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?

TOP = 0 Signup and view all the answers

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

Check for stack overflow Signup and view all the answers

What defines a sparse matrix?

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

Which of the following statements is true regarding dense matrices?

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

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

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

What happens when converting a polynomial equation to array representation?

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

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

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

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

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

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

Three fields: row, column, and value Signup and view all the answers

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

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

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

Row 2, Column 4 Signup and view all the answers

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

8 Signup and view all the answers

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

An 'EMPTY' message is written and the procedure returns. Signup and view all the answers

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

If R is equal to 0. Signup and view all the answers

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

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

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

To determine if the rear pointer should reset. Signup and view all the answers

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

An 'OVERFLOW' message is written and the procedure returns. 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?

To maintain the balance of the tree 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?

Node Y becomes the parent of node X Signup and view all the answers

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

Node T1 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?

90 Signup and view all the answers

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

T3 is attached as the right child of node X 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