"Mastering the Foundation: A Beginner's Guide to Data Structures and Algorithms"

Data Structures and Algorithm:

Organize the data in a way that is easy to handle and perform actions on.

Types of Data Structures:

Introduction to Algorithms: An algorithm consists of instructions to carry out a task or solve a problem (this is a theoretical way of explaining).

Let's consider an algorithm to calculate the sum of 'n' natural numbers.

There are two different ways to write it.

Way 1

public int findSum (int n){
    return n*(n+1)/2;
}

Way 2

public int findSum (int n){
              Int sum =0;
              for(int i = 1; i<=n;i++){
                           sum = sum +i;
               }
return sum;
}

Out of these two, we need to decide which is better based on time and space complexity.

Way 1 is better than Way 2 because the number of iterations is fewer and it requires less space to store the code.

A mathematical model that aids us in determining the Time and Space Complexity is called Asymptotic Analysis of an Algorithm.

Asymptotic Analysis of an Algorithm: assists in assessing the performance of an Algorithm concerning input size and its growth.

Asymptotic Notations aid us in identifying:

1. Best Case

2. Average Case

3. Worst Case

   Types of Asymptotic Notations: for performing runtime analysis of an algorithm.

• Omega(Ω) Notation

• Big O (O) Notation

• Theta (θ) Notation

Omega(Ω) Notation: denotes the lower bound of algorithm’s running time.

Big O (O) Notation: denotes the upper bound of algorithm’s running time.

Theta (θ) Notation: denotes both the upper and lower bound of an algorithm’s running time (i.e., average amount of time an algorithm can take to complete).

Big O Notation is the most used notation. Rules to be followed.

• If it’s a single processor and performs sequential execution of statements

• Assignment, Arithmetical, Logical Operations takes 1 unit of time.

• Return statements, other small/ Single operations takes 1 unit of time.

• Drop Lower order terms in polymorphic expression and constant multipliers.

  

  

  

  To be Continued..