目录
概述
跳表是一种有序数据结构，它通过在每个节点维持多个指向其他节点的指针，从而达到快速访问节点的目的。
跳表基于并联的链表，其效率可比拟于二叉查找树（对于大多数操作需要O(log n)平均时间）。
插入新节点时，该节点层数随机。
更详尽的解释参见维基百科或自行google。贴两张维基百科的图片，便于大家理解。
大家有兴趣也可以去看redis的skiplist实现（zskiplist）。
SkipList定义
// Thread safety
// -------------
//
// Writes require external synchronization, most likely a mutex.
// Reads require a guarantee that the SkipList will not be destroyed
// while the read is in progress. Apart from that, reads progress
// without any internal locking or synchronization.
//
// Invariants:
//
// (1) Allocated nodes are never deleted until the SkipList is
// destroyed. This is trivially guaranteed by the code since we
// never delete any skip list nodes.
//
// (2) The contents of a Node except for the next/prev pointers are
// immutable after the Node has been linked into the SkipList.
// Only Insert() modifies the list, and it is careful to initialize
// a node and use release-stores to publish the nodes in one or
// more lists.
//
// ... prev vs. next pointer ordering ...
//线程安全:读不需要外部同步，写需要外部同步(如mutex)
class SkipList {
private:
struct Node;
public:
// Create a new SkipList object that will use "cmp" for comparing keys,
// and will allocate memory using "*arena". Objects allocated in the arena
// must remain allocated for the lifetime of the skiplist object.
//skiplist用Arena做内存管理
//Comparator用来比较key，自行定义，例子可参考skiplist_test.cc
explicit SkipList(Comparator cmp, Arena* arena);
// Insert key into the list.
// REQUIRES: nothing that compares equal to key is currently in the list.
void Insert(const Key& key);
// Returns true iff an entry that compares equal to key is in the list.
bool Contains(const Key& key) const;
// Iteration over the contents of a skip list
//迭代器，在此省去
class Iterator {
.....
};
private:
//最高12层
//《efficetive C++》尽量不要使用宏定义定义常量，取代的办法是const常量和enum类型
enum { kMaxHeight = 12 };
// Immutable after construction
//const 构造后不可变
Comparator const compare_;
Arena* const arena_; // Arena used for allocations of nodes
Node* const head_;
// Modified only by Insert(). Read racily by readers, but stale
// values are ok.
port::AtomicPointer max_height_; // Height of the entire list
inline int GetMaxHeight() const {
return static_cast<int>(
reinterpret_cast<intptr_t>(max_height_.NoBarrier_Load()));
}
// Read/written only by Insert().
//随机数生成器
Random rnd_;
Node* NewNode(const Key& key, int height);
int RandomHeight();
bool Equal(const Key& a, const Key& b) const { return (compare_(a, b) == 0); }
// Return true if key is greater than the data stored in "n"
bool KeyIsAfterNode(const Key& key, Node* n) const;
// Return the earliest node that comes at or after key.
// Return NULL if there is no such node.
//
// If prev is non-NULL, fills prev[level] with pointer to previous
// node at "level" for every level in [0..max_height_-1].
Node* FindGreaterOrEqual(const Key& key, Node** prev) const;
// Return the latest node with a key < key.
// Return head_ if there is no such node.
Node* FindLessThan(const Key& key) const;
// Return the last node in the list.
// Return head_ if list is empty.
Node* FindLast() const;
// No copying allowed
SkipList(const SkipList&);
void operator=(const SkipList&);
};
节点定义
// Implementation details follow
template<typename Key, class Comparator>
struct SkipList<Key,Comparator>::Node {
explicit Node(const Key& k) : key(k) { }
Key const key;
// Accessors/mutators for links. Wrapped in methods so we can
// add the appropriate barriers as necessary.
Node* Next(int n) {
assert(n >= 0);
// Use an 'acquire load' so that we observe a fully initialized
// version of the returned Node.
return reinterpret_cast<Node*>(next_[n].Acquire_Load());
}
void SetNext(int n, Node* x) {
assert(n >= 0);
// Use a 'release store' so that anybody who reads through this
// pointer observes a fully initialized version of the inserted node.
next_[n].Release_Store(x);
}
// No-barrier variants that can be safely used in a few locations.
Node* NoBarrier_Next(int n) {
assert(n >= 0);
return reinterpret_cast<Node*>(next_[n].NoBarrier_Load());
}
void NoBarrier_SetNext(int n, Node* x) {
assert(n >= 0);
next_[n].NoBarrier_Store(x);
}
private:
// Array of length equal to the node height. next_[0] is lowest level link.
