Data Structures: Stack, Queue, Link list, Tree, Searching and sorting
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Questions and Answers

What action is taken when a stack overflow is detected during the PUSH procedure?

  • The operation is completed without changes.
  • The top element is removed.
  • An error message 'STACK OVERFLOW' is written. (correct)
  • The stack is automatically resized.
  • Which function would you use to safely remove the top element from the stack?

  • PUSH
  • POP (correct)
  • INSERT
  • PEEP
  • What is the main purpose of the PEEP function in stack operations?

  • To remove the top element and return it.
  • To check if the stack is full.
  • To retrieve the value of the ith element from the top without alteration. (correct)
  • To add an element without removing any.
  • During the POP operation, what condition indicates that a stack underflow has occurred?

    <p>TOP = 0</p> Signup and view all the answers

    What is the first step when performing the PUSH operation on a stack?

    <p>Check for stack overflow</p> Signup and view all the answers

    What defines a sparse matrix?

    <p>A matrix with a significant number of zero elements.</p> Signup and view all the answers

    Which of the following statements is true regarding dense matrices?

    <p>Dense matrices consist mostly of non-zero elements.</p> Signup and view all the answers

    How may non-zero entries of a sparse matrix be stored efficiently?

    <p>In a row-major order in a linear list.</p> Signup and view all the answers

    What happens when converting a polynomial equation to array representation?

    <p>It enables various operations to be performed on matrices.</p> Signup and view all the answers

    What is the significance of the algorithm for converting between polynomial equations and array representations?

    <p>It establishes a direct correlation between polynomial operations and matrix operations.</p> Signup and view all the answers

    What information is necessary to create a structure for a sparse matrix?

    <p>Row and column indices of non-zero entries and the number of rows and columns</p> Signup and view all the answers

    In a linear representation of the sparse matrix, how many fields does each non-zero entry need?

    <p>Three fields: row, column, and value</p> Signup and view all the answers

    What is a key advantage of using a linear list representation for sparse matrices?

    <p>It requires less memory than a dense matrix of the same size</p> Signup and view all the answers

    Which of the following entries corresponds to the location of the value '3' in the 4x8 matrix?

    <p>Row 2, Column 4</p> Signup and view all the answers

    From the given 4x8 matrix, how many non-zero entries are present?

    <p>8</p> Signup and view all the answers

    What happens if the front pointer F is equal to 0 during the DQINSERT_FRONT procedure?

    <p>An 'EMPTY' message is written and the procedure returns.</p> Signup and view all the answers

    In the DQDELETE_REAR procedure, what is checked first to prevent underflow?

    <p>If R is equal to 0.</p> Signup and view all the answers

    What is the effect of decrementing the front pointer F in the DQINSERT_FRONT procedure?

    <p>It moves the insertion point to the previous index in the queue.</p> Signup and view all the answers

    What is the purpose of the 'Queue empty?' check in the DQDELETE_REAR procedure?

    <p>To determine if the rear pointer should reset.</p> Signup and view all the answers

    During the DQINSERT_FRONT procedure, what happens if the procedure finds that F=1?

    <p>An 'OVERFLOW' message is written and the procedure returns.</p> Signup and view all the answers

    What is the primary purpose of attaching the old right child’s old left subtree to the right subtree of the new left child?

    <p>To maintain the balance of the tree</p> Signup and view all the answers

    In an unbalanced node where X is the node being rotated, what is the immediate consequence of performing a right rotation?

    <p>Node Y becomes the parent of node X</p> Signup and view all the answers

    Which of the following nodes remains unchanged during a right rotation around an unbalanced node X?

    <p>Node T1</p> Signup and view all the answers

    What is the largest value expected to be in the final structure after rotation if the initial node X has a right child Y with a value of 70?

    <p>90</p> Signup and view all the answers

    When performing a left rotation, what adjustment is made regarding T3?

    <p>T3 is attached as the right child of node X</p> Signup and view all the answers

    Study Notes

    Sparse Matrix

    • A sparse matrix is a matrix with many zero elements.
    • Dense matrices are matrices that are not sparse.
    • A sparse matrix can be represented as a linear list in row-major order, storing only the non-zero elements.
    • Each element in the linear list representation has three fields: row, column, and value.
    • This representation saves space and time compared to a traditional two-dimensional array.

    Stack Operations

    • PUSH (S, TOP, X): Inserts an element X to the top of a stack S, represented by a vector with a pointer TOP indicating the top element.
      • Steps:
        • Check for stack overflow (TOP ≥ N).
        • Increment TOP.
        • Insert element X at S[TOP].
    • POP (S, TOP): Removes the top element from a stack S and returns it.
      • Steps:
        • Check for stack underflow (TOP = 0).
        • Decrement TOP.
        • Return the former top element (S[TOP + 1]).
    • PEEP (S, TOP, I): Returns the value of the ith element from the top of the stack S without deleting it.

    Double-Ended Queue (DQueue) Operations

    • DQINSERT_FRONT (Q, F, R, N,Y): Inserts an element Y at the front of the queue Q, with pointers F and R for the front and rear elements, respectively.
      • Steps:
        • Check for overflow (if F = 0 or F = 1).
        • Decrement the front pointer (F  F-1).
        • Insert element Y at Q[F].
    • DQDELETE_REAR (Q, F, R): Deletes and returns the last element from the front of the queue Q.
      • Steps:
        • Check for underflow (if R = 0).
        • Store the last element in a temporary variable Y.
        • Check if the queue is empty (if R = F). If yes, set R  F  0. Otherwise, decrement R (R  R-1).
        • Return the element Y.

    AVL Tree Rotations

    • AVL Tree Rotations are used to maintain the balance of an AVL tree after insertion or deletion of nodes.
    • They involve a sequence of transformations to ensure the tree remains balanced and has a height difference of at most one between the left and right subtrees of any node.
    • Left Rotation: Performed when the right subtree of a node becomes too tall.
    • Right Rotation: Performed when the left subtree of a node becomes too tall.
    • The goal is to restore the balance and maintain the properties of an AVL tree.

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    Description

    This quiz covers the concepts of sparse matrices and stack,queue,link list,tree operations including push, pop, and peep.concepts of searching and sorting techniques given in pdf

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