跳表是一个很有意思的数据结构，它实现简单，但是性能又可以和平衡二叉搜索树差不多。
据MIT公开课上教授的讲解，它的想法和纽约地铁有异曲同工之妙，简而言之就是不断地增加“快线”，从而降低时间复杂度。
当“快线”的数量为lgn时，我们就得到了现在的快表——一个类似于平衡二叉搜索树的数据结构。
网上没有比较标准的实现方案，CLRS中也没有给出伪代码。（可能是因为他们觉得太容易实现了...）所以我给出是一个完全由我自己根据快表性质写的一个版本，如果大家有更好的实现版本欢迎和我分享。
增加层数的方案用的是抛硬币，即根据随机数来确定是否增加“快线”，这也是MIT公开课上给出的一个比较简单的实现方法。
代码如下：（仅供参考）
1 class Skiplist { 2 private : 3 struct Node { 4 int key; 5 Node * prev; 6 Node * next; 7 Node * down; 8 Node * top; 9 Node() : key(0), prev(nullptr), next(nullptr), down(nullptr), top(nullptr) {} 10 }; 11 private : 12 Node * head; 13 int level; 14 int size; 15 private : 16 void bindNewNode(Node * x, Node * p); 17 void delNode(Node * x); 18 Node * searchNode(int key); 19 public : 20 Skiplist() : head(new Node), level(1),size(0) 21 {head->key = INT_MIN; srand(static_cast<int>(time(0)));} 22 ~Skiplist() {delete head;} 23 void insert(int key); 24 void remove(int key); 25 bool search(int key) {return (searchNode(key) != nullptr);} 26 void showSkiplist(); 27 int getLevel() {return level;} 28 int getSize() {return size;} 29 }; 30 31 void Skiplist::bindNewNode(Node * x, Node * p) { 32 if (!x->next) { 33 x->next = p; 34 p->prev = x; 35 } 36 else { 37 p->next = x->next; 38 x->next->prev = p; 39 p->prev = x; 40 x->next = p; 41 } 42 } 43 44 void Skiplist::insert(int key) { 45 Node * p = new Node; 46 p->key = key; 47 48 Node * x = head; 49 while (1) { //find the prev node of p, which represents the right insert place 50 if (x->key <= key) { 51 if (x->next) 52 x = x->next; 53 else if (x->down) 54 x = x->down; 55 else break; 56 } 57 else if (x->prev->down) 58 x = x->prev->down; 59 else { 60 x = x->prev; 61 break; 62 } 63 } 64 bindNewNode(x, p); 65 while (rand() % 2) { //throw the coin, then judge whether it needs to be higher according to the results 66 Node * highp = new Node; 67 highp->key = key; 68 while (!x->top && x->prev) 69 x = x->prev; 70 if (x->top) { 71 x = x->top; 72 bindNewNode(x, highp); 73 highp->down = p; 74 p->top = highp; 75 } 76 else { //already the top, add a sentry 77 Node * top = new Node; 78 x = top; 79 top->key = INT_MIN; 80 top->down = head; 81 head->top = top; 82 head = top; 83 bindNewNode(top, highp); 84 highp->down = p; 85 p->top = highp; 86 ++level; 87 } 88 p = highp; 89 } 90 ++size; 91 } 92 93 void Skiplist::delNode(Node * x) { 94 if (!x->next) { //node x is the last one 95 if (x->prev == head && head->down) { //x is not at the bottom and x is the last one of this level 96 head = head->down; 97 head->top = nullptr; 98 delete x->prev; 99 --level; 100 } 101 else 102 x->prev->next = nullptr; 103 } 104 else { 105 x->prev->next = x->next; 106 x->next->prev = x->prev; 107 } 108 delete x; 109 } 110 111 void Skiplist::remove(int key) { 112 Node * x = searchNode(key); 113 if (x) { 114 while (x->down) { 115 Node * y = x->down; 116 delNode(x); 117 x = y; 118 } 119 delNode(x); 120 --size; 121 } 122 } 123 124 Skiplist::Node * Skiplist::searchNode(int key) { 125 Node * x = head; 126 while (1) { //find the prev node of p, which represents the right insert place 127 if (x->key == key) 128 return x; 129 else if (x->key < key) { 130 if (x->next) 131 x = x->next; 132 else if (x->down) 133 x = x->down; 134 else 135 return nullptr; 136 } 137 else if (x->prev->down) 138 x = x->prev->down; 139 else { 140 return nullptr; 141 } 142 } 143 } 144 145 void Skiplist::showSkiplist() { 146 Node * x = head, * y = head; 147 while (y) { 148 x = y; 149 while (x) { 150 if (x->prev != nullptr) 151 cout << x->key << ' '; 152 x = x->next; 153 } 154 cout << endl; 155 y = y->down; 156 } 157 }