//节点的层指针数组(弹性数组)
port::AtomicPointer next_[1];
};
创建新节点
template<typename Key, class Comparator>
typename SkipList<Key,Comparator>::Node*
SkipList<Key,Comparator>::NewNode(const Key& key, int height) {
char* mem = arena_->AllocateAligned(
sizeof(Node) + sizeof(port::AtomicPointer) * (height - 1));
//定位构造
//placement new就是在用户指定的内存位置上构建新的对象，
//这个构建过程不需要额外分配内存，只需要调用对象的构造函数即可
return new (mem) Node(key);
}
placement new（定位构造）的用法可参考手册，也可参考以下网址：
http://blog.csdn.net/songthin/article/details/1703966
节点插入
template<typename Key, class Comparator>
int SkipList<Key,Comparator>::RandomHeight() {
// Increase height with probability 1 in kBranching
static const unsigned int kBranching = 4;
int height = 1;
while (height < kMaxHeight && ((rnd_.Next() % kBranching) == 0)) { height++; } assert(height > 0);
assert(height <= kMaxHeight);
return height;
}
template<typename Key, class Comparator>
bool SkipList<Key,Comparator>::KeyIsAfterNode(const Key& key, Node* n) const {
// NULL n is considered infinite
return (n != NULL) && (compare_(n->key, key) < 0);
}
template<typename Key, class Comparator>
typename SkipList<Key,Comparator>::Node* SkipList<Key,Comparator>::FindGreaterOrEqual(const Key& key, Node** prev)
const {
Node* x = head_;
int level = GetMaxHeight() - 1;
while (true) {
Node* next = x->Next(level);
if (KeyIsAfterNode(key, next)) {
// Keep searching in this list
x = next;
} else {
if (prev != NULL) prev[level] = x;
if (level == 0) {
return next;
} else {
// Switch to next list
level--;
}
}
}
}
template<typename Key, class Comparator>
void SkipList<Key,Comparator>::Insert(const Key& key) {
// TODO(opt): We can use a barrier-free variant of FindGreaterOrEqual()
// here since Insert() is externally synchronized.
//TODO:因为插入需要外部同步，所以此处可以不用内存栅栏
Node* prev[kMaxHeight];
//找插入位置，prev记录每一层的前一指针
Node* x = FindGreaterOrEqual(key, prev);
// Our data structure does not allow duplicate insertion
assert(x == NULL || !Equal(key, x->key));
//随机插入节点层数，底层数为上层数的4倍(0层3/4 1层(1/4)*(3/4) ....)
int height = RandomHeight();
if (height > GetMaxHeight()) {
for (int i = GetMaxHeight(); i < height; i++) {
prev[i] = head_;
}
//fprintf(stderr, "Change height from %d to %d\n", max_height_, height);
// It is ok to mutate max_height_ without any synchronization
// with concurrent readers. A concurrent reader that observes
// the new value of max_height_ will see either the old value of
// new level pointers from head_ (NULL), or a new value set in
// the loop below. In the former case the reader will
// immediately drop to the next level since NULL sorts after all
// keys. In the latter case the reader will use the new node.
max_height_.NoBarrier_Store(reinterpret_cast<void*>(height));
}
x = NewNode(key, height);
for (int i = 0; i < height; i++) { // NoBarrier_SetNext() suffices since we will add a barrier when // we publish a pointer to "x" in prev[i]. x->NoBarrier_SetNext(i, prev[i]->NoBarrier_Next(i));
prev[i]->SetNext(i, x);
}
}
读redis的源码其random level函数写的也蛮漂亮
#define ZSKIPLIST_MAXLEVEL 32 /* Should be enough for 2^32 elements */
#define ZSKIPLIST_P 0.25 /* Skiplist P = 1/4 */
/* Returns a random level for the new skiplist node we are going to create.
* The return value of this function is between 1 and ZSKIPLIST_MAXLEVEL
* (both inclusive), with a powerlaw-alike distribution where higher
* levels are less likely to be returned. */
int zslRandomLevel(void) {
int level = 1;
while ((random()&0xFFFF) < (ZSKIPLIST_P * 0xFFFF))
level += 1;
return (level<ZSKIPLIST_MAXLEVEL) ? level : ZSKIPLIST_MAXLEVEL;
}
OK,插入有了（其中包含查询步骤），查询就不必写了。
卿若有意，可读redis的skiplist（zskiplist），其skiplist的定义
typedef struct zskiplistNode {
robj *obj;
double score;
struct zskiplistNode *backward;
struct zskiplistLevel {
struct zskiplistNode *forward;
unsigned int span;
} level[];
} zskiplistNode;
typedef struct zskiplist {
struct zskiplistNode *header, *tail;
unsigned long length;
int level;
} zskiplist;
redis的level不仅有前进指针，还有一个步长（unsigned int span），这使得根据rank（排名）做操作时更加简单效率。
参考
《redis设计与实现》