python實現跳表SkipList的示例代碼
跳表,又叫做跳躍表、跳躍列表,在有序鏈表的基礎上增加了“跳躍”的功能,由William Pugh于1990年發布,設計的初衷是為了取代平衡樹(比如紅黑樹)。Redis、LevelDB 都是著名的 Key-Value 數據庫,而Redis中 的 SortedSet、LevelDB 中的 MemTable 都用到了跳表。對比平衡樹,跳表的實現和維護會更加簡單,跳表的搜索、刪除、添加的平均時間復雜度是 O(logn)。跳表的結構如圖所示:
可以發現,對于一個節點Node,其含有多個next指針,不同索引的next分別代表不同層次的下一個節點,下次是節點類Node的python定義:
class Node(): def __init__(self,key,value,level): ’’’ :param level:每個node對應的nexts層數不同 ’’’ self.key=key self.value=value self.nexts=[None]*level#節點類型next指針,初始值為空 def __str__(self): #return '[key:'+str(self.key)+', value:'+str(self.value)+' len:'+str(len(self.nexts))+']' return '['+str(self.key)+','+str(self.value)+','+str(len(self.nexts))+']'
關于添加、刪除、查找見一下完整代碼:
’’’跳表 Skip List ,其初衷是為了替代紅黑樹’’’import randomimport mkl_randomimport timeclass SkipList(): def __init__(self):#頭節點不存儲任何數據self.MAX_LEVEL = 32 # 最大level層數self.__first=SkipList.Node(None, None, self.MAX_LEVEL)#頭節點self.__level=0#實際的level層數self.__size=0#Jiedian個數self.__p=0.25#用于生成添加節點時的隨機levelreturn class Node():def __init__(self,key,value,level): ’’’ :param level:每個node對應的nexts層數不同 ’’’ self.key=key self.value=value self.nexts=[None]*leveldef __str__(self): #return '[key:'+str(self.key)+', value:'+str(self.value)+' len:'+str(len(self.nexts))+']' return '['+str(self.key)+','+str(self.value)+','+str(len(self.nexts))+']' def get(self,key):’’’:param key::return: key對應的value’’’self.keyCheck(key)node=self.__firstfor level in range(self.__level - 1,-1,-1): #在該層查找,key大于節點的key向前查找 while node.nexts[level] and node.nexts[level].key<key:node=node.nexts[level] if node.nexts[level] and node.nexts[level].key==key:#相等則找到,否則向下尋找return node.nexts[level].valuereturn None def put(self,key,value):’’’return:原來的value,原來不存在key則為空’’’self.keyCheck(key)prev=[None]*self.__levelnode=self.__firstfor i in range(self.__level - 1, -1, -1): while node.nexts[i] and node.nexts[i].key<key:node=node.nexts[i] if node.nexts[i] and node.nexts[i].key==key:oldValue=node.nexts[i].valuenode.nexts[i].value=valuereturn oldValue prev[i]=node#保存當前level小于key的nodenewLevel=self.randomLevel()newNode=SkipList.Node(key,value,newLevel)for i in range(newLevel): if i<self.__level:newNode.nexts[i]=prev[i].nexts[i]prev[i].nexts[i]=newNode else:self.__first.nexts[i]=newNodeself.__size+=1self.__level=max(self.__level, newLevel)return None def remove(self,key):’’’:return: 節點對應的value值,不存在則返回None’’’self.keyCheck(key)prev=[None]*self.__levelnode=self.__firstflag=False#該節點是否被查找到for i in range(self.__level - 1, -1, -1): while node.nexts[i] and node.nexts[i].key<key:node=node.nexts[i] if node.nexts[i].key==key:flag=True prev[i]=nodeif not flag: return NoneremovedNode=node.nexts[0]#需要被刪除的節點for i in range(len(removedNode.nexts)):#該nexts一定小于等于prev的長度 prev[i].next[i]=removedNode.nexts[i]self.__size-=1newLevel=self.__levelwhile newLevel>0 and not self.__first.nexts[newLevel - 1]: newLevel-=1self.__level=newLevelreturn removedNode.value def keyCheck(self, key):’’’限制傳入key不能為空’’’if key!=0 and not key: raise AttributeError('key can not be None') def size(self):return self.__size def isEmpty(self):return self.__size == 0 def randomLevel(self):#生成一個隨機的層數level=1while mkl_random.rand()<self.__p and level<self.MAX_LEVEL: level+=1return level def __str__(self):result=''for i in range(self.__level - 1, -1, -1): result+=str(i) node = self.__first while node.nexts[i]:result+=str(node.nexts[i])node=node.nexts[i] result+=’n’print('level:'+str(self.__level))return result def showFirst(self):for item in self.__first.nexts: print(item,end=’ ’)print()def timeCalculate(container, size:int): begin=time.time() for i in range(size):if isinstance(container,dict): container[i]= i * 3else: container.put(i, i * 3) error_count = 0 for i in range(size):if container.get(i) != i * 3: #print('wrong ' + str(i) + ':' + str(skipList.get(i))) error_count+=1 end=time.time() print(type(container)) print(f’error rate:{float(error_count) / size:0.5f}’) print(f’time cost:{float(end-begin)*1000:0.3f} ms’)if __name__==’__main__’: timeCalculate({},1000000) timeCalculate(SkipList(),10000)
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