SkipList（跳錶）數據結構是用於Memtable，Immutable Memtable表中，對於此二表的作用點此查看Memtable作用。
Memtable是內存中的表，用於存儲插入的KV數據。SkipList的作用就是解決KV的快速插入和查詢。
一、介紹
SkipList使用空間換時間的設計思路，通過構建多級索引來提高查詢的效率，實現了基於鏈表的“二分查找”。跳錶是一種動態數據結構，支持快速的插入、刪除、查找操作，時間複雜度都是 O(logn)。
skiplist實現了基於鏈表的“二分查找”，其通過空間換時間的設計，利用構建多級所以來提高查詢效率。
複雜度如下：
- 插入、刪除、查找的時間複雜度都是O(logn)；
- 空間複雜度是O(n)。
二、結構
沿用網上一張圖，Leveldb實現的SkipLisp初始化時head部分是12個指針點。
三、源碼分析
Node
這裏用到了內存序的相關知識，有不清楚的可以百度查下，這裏就不介紹了。
// Implementation details follow
template <typename Key, class Comparator>
struct SkipList<Key, Comparator>::Node {
explicit Node(const Key& k) : key(k) {}
Key const key;
<!有內存屏障操作>
// 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 next_[n].load(std::memory_order_acquire);
}
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].store(x, std::memory_order_release);
}
<!無內存屏障操作，相比於無內存屏障操作，性能損耗更小>
// No-barrier variants that can be safely used in a few locations.
Node* NoBarrier_Next(int n) {
assert(n >= 0);
return next_[n].load(std::memory_order_relaxed);
}
void NoBarrier_SetNext(int n, Node* x) {
assert(n >= 0);
next_[n].store(x, std::memory_order_relaxed);
}
private:
// Array of length equal to the node height. next_[0] is lowest level link.
<!
*當前節點的每個等級的下一個結點
*第2級 N1 N2
*第1級 N1 N2
*如果N1是本節點，則next_[x] 保存的是N2
*
*next_[0]就是原始鏈表。
>
std::atomic<Node*> next_[1]; //大小是一個Node
};
SkipList
<!內存管理>
class Arena;
template <typename Key, class Comparator>
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.
explicit SkipList(Comparator cmp, Arena* arena);
SkipList(const SkipList&) = delete;
SkipList& operator=(const SkipList&) = delete;
// 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;
<!迭代器，英文註釋可直接看>
// Iteration over the contents of a skip list
class Iterator {
public:
// Initialize an iterator over the specified list.
// The returned iterator is not valid.
explicit Iterator(const SkipList* list);
// Returns true iff the iterator is positioned at a valid node.
bool Valid() const;
// Returns the key at the current position.
// REQUIRES: Valid()
const Key& key() const;
// Advances to the next position.
// REQUIRES: Valid()
void Next();
// Advances to the previous position.
// REQUIRES: Valid()
void Prev();
// Advance to the first entry with a key >= target
void Seek(const Key& target);
// Position at the first entry in list.
// Final state of iterator is Valid() iff list is not empty.
void SeekToFirst();
// Position at the last entry in list.
// Final state of iterator is Valid() iff list is not empty.
void SeekToLast();
private:
<!當前迭代器關聯的SkipList>
const SkipList* list_;
<!當前迭代器所指向的值>
Node* node_;
// Intentionally copyable
};
private:
<!跳錶的層數，最底層是第0層>
enum { kMaxHeight = 12 };
<!獲取當前跳錶是多少層>
inline int GetMaxHeight() const {
return max_height_.load(std::memory_order_relaxed);
}
<!新建一個節點>
Node* NewNode(const Key& key, int height);
<!返回需要插入值的隨機高度，比方說4，
那第0~3層都要插入對應的Node。
>
int RandomHeight();
<!等值判斷>
bool Equal(const Key& a, const Key& b) const { return (compare_(a, b) == 0); }
<!當前key是否在節點n後面>
// 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 nullptr 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;
// Immutable after construction
Comparator const compare_;
Arena* const arena_; // Arena used for allocations of nodes
<!跳錶第0層的頭指針，指向第一個元素>
Node* const head_;
// Modified only by Insert(). Read racily by readers, but stale
// values are ok.
std::atomic<int> max_height_; // Height of the entire list
<!用於產生隨機數>
// Read/written only by Insert().
Random rnd_;
};
<!產生一個新節點，值是key，height表示此key存在於多少層，
最底層是第0層，所以直接new,剩下的層就是（height - 1）個指針指示。
此處通過Arena獲取內對齊的內存，提升CPU訪問速度。
>
template <typename Key, class Comparator>
typename SkipList<Key, Comparator>::Node* SkipList<Key, Comparator>::NewNode(
const Key& key, int height) {
<!一個實際節點值，其它都是指針。>
char* const node_memory = arena_->AllocateAligned(
sizeof(Node) + sizeof(std::atomic<Node*>) * (height - 1));
<!在已經分配好內存的node_memory上構造一個Node對象>
return new (node_memory) Node(key);
}
<!迭代器構造，迭代器都是基於第0層進行操作的>
template <typename Key, class Comparator>
inline SkipList<Key, Comparator>::Iterator::Iterator(const SkipList* list) {
list_ = list;
node_ = nullptr;
}
<!當前迭代器指向節點是否有效>
template <typename Key, class Comparator>
inline bool SkipList<Key, Comparator>::Iterator::Valid() const {
return node_ != nullptr;
}
template <typename Key, class Comparator>
inline const Key& SkipList<Key, Comparator>::Iterator::key() const {
assert(Valid());
return node_->key;
}
template <typename Key, class Comparator>
inline void SkipList<Key, Comparator>::Iterator::Next() {
assert(Valid());
node_ = node_->Next(0); //迭代器都是操作的第0層的數據
}
<!當前節點的前一個節點>
template <typename Key, class Comparator>
inline void SkipList<Key, Comparator>::Iterator::Prev() {
// Instead of using explicit "prev" links, we just search for the
// last node that falls before key.
