Binary Search Tree Deletion
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Questions and Answers

When node A in the BST is deleted, which two nodes are the candidates to take its place?

  • J and I (correct)
  • D and E
  • H and E
  • L and M

    • What is correct about the insertion cases in an AVL tree?

  • The insertion occurs outside in cases 1 and 2, and single rotation can fix the balance. (correct)
  • The insertion occurs inside in cases 1 and 2, and single rotation can fix the balance.
  • The insertion occurs outside in cases 1 and 2, and single rotation cannot fix the balance.
  • The insertion occurs inside in cases 1 and 2, and single rotation cannot fix the balance.

    • How are elements accessed in an AVL Tree?

  • In both linear and non-linear ways (correct)
  • In a linear way only
  • In neither linear nor non-linear ways
  • In a non-linear way only

    • What type of data structure is an AVL Tree?

    <p>Non-linear data structure</p> Signup and view all the answers

    What happens when a node in a BST is deleted?

    <p>Its child nodes take its place</p> Signup and view all the answers

    What is the primary concern in an AVL Tree?

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

    What is the total number of nodes (Tn) in a complete binary tree of depth d?

    <p>2^(d+1) - 1</p> Signup and view all the answers

    What is the height of the complete binary tree?

    <p>h = log2(Tn+1)-1</p> Signup and view all the answers

    What is the postfix notation of the infix expression 5 + 6/2?

    <p>56/ + 2</p> Signup and view all the answers

    What type of data structure is a tree?

    <p>Non-Linear</p> Signup and view all the answers

    What type of operator is '+'?

    <p>Binary</p> Signup and view all the answers

    What happens to the pointer in a stack when new items are added?

    <p>It increments by 2</p> Signup and view all the answers

    What is the minimum number of nodes required at each level L in a complete binary tree?

    <p>2^L</p> Signup and view all the answers

    In an AVL tree, how many cases of rotation are there?

    <p>4</p> Signup and view all the answers

    What is the correct syntax for a conditional statement in postfix notation?

    <p>if (LessThan(alpha, beta))</p> Signup and view all the answers

    What is the fundamental difference between a queue and a stack?

    <p>A queue is FIFO, a stack is LIFO</p> Signup and view all the answers

    Which operator has the highest priority in expressions?

    <p>Exponentiation operator</p> Signup and view all the answers

    How many pointers does each node in a Binary Search Tree have?

    <p>2 pointers</p> Signup and view all the answers

    What is an incorrect statement about trees?

    <p>If Tree1's size is greater than Tree2's size, then the height of Tree1 must also be greater than Tree2's height</p> Signup and view all the answers

    Can the size of an array be changed after its creation?

    <p>No, it cannot be changed</p> Signup and view all the answers

    What is the time complexity of searching an element in an AVL tree?

    <p>O(log2(n+1))</p> Signup and view all the answers

    What is the primary concern in an AVL tree?

    <p>Balancing the tree</p> Signup and view all the answers

    What is the postfix notation of 5 + 6/2?

    <p>56+/2</p> Signup and view all the answers

    What type of data structure is a BST?

    <p>Non Linear</p> Signup and view all the answers

    Which operator has the highest precedence?

    <p>Exponentiation</p> Signup and view all the answers

    What type of rotation is required to delete a parent with two children in an AVL tree?

    <p>Double</p> Signup and view all the answers

    What happens to the size of an array after creation?

    <p>It can neither be increased nor decreased</p> Signup and view all the answers

    What is the valid postfix notation of A+B*C-D?

    <p>ABC*+D-</p> Signup and view all the answers

    What type of notation is used when an operator is placed between two operands?

    <p>Infix</p> Signup and view all the answers

    How many pointers does each node in a BST have?

    <p>2</p> Signup and view all the answers

    Study Notes

    Deleting a Node in a BST

    • When node A in a Binary Search Tree (BST) is deleted, the two candidates to take its place are H and E.

    Rebalancing a Node

    • The node that requires rebalancing is referred to as "a".

    Insertion Cases

    • In case 1, an insertion occurs into the left subtree of the left child of "a".
    • In case 2, an insertion occurs into the right subtree of the right child of "a".
    • In both cases, a single rotation can fix the balance if the insertion occurs outside (i.e., left-left or right-right).

    Accessing Elements in AVL Tree

    • Elements in an AVL Tree can be accessed in both linear and non-linear ways.

    AVL Tree Data Structure

    • An AVL Tree is a non-linear data structure.

    Binary Trees

    • The number of nodes in an AVL tree can be calculated using the formula Log2(n+1) - 1, which is approximately equal to 1.44 Log2n or 1.66 Log2n.
    • An AVL tree may have cases of rotation, specifically, there is 1 case of rotation.

    Binary Search Trees

    • A binary tree can contain at least 2L Nodes at level L.
    • A complete binary tree of depth d is a binary tree that contains 2L Nodes at each level L between 0 and d, both inclusive.
    • The total number of nodes (Tn) in a complete binary tree of depth d is 2^d+1 - 1.
    • The height of the complete binary tree can be written as h = log2 (Tn+1)-1 where Tn is the Total number of Nodes.

    Postfix Notation

    • The infix expression 5 + 6/2 can be converted into postfix notation as 56/ + 2 or 562/+.
    • The postfix notation of A+B*C-D is ABC+D- or ABC+D-.

    Data Structures

    • A tree is a nonlinear data structure.
    • A stack is a LIFO (Last-In-First-Out) data structure, whereas a queue is a FIFO (First-In-First-Out) data structure.
    • A binary search tree (BST) is a nonlinear data structure.

    Operators and Arrays

    • The multiplication operator has a higher priority than other operators.
    • Arrays have a fixed size that cannot be changed after creation.

    Linked Lists

    • Each item in a linked list is known as a node.
    • The next item in a linked list is known as a node.

    Binary Search Trees

    • Each node in a binary search tree has 2 pointers.
    • Searching an element in an AVL tree takes maximum Log2(n+1) time.

    AVL Trees

    • Deleting a parent with two childs in a straight line in an AVL tree requires single or double rotations.
    • The time taken to check the depth of an AVL tree is 1.66 Log2n or 1.44 Log2n.

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    Description

    Question about deleting a node in a Binary Search Tree and finding replacement nodes. Understanding of re-balancing is required.

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