一、树
1、模拟文件系统
class Node: def __init__(self, name, type='dir'): self.name = name self.type = type # "dir" or "file" self.children = [] self.parent = None def __repr__(self): return self.name class FileSystemTree: def __init__(self): self.root = Node("/") self.now = self.root def mkdir(self, name): # 创建目录 if name[-1] != "/": name += "/" node = Node(name) self.now.children.append(node) node.parent = self.now def ls(self): # 返回子目录 return self.now.children def cd(self, name): # 切换到name目录 if name[-1] != "/": name += "/" if name == "../": # 向上切换到parent self.now = self.now.parent return for child in self.now.children: # 向下切换 if child.name == name: self.now = child return else: raise ValueError("invalid dir") tree = FileSystemTree() tree.mkdir("var/") tree.mkdir("bin/") tree.mkdir("usr/") print(tree.now) # 输出”\“ print(tree.now.children) # 输出[var/, bin/, usr/] tree.cd("bin/") print(tree.now) # 输出 bin\ tree.cd("../") print(tree.now) # 输出”\“
二、二叉树
度不超过2的树。
二叉树的链式存储：将二叉树的节点定义为一个对象，节点之间通过类似链表的链接方式来连接。
class BiTreeNode: def __init__(self,data): self.data=data self.lchild=None #左孩子 self.rchild=None #右孩子
1、二叉树的遍历
前序遍历：EACBDGF
中序遍历：ABCDEGF
后序遍历：BDCAFGE
层次遍历：EAGCFBD
class BiTreeNode: def __init__(self, data): self.data = data self.lchild = None # 左孩子 self.rchild = None # 右孩子 a = BiTreeNode("A") b = BiTreeNode("B") c = BiTreeNode("C") d = BiTreeNode("D") e = BiTreeNode("E") f = BiTreeNode("F") g = BiTreeNode("G") e.lchild = a e.rchild = g a.rchild = c c.lchild = b c.rchild = d g.rchild = f root = e def pre_order(root): # 前序遍历[E[A[C[BD]]][G[F]] if root: print(root.data, end=',') pre_order(root.lchild) pre_order(root.rchild) def in_order(root): # 中序遍历[A[BCD]]E[GF] if root: in_order(root.lchild) print(root.data, end=',') in_order(root.rchild) def post_order(root): # 后序遍历 if root: post_order(root.lchild) post_order(root.rchild) print(root.data, end=',') from collections import deque def level_order(root): # 层次遍历 queue = deque() queue.append(root) while len(queue) > 0: node = queue.popleft() print(node.data, end=',') if node.lchild: queue.append(node.lchild) if node.rchild: queue.append(node.rchild)
2、二叉搜索树
二叉搜索树是一颗二叉树且满足性质：设x是二叉树的一个节点，如果y是x左子树的一个节点，那么y.key≤x.key；如果y是x右子树的一个节点，那么y.key≤≥.key。
2.1二叉搜索树的插入、搜索、删除
class BiTreeNode: def __init__(self, data): self.data = data self.lchild = None # 左孩子 self.rchild = None # 右孩子 self.parent = None class BST: def __init__(self, li=None): self.root = None if li: # 将列表中的元素按二叉搜索树插入 for val in li: self.insert(val) def insert(self, val): # 插入 p = self.root if not p: self.root = BiTreeNode(val) return while True: if val < p.data: if p.lchild: p = p.lchild else: p.lchild = BiTreeNode(val) p.lchild.parent = p return elif val > p.data: if p.rchild: p = p.rchild else: p.rchild = BiTreeNode(val) p.rchild.parent = p return else: return def query(self, val): # 查找 p = self.root while p: if p.data < val: p = p.rchild elif p.data > val: p = p.lchild else: return p return None def remove_node_1(self, node): # 情况1：node是叶子节点 if not node.parent: # node为根节点 self.root = None if node == node.parent.lchild: # node是它父亲的左孩子 node.parent.lchild = None else: # node是它父亲的右孩子 node.parent.rchild = None def remove_node_2_1(self, node): # 情况2_1：node只有一个左孩子 if not node.parent: # 根节点 self.root = node.lchild node.lchild.parent = None elif node == node.parent.lchild: node.parent.lchild = node.lchild node.lchild.parent = node.parent else: node.parent.rchild = node.lchild node.lchild.parent = node.parent def remove_node_2_2(self, node): # 情况2_2:node只有一个右孩子 if not node.parent: self.root = node.rchild elif node == node.parent.lchild: node.parent.lchild = node.rchild node.rchild.parent = node.parent else: node.parent.rchild = node.rchild node.rchild.parent = node.parent def delete(self, val): if self.root: # 不是空树 node = self.query(val) if not node: # node不存在 return False if not node.lchild and not node.rchild: # 情况1 self.remove_node_1(node) elif not node.rchild: # 情况2_1 self.remove_node_2_1(node) elif not node.lchild: # 情况2_2 self.remove_node_2_2(node) else: # 情况3：两个孩子都有 min_node = node.lchild while min_node.lchild: min_node = min_node.lchild node.data = min_node.data # 删除min_node(为叶子节点或者只有一个右孩子) if min_node.rchild: self.remove_node_2_2(min_node) else: self.remove_node_1(min_node) def in_order(self, root): # 中序遍历 if root: self.in_order(root.lchild) print(root.data, end=',') self.in_order(root.rchild) def pre_order(self, root): # 前序遍历 if root: print(root.data, end=',') self.pre_order(root.lchild) self.pre_order(root.rchild) tree = BST([5, 17, 35, 2, 11, 29, 38, 9, 8]) tree.in_order(tree.root) # 对于二叉搜索树，其中序遍历输出结果是升序排列 print("") tree.pre_order(tree.root) print("") print(tree.query(2).data) # 搜索 tree.delete(4) tree.in_order(tree.root)
3、AVL树
from bst import BiTreeNode, BST #将2.1处的代码存为bst.py，此处调用 class AVLNode(BiTreeNode): def __init__(self, data): BiTreeNode.__init__(self, data) self.bf = 0 class AVLTree(BST): def __init__(self, li=None): BST.__init__(self, li) def rotate_left(self, p, c): # 左旋 s2 = c.lchild p.rchild = s2 if s2: s2.parent = p c.lchild = p p.parent = c p.bf = 0 c.bf = 0 return c def rotate_right(self, p, c): # 右旋 s2 = c.rchild p.lchild = s2 if s2: s2.parent = p c.rchild = p p.parent = c p.bf = 0 c.bf = 0 return c def rotate_right_left(self, p, c): # 右旋——左旋 g = c.lchild s3 = g.rchild c.lchild = s3 if s3: s3.parent = c g.rchild = c c.parent = g s2 = g.lchild p.rchild = s2 if s2: s2.parent = p g.lchild = p p.parent = g # 更新bf if g.bf > 0: # g.bf==1 p.bf = -1 c.bf = 0 else: # g.bf==-1 p.bf = 0 c.bf = 1 g.bf = 0 return g def rotate_left_right(self, p, c): # 左旋——右旋 g = c.rchild s2 = g.lchild c.rchild = s2 if s2: s2.parent = c g.lchild = c c.parent = g s3 = g.rchild p.lchild = s3 if s3: s3.parent = p g.rchild = p p.parent = g # 更新bf if g.bf < 0: p.bf = 1 c.bf = 0 else: p.bf = 0 c.bf = -1 g.bf = 0 return g def insert(self, val): # 1、做插入 p = self.root if not p: self.root = AVLNode(val) return while True: if val < p.data: if p.lchild: p = p.lchild node = p.lchild # node存储的是插入的节点 else: p.lchild = AVLNode(val) p.lchild.parent = p node = p.lchild # node存储的是插入的节点 break elif val > p.data: if p.rchild: p = p.rchild else: p.rchild = AVLNode(val) p.rchild.parent = p node = p.rchild break else: return # 2、更新bf参数 while node.parent: # node.parent不空 if node.parent.lchild == node: # 传递是从左子树来的,更新后的node.parent的bf-=1 if node.parent.bf < 0: # 原来的node。parent。bf==-1,更新后变成-2 # 做旋转 g = node.parent.parent # 用于连接旋转之后的子树 x = node.parent # 旋转之前的子树的根 if node.bf > 0: n = self.rotate_left_right(node.parent, node) else: n = self.rotate_right(node.parent, node) elif node.parent.bf > 0: # 原来的node.parent.bf=1，更新之后变成0 node.parent.bf = 0 break else: # 原来的node.parent.bf=0，更新之后变成-1 node.parent.bf = -1 node = node.parent continue else: # 传递是从右子树来的,更新后的node.parent的bf+=1 if node.parent.bf > 0: # 原来的node。parent。bf==1,更新后变成2 # 做旋转 g = node.parent.parent x = node.parent if node.bf < 0: n = self.rotate_right_left(node.parent, node) else: n = self.rotate_left(node.parent, node) elif node.parent.bf < 0: # 原来的node。parent。bf==-1,更新后变成0 node.parent.bf = 0 break else: # 原来的node.parent.bf=0，更新之后变成1 node.parent.bf = 1 node.parent = node continue # 连接旋转之后的子树 n.parent = g if g: if x == g.lchild: g.lchild = n else: g.rchild = n break else: self.root = n break tree = AVLTree([9, 8, 7, 6, 5, 4, 3, 2, 1]) tree.pre_order(tree.root) print("") tree.in_order(tree.root)
