数据结构－树－学习笔记

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http://interactivepython.org/courselib/static/pythonds/index.html

Problem Solving with Algorithms and Data Structures

树

Examples of Trees

在计算机科学中有许多应用：

操作系统，数据库，计算机网络

文件系统

网页

Vocabulary and Definitions

元素：

root，branches，leaves

特性：

hierarchical

在每个节点问一个问题，选择合适的答案的路径继续向下走

可以移动任意一个子树，不影响低层的结构

一个节点的children和另一个节点的children是独立的

因此在改变子节点的时候不会影响其他子节点

每个叶节点是唯一的

因此从根到叶节点有唯一的一条路径

概念：

node： name->key, additional information->payload

edge: 节点间的关系，一个节点只有一个incoming edge，有多个outgoing edge

root：树里唯一一个没有incoming edge的节点

path，children，parent，sibling，subtree

leaf node：没有children的node

level：从root到节点的path中edge的个数

height：这个树里最大的level

binary tree：树里的每个节点都最多只有两个children

定义：

Definition One: A tree consists of a set of nodes and a set of edges that connect pairs of nodes.

Definition Two: A tree is either empty or consists of a root and zero or more subtrees, each of which is also a tree. The root of each subtree is connected to the root of the parent tree by an edge.

List of Lists Representation

a tree represented by a list of lists

creating a simple tree using a list

myTree = ['a',['b',['d',[],[]],['e',[],[]]],['c',['f',[],[]],[]]]print(myTree)print('left subtree =',myTree[1])print(myTree[1][1])print(myTree[1][1][1])

每个list的第一个元素是root，第二个元素是left subtree，第三个元素是right subtree

叶节点有一个root和两个空的list

def BinaryTree(r):    return [r, [], []]#to insert a left childdef insertLeft(root,newBranch):    t = root.pop(1)             #1st level left subtree    if len(t) > 1:              #if null, len is 0        root.insert(1,[newBranch,t,[]])       #insert newBranch in left position    else:        root.insert(1,[newBranch, [], []])    return rootr = BinaryTree(3)print(r)    #[3, [], []]print(len(r.pop(1)))    #0insertLeft(r,4)print(r)    #[3, [4, [], []]]insertLeft(r,5)print(r)    #[3, [5, [4, [], []], []]]root = rnewBranch = 6t = root.pop(1)print(t)    #[5, [4, [], []], []]print(len(t))    #3root.insert(1,[newBranch,t,[]])print(root)    #[3, [6, [5, [4, [], []], []], []]]t = root.pop(1)print(t)    #[6, [5, [4, [], []], []], []]print(len(t))    #3

def BinaryTree(r):    return [r, [], []]#to insert a left childdef insertLeft(root,newBranch):    t = root.pop(1)             #1st level left subtree    if len(t) > 1:              #if null, len is 0        root.insert(1,[newBranch,t,[]])       #insert newBranch in left position    else:        root.insert(1,[newBranch, [], []])    return rootr = BinaryTree(3)insertLeft(r,4)insertLeft(r,5)def insertRight(root,newBranch):    t = root.pop(2)    if len(t)>1:        root.insert(2,[newBranch,[],t])    else:        root.insert(2,[newBranch,[],[]])    return rootinsertRight(r,6)print(r)insertRight(r,7)print(r)def getLeftChild(root):    return root[1]def getRightChild(root):    return root[2]print(getLeftChild(r))print(getRightChild(r))print(getRightChild(getLeftChild(r)))def getRootVal(root):    return root[0]def setRootVal(root,newVal):    root[0] = newVal    return root[0]print(getRootVal(r))setRootVal(r,10)print(getRootVal(r))

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