Expression Trees and Binary Tree Traversal
40 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the primary goal of a Threaded Binary Tree?

  • To convert a binary tree into a balanced tree
  • To facilitate faster traversals without additional memory (correct)
  • To increase the depth of the tree
  • To reduce the number of nodes in the tree

    • In a Single Threaded Binary Tree, which pointer is specifically used to track the in-order successor?

  • Left child pointer
  • Right NULL pointer (correct)
  • Root pointer
  • Left NULL pointer

    • What is the significance of the boolean variable in a Single Threaded Binary Tree Node structure?

  • To denote whether the right pointer points to a child or a successor (correct)
  • To mark nodes that have been visited
  • To track the height of the tree
  • To indicate if the node is a leaf node

    • Which of the following describes a Double Threaded Binary Tree?

    <p>Both left and right NULL pointers point to predecessors and successors</p> Signup and view all the answers

    Which data structure is primarily used to hold pointers in a Threaded Binary Tree?

    <p>Node structure</p> Signup and view all the answers

    What additional feature does a Double Threaded Binary Tree have compared to a Single Threaded Binary Tree?

    <p>Tracking of both predecessors and successors</p> Signup and view all the answers

    What type of data can the data_value field in the Node structure of a Threaded Binary Tree hold?

    <p>Integer values only</p> Signup and view all the answers

    Which statement about the right_thread variable in a Single Threaded Binary Tree is true?

    <p>It indicates whether the right pointer is pointing to a child node</p> Signup and view all the answers

    What is the primary characteristic of the left subtree in a binary search tree?

    <p>It contains nodes with keys lesser than the node's key.</p> Signup and view all the answers

    Which of the following operations is simplified in a binary search tree due to the sorted order of elements?

    <p>Searching for a specific element.</p> Signup and view all the answers

    What will the search algorithm return if the element is not found in a binary search tree?

    <p>NULL.</p> Signup and view all the answers

    In a binary search tree, if the value of the element to be searched is less than the root value, what should the search algorithm do?

    <p>Traverse the left subtree.</p> Signup and view all the answers

    Which of the following statements about binary search trees is NOT true?

    <p>They can contain duplicate nodes.</p> Signup and view all the answers

    What happens if a binary tree violates the binary search tree property?

    <p>It can no longer be considered a binary search tree.</p> Signup and view all the answers

    Which algorithm step is performed first in searching for an element in a binary search tree?

    <p>Compare the element with the root node.</p> Signup and view all the answers

    Why is it necessary for both left and right subtrees of a node in a binary search tree to be binary search trees?

    <p>To allow faster search, insertion, and deletion operations.</p> Signup and view all the answers

    What is the first step in inserting an element into a binary search tree?

    <p>Begin the search from the root node.</p> Signup and view all the answers

    Which of the following correctly describes the action taken when inserting a value less than the current node's value?

    <p>The search continues in the left subtree.</p> Signup and view all the answers

    When deleting a leaf node from a binary search tree, what is the outcome?

    <p>The node is simply removed and memory is deallocated.</p> Signup and view all the answers

    If the node to be deleted has one child, what happens to that child?

    <p>It replaces the node to be deleted.</p> Signup and view all the answers

    What is a necessary condition for the deletion of a node in a binary search tree?

    <p>The properties of the binary search tree must remain intact.</p> Signup and view all the answers

    In which scenario does the deletion operation involve replacing a node with NULL?

    <p>When the node is a leaf.</p> Signup and view all the answers

    What occurs when attempting to delete a node that has both subtrees?

    <p>The node's in-order predecessor or successor is needed for replacement.</p> Signup and view all the answers

    Which operation must be performed to ensure memory is properly managed during deletion?

    <p>Free the allocated space for the node being deleted.</p> Signup and view all the answers

    What is the initial action taken when processing operands in the construction of an expression tree?

    <p>Generate a one-node tree and store the data.</p> Signup and view all the answers

    During the construction of the expression tree from the expression 'ab+c*', what happens when the '+' operator is read?

    <p>The tree is formed using the last two operands and '+' as the root.</p> Signup and view all the answers

    What is the primary purpose of Morris traversal in the context of binary tree traversal?

    <p>To traverse the tree without using extra space for the stack.</p> Signup and view all the answers

    In the Morris traversal algorithm, what action is taken when the current node has a left child?

    <p>The rightmost node in the left subtree is found or the node whose right child is current.</p> Signup and view all the answers

    What characterizes a successor in the context of binary tree traversal?

