[工程師阿偉]正在和[機器小偉]一起研究[計算幾何]]。

<span style="font-size:18px;">#
#!/usr/bin/env python
from random import randint, choice
from bisect import bisect_right, bisect_left
from collections import deque

class InitError(Exception):
    pass
class ParaError(Exception):
    pass

#生成鍵值對
class KeyValue(object):
    __slots__=('key', 'value')
    def __init__(self, key, value):
        self.key=int(key) #一定要保證鍵值是整型
        self.value=value
        
    def __str__(self):
        return str((self.key, self.value))
    
    def __cmp__(self, key):
        if self.key>key:
            return 1
        elif self.key < key:
            return -1
        else:
            return 0
    
    def __lt__(self, other):
        if (type(self) == type(other)):
            return self.key < other.key;
        else:
            return int(self.key) < int(other);
            
    def __eq__(self, other):
        if (type(self) == type(other)):
            return self.key == other.key;
        else:
            return int(self.key) == int(other);

    def __gt__(self, other):
        return not self < other;   
        

#B+樹實現
#實現過程和btree很像，不過有幾點顯著不同。
#1.內節點不儲存key-value，只存放key
#
#2.沿著內節點搜尋的時候，查到索引相等的數要向樹的右邊走。所以二分查詢要選擇
#bisect_right
#
#3.在葉子節點滿的時候，並不是先分裂再插入而是先插入再分裂。因為b+tree無法保證
#分裂的兩個節點的大小都是相等的。在奇數大小的資料分裂的時候右邊的子節點會比左
#邊的大。如果先分裂再插入無法保證插入的節點一定會插在數量更少的子節點上，滿足
#節點數量平衡的條件。
#
#4.在刪除資料的時候，b+tree的左右子節點借資料的方式比btree更加簡單有效，只把子
#節點的子樹直接剪下過來，再把索引變一下就行了，而且葉子節點的兄弟指標也不用動。
#
class Bptree(object):
    class __InterNode(object):
        def __init__(self, M):
            if not isinstance(M, int):
                raise InitError('M must be int')
            if M<=3:
                raise InitError('M must be greater then 3')
            else:
                self.__M=M
                self.clist=[] #存放區間
                self.ilist=[] #存放索引/序號
                self.par=None
        def isleaf(self):
            return False
        def isfull(self):
            return len(self.ilist)>=self.M-1
        def isempty(self):
            return len(self.ilist)<=(self.M+1)/2-1
        @property
        def M(self):
            return self.__M

    #葉子
    class __Leaf(object):
        def __init__(self,L):
            if not isinstance(L,int):
                raise InitError('L must be int')
            else:
                self.__L=L
                self.vlist=[]
                self.bro=None #兄弟結點
                self.par=None #父結點
        def isleaf(self):
            return True
        def isfull(self):
            return len(self.vlist)>self.L
        def isempty(self):
            return len(self.vlist)<=(self.L+1)/2
        @property
        def L(self):
            return self.__L

    #初始化
    def __init__(self,M,L):
        if L>M:
            raise InitError('L must be less or equal then M')
        else:
            self.__M=M
            self.__L=L
            self.__root=Bptree.__Leaf(L)
            self.__leaf=self.__root
    @property
    def M(self):
        return self.__M
    @property
    def L(self):
        return self.__L

