[从头学数学] 第258节 Python实现数据结构：伸展树(splay tree)

剧情提要：
阿伟看到了一本比较有趣的书，是关于《计算几何》的，2008年由北清派出版。很好奇
它里面讲了些什么，就来看看啦。


正剧开始：
星历2016年09月07日 08:41:50, 银河系厄尔斯星球中华帝国江南行省。

[工程师阿伟]正在和[机器小伟]一起研究[计算几何]]。

##### @usage   splayTree（伸展树），具有根元素记忆及动态调整功能的二叉搜索树# @author  mw# @date    2016年09月07日  星期三  08:37:17 # @param# @return####class SplayTree(object):          class __SplayNode(object):        def __init__(self, key, left = None, right = None):            self.key=key            self.left=left            self.right=right        def __iter__(self):            if self.left != None:                for elem in self.left:                    yield elem            if (self.key != None):                yield self.key            if self.right != None:                for elem in self.right:                    yield elem        #迭代的是Node类型，用于删除结点        def iternodes(self):            if self.left != None:                for elem in self.left.iternodes():                    yield elem            if self != None and self.key != None:                yield self            if self.right != None:                for elem in self.right.iternodes():                    yield elem        def info(self):            s = 'Key='+str(self.key)+', '+\                'LChild='+str(self.left)+', '+\                'RChild='+str(self.right);            print(s);                    def __str__(self):            return str(self.key);        def __repr__(self):            if self != None:                s_1 = str(self.key);            else:                s_1 = 'None';            if self.left != None:                s_2 = str(self.left.key);            else:                s_2 = 'None';            if self.right != None:                s_3 = str(self.right.key);            else:                s_3 = 'None';                            return '__SplayNode('+s_1+', ' + s_2 +', ' + s_3 +')';            def __init__(self):        self.root=None        self.header = SplayTree.__SplayNode(None) #For splay()    #LL    def singleLeftRotate(self,node):        k1=node.left        node.left=k1.right        k1.right=node        return k1        #RR    def singleRightRotate(self,node):        k1=node.right        node.right=k1.left        k1.left=node        return k1            #RL    def doubleLeftRotate(self,node):        node.left=self.singleRightRotate(node.left)        return self.singleLeftRotate(node)            #LR    def doubleRightRotate(self,node):        node.right=self.singleLeftRotate(node.right)        return self.singleRightRotate(node)    #伸展运动    def splay(self, key):        l = r = self.header          t = self.root          if t is None:              return                self.header.left = self.header.right = None                while True:            if key < t.key:                                if t.left == None:                    break;                if key < t.left.key:                    t = self.singleLeftRotate(t);                    if t.left == None:                        break;                r.left = t                  r = t                  t = t.left                             elif key > t.key:                if t.right == None:                    break;                if key > t.right.key:                    t = self.singleRightRotate(t);                    if t.right == None:                        break;                l.right = t                  l = t                  t = t.right             else:                break;        l.right = t.left          r.left = t.right          t.left = self.header.right          t.right = self.header.left          self.root = t            #    #和splay操作捆绑的方法    #        #插入    def insert(self, key):          if (self.root == None):              self.root = SplayTree.__SplayNode(key)              return            self.splay(key)          if self.root.key == key:              # If the key is already there in the tree, don't do anything.              return            n = SplayTree.__SplayNode(key)          if key < self.root.key:              n.left = self.root.left              n.right = self.root              self.root.left = None          else:              n.right = self.root.right              n.left = self.root              self.root.right = None          self.root = n    def remove(self, key):          self.splay(key)          if self.root is None or key != self.root.key:              return None;          # Now delete the root.          if self.root.left== None:              self.root = self.root.right          else:              x = self.root.right              self.root = self.root.left              self.splay(key)              self.root.right = x        return key;              def findMin(self):          if self.root == None:              return None          x = self.root          while x.left != None:              x = x.left          self.splay(x.key)          return x.key        def findMax(self):          if self.root == None:              return None          x = self.root          while (x.right != None):              x = x.right          self.splay(x.key)          return x.key        def find(self, key):          if self.root == None:              return None          self.splay(key)          if self.root.key != key:              return None          return self.root.key        def isEmpty(self):          return self.root == None    #    #结构信息查询，不与splay操作捆绑    #        def getRoot(self):        return repr(self.root);    def info(self):        a = [];        for x in self:            a.append(x);        print(a);    def __iter__(self):        if self.root != None:            return self.root.__iter__()        else:            return [].__iter__()    def __contains__(self, val):        for x in self:            if (x == val):                return True;        return False;    def __len__(self):        a = [];        for x in self:            a.append(x);        return len(a);    #求结点高度    def height(self, node):        if (node == None):            return 0;        else:            m = self.height(node.left);            n = self.height(node.right);            return max(m, n)+1;        #传回结点的原始信息    def iternodes(self):        if self.root != None:            return self.root.iternodes()        else:            return [None];    #寻找节点路径    def findNodePath(self, root, node):        path = [];        if root == None or root.key == None:            path = [];            return path                    while (root != node):            if node.key < root.key:                path.append(root);                root = root.left;            elif node.key >= root.key:                path.append(root);                root = root.right;            else:                break;        path.append(root);        return path;    #寻找父结点    def parent(self, root, node):        path = self.findNodePath(root, node);        if (len(path)>1):            return path[-2];        else:            return None;    #是否左孩子    def isLChild(self, parent, lChild):        if (parent.getLeft() != None and parent.getLeft() == lChild):            return True;        return False;    #是否右孩子    def isRChild(self, parent, rChild):        if (parent.getRight() != None and parent.getRight() == rChild):            return True;        return False;    #求某元素是在树的第几层    #约定根为0层    #这个计算和求结点的Height是不一样的    def level(self, elem):        if self.root != None:            node = self.root;            lev = 0;            while (node != None):                if elem < node.key:                    node = node.left;                    lev+=1;                elif elem > node.key:                    node = node.right;                    lev+=1;                else:                    return lev;            return -1;        else:            return -1;#

