String and Rational Numbers ADT Quiz

String ADT

• StringLength Function: Takes a string as input and returns the number of characters in the string.
• StringConcat Function: Takes two strings as input and concatenates them, returning a new string with characters from the first string followed by characters from the second string.
• StringCompare Function: Takes two strings as input and returns 'True' if they are equal and 'False' otherwise, indicating whether the strings are the same.
• StringCopy Function: Takes two strings as input and copies all characters from the second string into the first string, overwriting its content.

Rational Numbers ADT

• Definition: Represents a rational number as the quotient of two integers.
• Operations: Provides operations to compare, multiply and add rational numbers.
• Value Definition: A rational number is defined as RATIONALType and it must not be equal to 0.

Rational Number Operator Definition

• makerational Function: Takes two integers (a and b) as input, ensuring that b is not 0. It creates and returns a rational number object represented by the quotient a/b.
• Add Function: Takes two rational numbers (a and b) as input and returns a new rational number object representing the sum of the two input rational numbers, calculated as (ab+ba)/(a*b).

Algorithm Design

• Definition: Specifies the step-by-step instructions to solve a problem, taking an input instance and producing the required output.
• Multiple Correct Algorithms: A single problem can have various algorithms, ensuring the desired output.

Evaluating Algorithms

• Good algorithm characteristics:
  • Efficiency: Considers both the running time and the space used by the algorithm.
  • Input Size Dependency: Its efficiency is measured in relation to the size of the input data.

Measuring Running Time

• Method: Involves implementing the algorithm, running it with different input sizes and compositions, and measuring the time taken using functions like clock() to get an accurate execution time.
• Limitations of Experimental Studies: It requires implementation and testing, is limited to a specific set of inputs, and demands identical hardware and software environments for comparing different algorithms.

Pseudo-Code

• Description: A mixture of natural language and high-level programming constructs that represents the main ideas of an algorithm implementation.
• Components:
  • Expressions: Uses mathematical symbols for numeric and boolean expressions, along with assignment (←) for assignment and equality (=) for comparison.
  • Method Declarations: Defined as Algorithm name(param1, param2).
  • Programming Constructs: Includes decision structures (if-then-else), while-loops, repeat-loops, for-loops, and array indexing.
  • Methods: Involves calls to methods like object method(args) and returns return value.

Sorting Algorithm Analysis

• Requirements:
  • Correctness: Ensures that for any given input, the algorithm halts with a sorted output where b1 < b2 < b3 ...
  • Running Time: Dependent on the number of elements in the input sequence and the level of initial sortedness.

realloc() Function

• Purpose: Resizes an existing memory block allocated previously using malloc.
• Situations: Used when the allocated memory is insufficient or too generous for the current application.
• Syntax: ptr_var = realloc(ptr_var, new_size); where ptr_var is the pointer to the starting address of the memory block and new_size is the desired size.

malloc() Function Example

• Code Illustration: Demonstrates the usage of malloc and realloc for dynamic memory allocation.
• Steps:
  • Allocates 20 characters of memory using malloc.
  • Copies "ABCD" string into the allocated memory.
  • Uses realloc to resize the memory to 100 characters.
  • Copies "space is extended upto 100 characters" into the resized memory.
  • Finally, frees the allocated memory using free.

Advantages of Dynamic Data Structures

• Efficient Memory Utilization: Dynamic structures only allocate memory when needed and free it when not in use.
• Adaptability: Allows resizing at runtime to adjust for varying data sizes.

Application of Stacks

• Expression Evaluation and Syntax Parsing: Processing expressions and parsing syntax.
• Balancing of Symbols: Checking for balanced parentheses, brackets, and braces.
• Infix to Postfix/Prefix Conversion: Converting expressions between different notations.
• Reverse a String: Reversing the order of characters in a string.
• Redo-Undo Features: Implementing features like undo/redo in editors and other applications.
• Forward/Backward Navigation: Using stacks for navigation history in web browsers.
• Algorithmic Applications: Employed in diverse algorithms like Tower of Hanoi, tree traversals, stock span problem, and histogram problem.

Backtracking

• Definition: A recursive technique that incrementally builds solutions to problems by adding one piece at a time and discarding incorrect solutions.
• Example: Finding the correct path in a maze, Knight's Tour problem, Rat in a Maze, N-Queens problem, and Sudoku Solver.

Backtracking and Maze Problem

• Illustration: Describes how stacks can be used to track and revert back from incorrect paths in a maze, enabling exploration of alternate paths.
• Stack Usage: Push each reached point onto the stack to remember the route taken. When encountering a wrong path, pop the stack to backtrack to the previous point.

Test your knowledge on the Abstract Data Types (ADTs) related to strings and rational numbers. This quiz covers essential functions such as string length, concatenation, comparison, and the definition and operations of rational numbers. Challenge yourself with questions designed to reinforce your understanding of these concepts.