    #插入
    def insert(self, key_value):
        node=self.__root
        def split_node(n1):
            mid=self.M//2 #此處注意，可能出錯
            newnode=Bptree.__InterNode(self.M)
            newnode.ilist=n1.ilist[mid:]
            newnode.clist=n1.clist[mid:]
            newnode.par=n1.par
            for c in newnode.clist:
                c.par=newnode
            if n1.par is None:
                newroot=Bptree.__InterNode(self.M)
                newroot.ilist=[n1.ilist[mid-1]]
                newroot.clist=[n1,newnode]
                n1.par=newnode.par=newroot
                self.__root=newroot
            else:
                i=n1.par.clist.index(n1)
                n1.par.ilist.insert(i,n1.ilist[mid-1])
                n1.par.clist.insert(i+1,newnode)
            n1.ilist=n1.ilist[:mid-1]
            n1.clist=n1.clist[:mid]
            return n1.par
        def split_leaf(n2):
            mid=(self.L+1)//2
            newleaf=Bptree.__Leaf(self.L)
            newleaf.vlist=n2.vlist[mid:]
            if n2.par==None:
                newroot=Bptree.__InterNode(self.M)
                newroot.ilist=[n2.vlist[mid].key]
                newroot.clist=[n2,newleaf]
                n2.par=newleaf.par=newroot
                self.__root=newroot
            else:
                i=n2.par.clist.index(n2)
                n2.par.ilist.insert(i,n2.vlist[mid].key)
                n2.par.clist.insert(i+1,newleaf)
                newleaf.par=n2.par
            n2.vlist=n2.vlist[:mid]
            n2.bro=newleaf
        def insert_node(n):
            if not n.isleaf():
                if n.isfull():
                    insert_node(split_node(n))
                else:
                    p=bisect_right(n.ilist,key_value)
                    insert_node(n.clist[p])
            else:
                p=bisect_right(n.vlist,key_value)
                n.vlist.insert(p,key_value)
                if n.isfull():
                    split_leaf(n)
                else:
                    return
        insert_node(node)

    #搜尋
    def search(self,mi=None,ma=None):
        result=[]
        node=self.__root
        leaf=self.__leaf
        if mi is None or ma is None:
            raise ParaError('you need to setup searching range')
        elif mi > ma:
            raise ParaError('upper bound must be greater or equal than lower bound')
        def search_key(n,k):
            if n.isleaf():
                p=bisect_left(n.vlist,k)
                return (p,n)
            else:
                p=bisect_right(n.ilist,k)
                return search_key(n.clist[p],k)
        if mi is None:
            while True:
                for kv in leaf.vlist:
                    if kv<=ma:
                        result.append(kv)
                    else:
                        return result
                if leaf.bro==None:
                    return result
                else:
                    leaf=leaf.bro
        elif ma is None:
            index,leaf=search_key(node,mi)
            result.extend(leaf.vlist[index:])
            while True:
                if leaf.bro==None:
                    return result
                else:
                    leaf=leaf.bro
                    result.extend(leaf.vlist)
        else:
            if mi==ma:
                i,l=search_key(node,mi)
                try:
                    if l.vlist[i]==mi:
                        result.append(l.vlist[i])
                        return result
                    else:
                        return result
                except IndexError:
                    return result
            else:
                i1,l1=search_key(node,mi)
                i2,l2=search_key(node,ma)
                if l1 is l2:
                    if i1==i2:
                        return result
                    else:
                        result.extend(l2.vlist[i1:i2])
                        return result
                else:
                    result.extend(l1.vlist[i1:])
                    l=l1
                    while True:                        
                        if l.bro==l2:
                            result.extend(l2.vlist[:i2])
                            return result
                        elif l.bro != None:
                            result.extend(l.bro.vlist)
                            l=l.bro
                        else:
                            return result;
    def traversal(self):
        result=[]
        l=self.__leaf
        while True:
            result.extend(l.vlist)
            if l.bro==None:
                return result
            else:
                l=l.bro
    def show(self):
        print('this b+tree is:\n')
        q=deque()
        h=0
        q.append([self.__root,h])
        while True:
            try:
                w,hei=q.popleft()
            except IndexError:
                return
            else:
                if not w.isleaf():
                    print(w.ilist,'the height is',hei)
                    if hei==h:
                        h+=1
                    q.extend([[i,h] for i in w.clist])
                else:
                    print([(v.key,v.value) for v in w.vlist],'the leaf is,',hei)

