Download Parse Tree - Data Structures - Lecture Notes and more Study notes Data Structures and Algorithms in PDF only on Docsity!
1. Consider the parse tree for (9 + (5 * 3)) / (8 - 4):
a) Indentify the following items in the above tree:
parent of the node containing โ3โ branch from root node to โ3โ
children of the node containing โ+โ path from node containing โ+โ to node containing โ5โ
root node subtree whoโs root is node contains โ+โ
edge from node containing โ-โ to node containing โ8โ leaf nodes of the tree
node containing โโ siblings of the node containing โโ
b) Mark the levels of the tree (level is the number of edges on the path from the root)
c) What is the height (max. level) of the tree?
2. In Python an easy way to implement a tree is as a list of lists where a tree look like:
[ โnode valueโ, remaining items are subtrees for the node each implemented as a list of lists]
Complete the list-of-lists representation look like for the above parse tree:
[โ/โ, [โ+โ, ], [โ-โ, ] ]
3. Consider a โlinkedโ representations of a BinaryTree. For the expression ((4 + 5) * 7), the binary tree would be:
class BinaryTree: def init(self,rootObj): self.key = rootObj self.leftChild = None self.rightChild = None
key
key
key
key
key
leftChild
leftChild
leftChild
leftChild
leftChild
rightChild
rightChild
rightChild
rightChild
rightChild
Lecture 18 Page 1
a) Fix the insertLeft and insertRight code:
( (Listing 6.6 and 6.7 are wrong in the text on pp. 242-3)
b) Use these functions to build the BinaryTree for the
expression ((4 + 5) * 7).
Some corresponding external (non-class) functions:
Lecture 18 Page 2
def inorder(tree): if tree != None: inorder(tree.getLeftChild()) print(tree.getRootVal()) inorder(tree.getRightChild())
def printexp(tree): if tree.leftChild: print('(', end=' ') printexp(tree.getLeftChild()) print(tree.getRootVal(), end=' ') if tree.rightChild: printexp(tree.getRightChild()) print(')', end=' ')
def height(tree): if tree == None: return - else: return 1 + max(height(tree.leftChild), height(tree.rightChild))
def printexp(tree): sVal = "" if tree: sVal = '(' + printexp(tree.getLeftChild()) sVal = sVal + str(tree.getRootVal()) sVal = sVal + printexp(tree.getRightChild()) + ')' return sVal
def postordereval(tree): opers = {'+':operator.add, '-':operator.sub, '*':operator.mul, '/':operator.truediv} res1 = None res2 = None if tree: res1 = postordereval(tree.getLeftChild()) res2 = postordereval(tree.getRightChild()) if res1 and res2: return operstree.getRootVal() else: return tree.getRootVal()
import operator class BinaryTree: def init(self,rootObj): self.key = rootObj self.leftChild = None self.rightChild = None
def insertLeft(self,newNode): if self.leftChild == None: self.leftChild=BinaryTree(newNode) else: t = BinaryTree(newNode) t.left = self.leftChild self.leftChild = t
def insertRight(self,newNode): if self.rightChild == None: self.rightChild=BinaryTree(newNode) else: t = BinaryTree(newNode) t.right = self.rightChild self.rightChild = t
def isLeaf(self): return ((not self.leftChild) and (not self.rightChild))
def getRightChild(self): return self.rightChild
def getLeftChild(self): return self.leftChild
def setRootVal(self,obj): self.key = obj
def getRootVal(self,): return self.key
def inorder(self): if self.leftChild: self.leftChild.inorder() print(self.key) if self.rightChild: self.rightChild.inorder()
def postorder(self): if self.leftChild: self.leftChild.postorder() if self.rightChild: self.rightChild.postorder() print(self.key)
def preorder(self): print(self.key) if self.leftChild: self.leftChild.preorder() if self.rightChild: self.rightChild.preorder()
def printexp(self): if self.leftChild: print('(', end=' ') self.leftChild.printexp() print(self.key, end=' ') if self.rightChild: self.rightChild.printexp() print(')', end=' ') def postordereval(self): opers = {'+':operator.add, '-':operator.sub, '*':operator.mul, '/':operator.truediv} res1 = None res2 = None if self.leftChild: res1 = self.leftChild.postordereval() if self.rightChild: res2 = self.rightChild.postordereval() if res1 and res2: return opersself.key else: return self.key