assert(Valid());
node_ = list_->FindLessThan(node_->key);
if (node_ == list_->head_) {
node_ = nullptr;
}
}
<!定位到大於or等於此target的位置>
template <typename Key, class Comparator>
inline void SkipList<Key, Comparator>::Iterator::Seek(const Key& target) {
node_ = list_->FindGreaterOrEqual(target, nullptr);
}
<!定位到第0層的一個節點值>
template <typename Key, class Comparator>
inline void SkipList<Key, Comparator>::Iterator::SeekToFirst() {
node_ = list_->head_->Next(0); //迭代器操作的都是第0層，head是一個無值，只是一個指針。
}
template <typename Key, class Comparator>
inline void SkipList<Key, Comparator>::Iterator::SeekToLast() {
node_ = list_->FindLast();
if (node_ == list_->head_) {
node_ = nullptr;
}
}
<!生成要隨機插入的層高，比如4，那就是[0...3]都要插入>
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;
}
<!判斷key是否在節點node之後>
template <typename Key, class Comparator>
bool SkipList<Key, Comparator>::KeyIsAfterNode(const Key& key, Node* n) const {
// null n is considered infinite
return (n != nullptr) && (compare_(n->key, key) < 0);
}
<!找到大於或等於key的節點，從最高層開始。
1、如果未找到對應的Node，這返回的next是null。
2、如果prev不爲null，則將每一層最近小於key的node
地址保存起來。
>
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 != nullptr) prev[level] = x;
if (level == 0) {
return next;
} else {
// Switch to next list
level--;
}
}
}
}
<!查找最近小於key的node，從最高層開始查起，
如果未找到，返回head_。
>
template <typename Key, class Comparator>
typename SkipList<Key, Comparator>::Node*
SkipList<Key, Comparator>::FindLessThan(const Key& key) const {
Node* x = head_;
int level = GetMaxHeight() - 1;
while (true) {
assert(x == head_ || compare_(x->key, key) < 0);
Node* next = x->Next(level);
if (next == nullptr || compare_(next->key, key) >= 0) {
if (level == 0) {
return x;
} else {
// Switch to next list
level--;
}
} else {
x = next;
}
}
}
<!從最高層開始，定位到最後一個元素>
template <typename Key, class Comparator>
typename SkipList<Key, Comparator>::Node* SkipList<Key, Comparator>::FindLast()
const {
Node* x = head_;
int level = GetMaxHeight() - 1;
while (true) {
Node* next = x->Next(level);
if (next == nullptr) {
if (level == 0) {
return x;
} else {
// Switch to next list
level--;
}
} else {
x = next;
}
}
}
<!SkipList構造，及一些值的初始化>
template <typename Key, class Comparator>
SkipList<Key, Comparator>::SkipList(Comparator cmp, Arena* arena)
: compare_(cmp),
arena_(arena),
head_(NewNode(0 /* any key will do */, kMaxHeight)),
max_height_(1),
rnd_(0xdeadbeef) {
for (int i = 0; i < kMaxHeight; i++) {
head_->SetNext(i, nullptr);
}
}
<!插入key>
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.
<!找到大於等於key的節點x，並記錄沒一層最近不大於key的節點>
Node* prev[kMaxHeight];
Node* x = FindGreaterOrEqual(key, prev);
<!要麼未找到這樣節點，如果找到了也可能和插入的值相等>
// Our data structure does not allow duplicate insertion
assert(x == nullptr || !Equal(key, x->key));
<!產生需要隨機插入的高度>
int height = RandomHeight();
if (height > GetMaxHeight()) {
<!如果高度超過現有的，則超過部分的前置節點賦值爲head_>
for (int i = GetMaxHeight(); i < height; i++) {
prev[i] = head_;
}
// 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_ (nullptr), or a new value set in
// the loop below. In the former case the reader will
// immediately drop to the next level since nullptr sorts after all
// keys. In the latter case the reader will use the new node.
max_height_.store(height, std::memory_order_relaxed);
}
<!生存一個新節點>
x = NewNode(key, height);
<!以下插入過程就是移動指針，從這裏我們也明白了爲什麼
要有prev[kMaxHeight]了。
>
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);
}
}
<!跳錶中是否存在此key>
template <typename Key, class Comparator>
bool SkipList<Key, Comparator>::Contains(const Key& key) const {
Node* x = FindGreaterOrEqual(key, nullptr);
if (x != nullptr && Equal(key, x->key)) {
return true;
} else {
return false;
}
}
四、總結
- SkipList的所有操作都是從上到下去執行。
- 隨機層數爲什麼是%4？因爲第x層節點數是第x-1層的1/4，換一個角度每個元素出現在每層的概率就是1/4，這樣通過%4來決定節點一共出現在多少層。
- leveldb用模板方式實現的SkipList，這樣更通用。
- leveldb的SkipList未實現del操作是因爲元素刪除也是插入，刪除某個Key的Value在 Memtable 內是作爲插入一條記錄實施的，但是會打上一個 Key 的刪除標記，真正的刪除操作是Lazy的，會在以後的 Compaction 過程中去掉這個KV。
- leveldb爲什麼使用SkipList來實現數據的插入查詢呢？爲什麼不是紅黑樹或其它數據結構？
SkipList按照區間查找數據效率比較高，而且實現起來也不是太複雜。