    #刪除                                                                                                                                                                                                                                                                                                                          
    def delete(self,key_value):
        def merge(n,i):
            if n.clist[i].isleaf():
                n.clist[i].vlist=n.clist[i].vlist+n.clist[i+1].vlist
                n.clist[i].bro=n.clist[i+1].bro
            else:
                n.clist[i].ilist=n.clist[i].ilist+[n.ilist[i]]+n.clist[i+1].ilist
                n.clist[i].clist=n.clist[i].clist+n.clist[i+1].clist
            n.clist.remove(n.clist[i+1])
            n.ilist.remove(n.ilist[i])
            if n.ilist==[]:
                n.clist[0].par=None
                self.__root=n.clist[0]
                del n
                return self.__root
            else:
                return n
        def tran_l2r(n,i):
            if not n.clist[i].isleaf():
                n.clist[i+1].clist.insert(0,n.clist[i].clist[-1])
                n.clist[i].clist[-1].par=n.clist[i+1]
                n.clist[i+1].ilist.insert(0,n.ilist[i])
                n.ilist[i]=n.clist[i].ilist[-1]
                n.clist[i].clist.pop()
                n.clist[i].ilist.pop()
            else:
                n.clist[i+1].vlist.insert(0,n.clist[i].vlist[-1])
                n.clist[i].vlist.pop()
                n.ilist[i]=n.clist[i+1].vlist[0].key
        def tran_r2l(n,i):
            if not n.clist[i].isleaf():
                n.clist[i].clist.append(n.clist[i+1].clist[0])
                n.clist[i+1].clist[0].par=n.clist[i]
                n.clist[i].ilist.append(n.ilist[i])
                n.ilist[i]=n.clist[i+1].ilist[0]
                n.clist[i+1].clist.remove(n.clist[i+1].clist[0])
                n.clist[i+1].ilist.remove(n.clist[i+1].ilist[0])
            else:
                n.clist[i].vlist.append(n.clist[i+1].vlist[0])
                n.clist[i+1].vlist.remove(n.clist[i+1].vlist[0])
                n.ilist[i]=n.clist[i+1].vlist[0].key
        def del_node(n,kv):
            if not n.isleaf():
                p=bisect_right(n.ilist,kv)
                if p==len(n.ilist):
                    if not n.clist[p].isempty():
                        return del_node(n.clist[p],kv)
                    elif not n.clist[p-1].isempty():
                        tran_l2r(n,p-1)
                        return del_node(n.clist[p],kv)
                    else:
                        return del_node(merge(n,p),kv)
                else:
                    if not n.clist[p].isempty():
                        return del_node(n.clist[p],kv)
                    elif not n.clist[p+1].isempty():
                        tran_r2l(n,p)
                        return del_node(n.clist[p],kv)
                    else:
                        return del_node(merge(n,p),kv)
            else:
                p=bisect_left(n.vlist,kv)
                try:
                    pp=n.vlist[p]
                except IndexError:
                    return -1
                else:
                    if pp!=kv:
                        return -1
                    else:
                        n.vlist.remove(kv)
                        return 0
        del_node(self.__root,key_value)

        
def test():
    #初始化資料來源
    mini=50
    maxi=200
    testlist=[]
    for i in range(20):
        key=randint(1,1000)
        #key=i
        value=choice(['Do', 'Re', 'Mi', 'Fa', 'So', 'La', 'Si'])
        testlist.append(KeyValue(key,value))

    #初始化B樹
    mybptree=Bptree(4, 4)

    #插入操作
    for x in testlist:
        mybptree.insert(x)

    mybptree.show()

    #查詢操作
    print('\nnow we are searching item between %d and %d\n==>'%(mini,maxi))
    print([v.key for v in mybptree.search(mini,maxi)])

    
    #刪除操作
    mybptree.delete(testlist[0])
    print('\n刪除 {0}後， the newtree is:\n'.format(testlist[0]));
    mybptree.show()

    
    #深度遍歷操作
    print('\nkey of this b+tree is \n')
    print([kv.key for kv in mybptree.traversal()])
    
    


if __name__ == '__main__':
    test();

#</span>
 

本節到此結束，欲知後事如何，請看下回分解。