现

//定义key和value的类型
typedef int KeyType;
typedef int ValueType;
    
//定义结点
typedef struct nodeStructure* Node;
struct nodeStructure{
    KeyType key;
    ValueType value;
    Node forward[1];
};
    
//定义跳跃表
typedef struct listStructure* List;
struct listStructure{
    int level;
    Node header;
};

void SkipList::NewList(){
    //设置NIL结点
    NewNodeWithLevel(0, NIL_);
    NIL_->key = 0x7fffffff;
    //设置链表List
    list_ = (List)malloc(sizeof(listStructure));
    list_->level = 0;
    //设置头结点
    NewNodeWithLevel(MAX_LEVEL,list_->header);
    for(int i = 0; i < MAX_LEVEL; ++i){
        list_->header->forward[i] = NIL_;
    }
    //设置链表元素的数目
    size_ = 0;
}

void SkipList::NewNodeWithLevel(const int& level,
                                Node& node){
    //新结点空间大小
    int total_size = sizeof(nodeStructure) + level*sizeof(Node);
    //申请空间
    node = (Node)malloc(total_size);
    assert(node != NULL);
}

bool SkipList::Search(const KeyType& key,
                      ValueType& value){
    Node x = list_->header;
    int i;
    for(i = list_->level; i >= 0; --i){
        while(x->forward[i]->key < key){
            x = x->forward[i];
        }
    }
    x = x->forward[0];
    if(x->key == key){
        value = x->value;
        return true;
    }else{
        return false;
    }
}

bool SkipList::Insert(const KeyType& key,
                      const ValueType& value){
    Node update[MAX_LEVEL];
    int i;
    Node x = list_->header;
    //寻找key所要插入的位置
    //保存大于key的位置信息
    for(i = list_->level; i >= 0; --i){
        while(x->forward[i]->key < key){
            x = x->forward[i];
        }

        update[i] = x;
    }

    x = x->forward[0];
    //如果key已经存在
    if(x->key == key){
        x->value = value;
        return false;
    }else{
        //随机生成新结点的层数
        int level = RandomLevel();
        //为了节省空间，采用比当前最大层数加1的策略
        if(level > list_->level){
            level = ++list_->level;
            update[level] = list_->header;
        }
        //申请新的结点
        Node newNode;
        NewNodeWithLevel(level, newNode);
        newNode->key = key;
        newNode->value = value;

        //调整forward指针
        for(int i = level; i >= 0; --i){
            x = update[i];
            newNode->forward[i] = x->forward[i];
            x->forward[i] = newNode;
        }
        
        //更新元素数目
        ++size_;

        return true;
    }
}

bool SkipList::Delete(const KeyType& key,
                      ValueType& value){
    Node update[MAX_LEVEL];
    int i;
    Node x = list_->header;
    //寻找要删除的结点
    for(i = list_->level; i >= 0; --i){
        while(x->forward[i]->key < key){
            x = x->forward[i];
        }

        update[i] = x;
    }

    x = x->forward[0];
    //结点不存在
    if(x->key != key){
        return false;
    }else{
        value = x->value;
        //调整指针
        for(i = 0; i <= list_->level; ++i){
            if(update[i]->forward[i] != x)
                break;
            update[i]->forward[i] = x->forward[i];
        }
        //删除结点
        free(x);
        //更新level的值，有可能会变化，造成空间的浪费
        while(list_->level > 0
            && list_->header->forward[list_->level] == NIL_){
            --list_->level;
        }
        
        //更新链表元素数目
        --size_;

        return true;
    }
}

// Copyright (c) 2011 The LevelDB Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file. See the AUTHORS file for names of contributors.


#include <stdint.h>

//typedef unsigned int           uint32_t;
//typedef unsigned long long     uint64_t;

// A very simple random number generator.  Not especially good at
// generating truly random bits, but good enough for our needs in this
// package.
class Random {
 private:
  uint32_t seed_;
 public:
  explicit Random(uint32_t s) : seed_(s & 0x7fffffffu) {
    // Avoid bad seeds.
    if (seed_ == 0 || seed_ == 2147483647L) {
      seed_ = 1;
    }
  }
  uint32_t Next() {
    static const uint32_t M = 2147483647L;   // 2^31-1
    static const uint64_t A = 16807;  // bits 14, 8, 7, 5, 2, 1, 0
    // We are computing
    //       seed_ = (seed_ * A) % M,    where M = 2^31-1
    //
    // seed_ must not be zero or M, or else all subsequent computed values
    // will be zero or M respectively.  For all other values, seed_ will end
    // up cycling through every number in [1,M-1]
    uint64_t product = seed_ * A;

    // Compute (product % M) using the fact that ((x << 31) % M) == x.
    seed_ = static_cast<uint32_t>((product >> 31) + (product & M));
    // The first reduction may overflow by 1 bit, so we may need to
    // repeat.  mod == M is not possible; using > allows the faster
    // sign-bit-based test.
    if (seed_ > M) {
      seed_ -= M;
    }
    return seed_;
  }
  // Returns a uniformly distributed value in the range [0..n-1]
  // REQUIRES: n > 0
  uint32_t Uniform(int n) { return (Next() % n); }

  // Randomly returns true ~"1/n" of the time, and false otherwise.
  // REQUIRES: n > 0
  bool OneIn(int n) { return (Next() % n) == 0; }

  // Skewed: pick "base" uniformly from range [0,max_log] and then
  // return "base" random bits.  The effect is to pick a number in the
  // range [0,2^max_log-1] with exponential bias towards smaller numbers.
  uint32_t Skewed(int max_log) {
    return Uniform(1 << Uniform(max_log + 1));
  }
};

void SkipList::FreeList(){
    Node p = list_->header;
    Node q;
    while(p != NIL_){
        q = p->forward[0];
        free(p);
        p = q;
    }
    free(p);
    free(list_);
}