用例：

#if __name__ == '__main__':    splay = SplayTree();        a = [20, 30, 40, 120, 13, 39, 38, 40, 18, 101];    for item in a:        splay.insert(item);        print(splay.getRoot());        print(splay.height(splay.root));    splay.info();    print(len(splay));    for node in splay.iternodes():        print(splay.findNodePath(splay.root, node), '\n');    '''    for item in reversed(a):        print('remove:', splay.remove(item));        splay.getRoot();        print(splay.height(splay.root));    '''    print(splay.findMax());    print(splay.getRoot());>>>__SplayNode(20, None, None)1__SplayNode(30, 20, None)2__SplayNode(40, 30, None)3__SplayNode(120, 40, None)4__SplayNode(13, None, 20)4__SplayNode(39, 30, 40)4__SplayNode(38, 30, 39)4__SplayNode(40, 39, 120)6__SplayNode(18, 13, 39)4__SplayNode(101, 39, 120)5[13, 18, 20, 30, 38, 39, 40, 101, 120]9[__SplayNode(101, 39, 120), __SplayNode(39, 18, 40), __SplayNode(18, 13, 30), __SplayNode(13, None, None)] [__SplayNode(101, 39, 120), __SplayNode(39, 18, 40), __SplayNode(18, 13, 30)] [__SplayNode(101, 39, 120), __SplayNode(39, 18, 40), __SplayNode(18, 13, 30), __SplayNode(30, 20, 38), __SplayNode(20, None, None)] [__SplayNode(101, 39, 120), __SplayNode(39, 18, 40), __SplayNode(18, 13, 30), __SplayNode(30, 20, 38)] [__SplayNode(101, 39, 120), __SplayNode(39, 18, 40), __SplayNode(18, 13, 30), __SplayNode(30, 20, 38), __SplayNode(38, None, None)] [__SplayNode(101, 39, 120), __SplayNode(39, 18, 40)] [__SplayNode(101, 39, 120), __SplayNode(39, 18, 40), __SplayNode(40, None, None)] [__SplayNode(101, 39, 120)] [__SplayNode(101, 39, 120), __SplayNode(120, None, None)] 120__SplayNode(120, 101, None)#