Data Structures and Algorithms Exam Notes

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Questions and Answers

Recursion is a method in which the solution of a problem depends on:

Smaller instances of the same problem (correct)

Larger instances of different problems

Smaller instances of different problems

Larger instances of the same problem

The number of nodes in a full binary tree at level 'L' is:

$2^{L-1}$ (correct)

$2^{L+1} - 1$

$2^{L} - 1$

A queue follows the Last In First Out (LIFO) principle.

False

What is the purpose of a hash function?

To compute the location of the key in the array. Signup and view all the answers

The minimum possible height of a binary tree with 13 nodes is ___.

3 Signup and view all the answers

Which of the following data structures is more appropriate for implementing quick sort iteratively?

Stack Signup and view all the answers

Which of the following data structures permits insertion and deletion operations only on one end?

Stack Signup and view all the answers

Match the following concepts with their definitions:

Completeness = Is the strategy guaranteed to find the solution when there is one. Time Complexity = How long does it take to find a solution. Space Complexity = How much memory is needed to perform the search. Signup and view all the answers

The goal of hashing is to produce a search that takes:

O(1) time Signup and view all the answers

Which of the following data structures is linear type?

Array Signup and view all the answers

What is the time complexity of bubble sort in the best case?

O(n) Signup and view all the answers

The time complexity of bubble sort in the worst case is O(n^2).

True Signup and view all the answers

Differentiate between Linear and Non-Linear data structures.

Linear data structures have a sequential arrangement (e.g., arrays, linked lists) while non-linear data structures have a hierarchical arrangement (e.g., trees, graphs). Signup and view all the answers

In row major order, the index of an element is calculated using ______ and its row and column indices.

row size Signup and view all the answers

Match the following algorithms with their primary operations:

Bubble Sort = Rearranging elements in ascending order Postfix Evaluation = Evaluating expressions Insertion Sort = Building a sorted array incrementally Stack Operations = Pushing and popping elements Signup and view all the answers

Which of the following is NOT a characteristic of a stack?

First In First Out Signup and view all the answers

In a circular queue, the end of the queue wraps around to the front.

True Signup and view all the answers

What is a sparse matrix?

A sparse matrix is a matrix in which most of the elements are zero. Signup and view all the answers

The algorithm for quick sort has a time complexity of ______ on average.

O(n log n) Signup and view all the answers

Explain how to convert the infix expression (A + B * C) / (D - E) + F to postfix form.

Use a stack to manage operators and output the operands in the correct order by applying operator precedence. Signup and view all the answers

Study Notes

Data Structures and Algorithms Exam Notes

Recursion: A method where the solution to a problem relies on smaller instances of the same problem.
Full Binary Tree Nodes: The number of nodes at level 'L' (starting with 0) in a full binary tree is 2^L.
Data Structure for Quick Sort: A stack is a suitable data structure for implementing quick sort iteratively.
Hashing Goal: Hashing aims to achieve constant time (O(1)) for search operations.
Completeness/Time/Space Complexity:
- Completeness – Whether a strategy guarantees finding a solution if one exists.
- Time Complexity – The time taken for an algorithm to complete.
- Space Complexity – The memory required by an algorithm.
Linear Data Structure: An array is a linear data structure.
Stack Push Algorithm: When pushing an item onto a stack, you first add the item to the top location, then increment the top pointer.
Stack/Queue Operations: A stack operates on a Last-In, First-Out (LIFO) principle, whereas a queue follows First-In, First-Out (FIFO).
Hash Function: A hash function maps keys to their locations in an array.
Binary Tree Height: The minimum height of a binary tree with 13 nodes is 4.
Bubble Sort Best Case Complexity: O(n)
Linear vs. Non-Linear Data Structures: Linear data structures like arrays, linked lists, and stacks have elements arranged sequentially. Non-linear data structures like trees and graphs have more complex relationships between elements.
Row/Column Major Array Indices: How array elements are stored in memory. Row major stores row by row, and column major column by column. Index calculation depends on the method.
Postfix Expression Evaluation: Algorithm to evaluate an expression written in postfix notation using a stack.
Circular Queue Overflow/Underflow: Conditions to check for whether a circular queue is full or empty, as it's implemented in a circular array.
Stack Applications: Stacks are frequently used in function calls, undo/redo operations, and expression evaluation.
Postfix Expression Evaluation (Example): Evaluate expressions like 56 2 + *124/- by showing stack manipulation steps and final output.
Static vs. Dynamic Memory Allocation: Static memory is allocated at compile time, whereas dynamic memory allocation happens during program execution.
Sparse Matrix: A matrix with a large number of zero elements.
Polynomial Addition: Algorithm to add two polynomials.
Doubly Linked Lists: Data structure with nodes that have pointers to both the next and previous nodes.
Stack vs. Queue: Key differences explaining how they process and structure elements.
Stack Implementation using Linked List: Algorithm describing a stack's structure and operations using a linked list.
Infix to Postfix Conversion: Convert infix expressions using a stack to postfix notation.
Quick Sort Complexity: Algorithm and time complexity of quick sort, along with examples.
Insertion Sort: Algorithm and examples of insertion sort.

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Description

This quiz covers essential concepts in data structures and algorithms, focusing on recursion, binary trees, quicksort, and complexities. Understand the key operations and their characteristics, including time and space complexity, to excel in your exam. Test your knowledge to prepare effectively for your assessments!