Introduction to Data Structures and Algorithms

Introduction to Data Structure

• Data structure is a fundamental concept in computer science
• It deals with the organization, storage, and retrieval of data in a computer

Pointers and Dynamic Memory Allocation

• Pointers are variables that hold memory addresses as their values
• Dynamic memory allocation is a technique to allocate memory at runtime
• It allows for efficient use of memory and enables the creation of dynamic data structures

Algorithm Definition and Characteristics

• An algorithm is a well-defined procedure to solve a problem
• Characteristics of an algorithm include:
  • Finiteness: it must terminate after a finite number of steps
  • Definiteness: each step is precisely defined
  • Effectiveness: it can be performed by a computer
  • Correctness: it produces the correct output

Algorithm Analysis

• Algorithm analysis is the process of evaluating the performance of an algorithm
• Two key metrics used in algorithm analysis are:
  • Time Complexity: the amount of time an algorithm takes to complete
  • Space Complexity: the amount of memory an algorithm uses

Asymptotic Notation

• Asymptotic notation is a mathematical notation used to describe the time and space complexity of an algorithm
• It provides a way to measure the performance of an algorithm as the input size increases

Types of Data Structure

• Data structures can be classified into:
  • Primitive data structures (e.g., integers, characters)
  • Composite data structures (e.g., arrays, linked lists)
  • Abstract data structures (e.g., stacks, queues)

Abstract Data Types (ADT)

• An ADT is a high-level representation of a data structure
• It defines the operations that can be performed on a data structure without specifying how it is implemented

Introduction to Arrays and Structure

• An array is a collection of elements of the same data type stored in contiguous memory locations
• A structure is a collection of elements of different data types stored in contiguous memory locations

Types of Array and Representation of Array

• Arrays can be classified into:
  • One-dimensional arrays
  • Multi-dimensional arrays
• Arrays can be represented in memory using:
  • Row-major order
  • Column-major order

Polynomial Representation and Evaluation

• A polynomial is an expression consisting of variables and coefficients
• Polynomial representation can be done using:
  • Coefficient representation
  • Array representation
• Polynomial evaluation involves computing the value of a polynomial for a given input

Addition of Polynomial

• Polynomial addition involves adding two or more polynomials
• It can be performed using the following steps:
  • Add corresponding coefficients
  • Combine like terms

Self Referential Structure

• A self-referential structure is a data structure that references itself
• Examples of self-referential structures include:
  • Linked lists
  • Trees