In-depth analysis of B-tree algorithm and its Python implementation
B树,和二叉搜索树很像,每个节点可以包含多个节点,但B树的子节点可以超过两个。
B树数据结构
B树可以在单个节点中存储许多键,并且可以有多个子节点。
B树搜索算法
BtreeSearch(x,k) i=1 while i≤n[x]and k≥keyi[x] do i=i+1 if i n[x]and k=keyi[x] then return(x,i) if leaf[x] then return NIL else return BtreeSearch(ci[x],k)
B树搜索示例
指定K=17,从根节点开始,将k与根进行比较。
ķ>11,转到根的右子节点;比较k和16,因为>16,比较k和下一个键18。
由于k<18,k介于16和18之间。在16的右子节点或18左子节点中搜索,k被发现。
Python实现B树
class BTreeNode: def __init__(self,leaf=False): self.leaf=leaf self.keys=[] self.child=[] class BTree: def __init__(self,t): self.root=BTreeNode(True) self.t=t def insert(self,k): root=self.root if len(root.keys)==(2*self.t)-1: temp=BTreeNode() self.root=temp temp.child.insert(0,root) self.split_child(temp,0) self.insert_non_full(temp,k) else: self.insert_non_full(root,k) def insert_non_full(self,x,k): i=len(x.keys)-1 if x.leaf: x.keys.append((None,None)) while i>=0 and k[0]<x.keys<i>[0]: x.keys[i+1]=x.keys<i> i-=1 x.keys[i+1]=k else: while i>=0 and k[0]<x.keys<i>[0]: i-=1 i+=1 if len(x.child<i>.keys)==(2*self.t)-1: self.split_child(x,i) if k[0]>x.keys<i>[0]: i+=1 self.insert_non_full(x.child<i>,k) def split_child(self,x,i): t=self.t y=x.child<i> z=BTreeNode(y.leaf) x.child.insert(i+1,z) x.keys.insert(i,y.keys[t-1]) z.keys=y.keys[t:(2*t)-1] y.keys=y.keys[0:t-1] if not y.leaf: z.child=y.child[t:2*t] y.child=y.child[0:t-1] def print_tree(self,x,l=0): print("Level",l,"",len(x.keys),end=":") for i in x.keys: print(i,end="") print() l+=1 if len(x.child)>0: for i in x.child: self.print_tree(i,l) def search_key(self,k,x=None): if x is not None: i=0 while i<len(x.keys)and k>x.keys<i>[0]: i+=1 if i<len(x.keys)and k==x.keys<i>[0]: return(x,i) elif x.leaf: return None else: return self.search_key(k,x.child<i>) else: return self.search_key(k,self.root) def main(): B=BTree(3) for i in range(10): B.insert((i,2*i)) B.print_tree(B.root) if B.search_key(8)is not None: print("\nFound") else: print("\nNot Found") if __name__=='__main__': main()
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