    <p>It is the first node encountered that is greater than a given node.</p> Signup and view all the answers

    What occurs finally when processing the '' operator in the expression 'ab+c'?

    <p>A new tree is built with '*' as root by popping the previous trees from the stack.</p> Signup and view all the answers

    In the context of threaded binary trees, what is a key characteristic?

    <p>Nodes have additional pointers to their in-order predecessor and successor.</p> Signup and view all the answers

    What is the primary goal when finding the rightmost node in the left subtree of a current node during Morris traversal?

    <p>To allow a temporary right child to facilitate backtracking later.</p> Signup and view all the answers

    What is a key advantage of using a Threaded Binary Tree over a Non-Threaded Binary Tree?

    <p>Faster traversal operations due to non-recursive implementation</p> Signup and view all the answers

    Which of the following statements best describes the capability of accessing nodes in a Threaded Binary Tree?

    <p>Nodes can be accessed in both upward and downward directions using threads</p> Signup and view all the answers

    What is one disadvantage of using a Threaded Binary Tree?

    <p>Increased complexity of insertion and deletion operations</p> Signup and view all the answers

    In a Threaded Binary Tree, how is memory waste reduced?

    <p>By storing in-order predecessor/successor nodes instead of using NULL</p> Signup and view all the answers

    What time complexity does in-order traversal take in a Threaded Binary Tree compared to a normal Binary Tree?

    <p>O(1) for the Threaded Binary Tree, O(height) for the normal Binary Tree</p> Signup and view all the answers

    What mechanism does a Threaded Binary Tree use to determine predecessor and successor nodes?

    <p>Using threads instead of a stack mechanism</p> Signup and view all the answers

    Which operation is generally more time-consuming in Threaded Binary Trees compared to normal Binary Trees?

    <p>Insertion and deletion</p> Signup and view all the answers

    How does a Double-Threaded Binary Tree enhance traversal capabilities?

    <p>By allowing backward traversal</p> Signup and view all the answers

    Study Notes

    Expression Trees

    • Expression trees are used to represent expressions
    • The expression tree is built using a stack
    • Each operand is represented by a single-node tree
    • Operators act as the root of a new tree, with the two most recently pushed operands acting as their children

    Binary Tree Traversal

    • In-order traversal is the process of visiting nodes in a specific order
    • Successor is the next node in the in-order traversal
    • Predecessor is the previous node in the in-order traversal

    Morris Traversal

    • Morris traversal is an iterative way of implementing in-order traversal
    • The algorithm involves:
      • Finding the rightmost node in the left subtree of the current node
      • Relinking the rightmost node's right child to the current node
      • Traversing to the right

    Threaded Binary Trees

    • A threaded binary tree is a variation of a binary tree where null pointers are utilized to point to the inorder successor or predecessor
    • Single threaded binary trees use a single boolean variable (right_thread)
    • Double threaded binary trees use two boolean variables (left_thread and right_thread)
    • The purpose is to facilitate quicker in-order traversal and predecessor/successor lookup
    • Advantages:
      • Faster traversal
      • Efficient predecessor and successor identification
      • Reduces memory waste
    • Disadvantages:
      • More complex insertion and deletion operations
      • Uses additional memory to store the boolean variables

    Binary Search Tree (BST)

    • A BST is a binary tree that maintains sorted order
    • Left subtree of a node contains values less than the node's value
    • Right subtree of a node contains values greater than the node's value
    • No duplicate nodes are allowed in a BST

    BST Operations

    • Search:
      • Compares the target value with the root node
      • If the target is less than the root, it searches the left subtree
      • If the target is greater than the root, it searches the right subtree
      • Returns NULL if the target is not found
    • Insert:
      • Inserts a value into the BST in a specific order (maintaining BST properties)
      • If the value is less than the current node, it is inserted in the left subtree
      • If the value is greater than the current node, it is inserted in the right subtree
    • Delete:
      • Leaf node: Replaces the node with NULL
      • Single child: Replaces the node with its child
      • Two children: Finds the inorder successor, copies the value, and deletes the successor node

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Related Documents

    DSA Unit 3 2024 PDF

    Description

    This quiz covers the key concepts of expression trees and various binary tree traversal techniques, including in-order, Morris, and threaded binary trees. Test your understanding of how these structures operate and their applications in computing. Perfect for students in computer science courses!

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser