跳表

跳表，一种链表数据结构，其增删改茶的效率能和平衡树相媲美

leecode1206

可以看上面的那个动画，动画效果很贴切。

我简单讲讲它的机制吧，每个节点不单单是一个，测试好几层，然后同一层的节点和统一节点的next 采用单链表产生联系

最核心的东西在于find

这也是为什么单链表的增删改查，花费开销最多的地方。

那它是怎么查的？
我们已经知道了跳表的结构了，最底层肯定是最全的，如果暴力最底层，那就和单链表没什么区别了。

它的这个查恰巧结合了跳表的结构，如果在上面某个层找到了节点x 的pre那么接下来的操作都好办了。
那它是怎么找到节点x 的pre呢？
从最上层，依次找该节点的next 知道找到pre 如果在这一层还没找到(因为最后一个节点的next 为nullptr)，那么会在这个节点的下一层继续找同层找next。依此类推，最后肯定能找到的。

class Skiplist {
private:
    static const int MAX_LEVEL = 10;
    struct Node{
        int val;
        std::vector<Node*> ne;
        Node(int _val, int level):val(_val), ne(level, nullptr){};
    };
    int level;
    Node* head;
    float probability;

    int randomLevel(){
        int lvl = 1;
        while((float) std::rand() / RAND_MAX < probability && lvl < MAX_LEVEL){
            lvl++;
        }
        return lvl;
    }

    void find(int t, std::vector<Node*>& ns){
        Node* cur = head;
        for(int i = level - 1; i >= 0; i--){
            while(cur->ne[i] != nullptr && cur->ne[i]->val < t){
                cur = cur->ne[i];
            }
            ns[i] = cur;
        }
    }
public:
    Skiplist() :level(MAX_LEVEL), head(new Node(-1, MAX_LEVEL)), probability(0.5){
        std::srand(std::time(0));

    }
    
    bool search(int t) {
        std::vector<Node*> ns(level, nullptr);
        find(t, ns);
        Node* target = ns[0]->ne[0];
        return target != nullptr && target->val == t;
    }
    
    void add(int t) {
        std::vector<Node*> ns(level, nullptr);
        find(t, ns);

        int nodeLevel = randomLevel();
        Node* newNode = new Node(t, nodeLevel);
        for(int i = 0; i < nodeLevel; i++){
            newNode->ne[i] = ns[i]->ne[i];
            ns[i]->ne[i] = newNode;
        }
    }
    
    bool erase(int t) {
        std::vector<Node*> ns(level, nullptr);
        find(t, ns);
        Node* target = ns[0]->ne[0];
        if(target == nullptr || target->val != t){
            return false;
        }

        for(int i = 0; i < level && ns[i]->ne[i] == target; i++){
            ns[i]->ne[i] = ns[i]->ne[i]->ne[i];
        }
        delete target;
        return true;

    }

    ~Skiplist(){
        Node* cur = head;
        while(cur){
            Node* next = cur->ne[0];
            delete cur;
            cur = next;
        }
    }
};

/**
 * Your Skiplist object will be instantiated and called as such:
 * Skiplist* obj = new Skiplist();
 * bool param_1 = obj->search(target);
 * obj->add(num);
 * bool param_3 = obj->erase(num);
 */

---

再贴一份，

#include <iostream>
#include <vector>
#include <cstdlib>
#include <ctime>

class Skiplist {
private:
    static const int MAX_LEVEL = 10;
    struct Node {
        int val;
        std::vector<Node*> ne;
        Node(int _val, int level) : val(_val), ne(level, nullptr) {}
    };

    int level;
    Node* head;
    float probability;

    int randomLevel() {
        int lvl = 1;
        while ((float)std::rand() / RAND_MAX < probability && lvl < MAX_LEVEL) {
            lvl++;
        }
        return lvl;
    }

    void find(int t, std::vector<Node*>& ns) {
        Node* cur = head;
        for (int i = level - 1; i >= 0; i--) {
            while (cur->ne[i] != nullptr && cur->ne[i]->val < t) {
                cur = cur->ne[i];
            }
            ns[i] = cur;
        }
    }

public:
    Skiplist() : level(MAX_LEVEL), head(new Node(-1, MAX_LEVEL)), probability(0.5) {
        std::srand(std::time(0));
    }

    bool search(int t) {
        std::vector<Node*> ns(level, nullptr);
        find(t, ns);
        Node* target = ns[0]->ne[0];
        return target != nullptr && target->val == t;
    }

    void add(int t) {
        std::vector<Node*> ns(level, nullptr);
        find(t, ns);
        int nodeLevel = randomLevel();
        Node* newNode = new Node(t, nodeLevel);
        for (int i = 0; i < nodeLevel; i++) {
            newNode->ne[i] = ns[i]->ne[i];
            ns[i]->ne[i] = newNode;
        }
    }

    bool erase(int t) {
        std::vector<Node*> ns(level, nullptr);
        find(t, ns);
        Node* target = ns[0]->ne[0];
        if (target == nullptr || target->val != t) {
            return false;
        }
        for (int i = 0; i < level && ns[i]->ne[i] == target; i++) {
            ns[i]->ne[i] = ns[i]->ne[i]->ne[i];
        }
        delete target;
        return true;
    }

    ~Skiplist() {
        Node* cur = head;
        while (cur) {
            Node* next = cur->ne[0];
            delete cur;
            cur = next;
        }
    }
};

int main() {
    Skiplist skiplist;
    skiplist.add(1);
    skiplist.add(2);
    skiplist.add(3);
    std::cout << skiplist.search(1) << std::endl;  // returns true
    std::cout << skiplist.search(4) << std::endl;  // returns false
    skiplist.add(4);
    std::cout << skiplist.search(4) << std::endl;  // returns true
    std::cout << skiplist.erase(4) << std::endl;   // returns true
    std::cout << skiplist.search(4) << std::endl;  // returns false
    return 0;
}

---

redis

参考