Definition and Characteristics of Algorithms

What is an Algorithm?

• A finite set of steps to solve a particular problem.
• Can be written in any programming language (C, Java, Python) or in layman terms as steps.
• Example: Sum of two numbers
  • Step 1: Read A
  • Step 2: Read B
  • Step 3: Sum = A + B
  • Step 4: Print Sum

Characteristics of an Algorithm

1. Finite Steps
   • Must contain a finite number of steps/instructions.
   • Each instruction should take a finite amount of time.
2. Unambiguous
   • Instructions should be clear and unambiguous.
   • Use relevant and correct symbols.
3. Analysis
   • Process of comparing two algorithms.
   • Involves constraints like time, space, number of registers, and network bandwidth.
   • Most important parameters: Time and Space.

Types of Analysis

1. Priory Analysis
   • Analysis before execution.
   • Independent of hardware.
   • Calculate the number of iterations.
   • Example: Time complexity in terms of iterations.
2. Posterior Analysis
   • Analysis after execution.
   • Dependent on hardware.
   • Measures exact time taken (e.g., 0.4 seconds).
   • Example: Program execution time varies with hardware.

Comparison of Priory and Posterior Analysis

• Priory gives an approximate value.
• Posterior gives an exact value but is hardware-dependent.
• Priory is preferred due to its hardware independence and uniform values.

Asymptotic Notations

• Used to represent time complexity.
• Types:
  • Big O notation
  • Big Omega
  • Theta
  • Small o
  • Small omega

Upcoming Topics

• Detailed explanation of asymptotic notations in the next video.

Thank you!