An algorithm is a defined set of rules or instructions used to solve problems or perform calculations, transforming input into output. Key characteristics include input, output, finiteness, and effectiveness, while factors to consider during design involve modularity and maintainability. Efficiency is analyzed both theoretically and practically using asymptotic notations such as big-O, omega, and theta to evaluate time and space requirements.

1. Algorithm
What is an Algorithm?
• An algorithm is a process or a set of rules required to
perform calculations or some other problem-solving
operations.
• Contains the finite set of instructions which are being
carried in a specific order to perform the specific task.
• It is not the complete program or code; it is just a
solution (logic) of a problem
• Transforms input of a problem to output
Algorithm = Input + Process + Output

2. Algorithm
Characteristics of an Algorithm
The following are the characteristics of an algorithm:
• Input
• Output
• Unambiguity
• Finiteness
• Effectiveness
• Language Independent

3. Algorithm
Why do we need algorithm?
• Scalability
• Performance
Any real time example

4. Algorithm
Factors of Algorithm:
Consider during Algorithm Design:
• Modularity
• Correctness
• Maintainability
• Functionality
• Robustness
• User friendly
• Extensibility

5. Algorithm
Categories of Algorithm:
• Sort
• Search
• Insert
• Delete
• Update

6. Analysis of Algorithm
2 levels of Analysis
1. Priori Analysis
Theoretical analysis
Done before implementing the algorithm
2. Posterior Analysis
Practical analysis
Achieved by using any programming language
How much running time and space

7. Asymptotic notations
• The efficiency of an algorithm depends on the amount of
time, storage and other resources required to execute the
algorithm.
• The efficiency is measured with the help of asymptotic
notations.
• Algorithm not have same performance for different input
types
• “The study of change in performance of the algorithm
with the change in the order of the input size is defined as
asymptotic analysis”.

8. Asymptotic notations
• Mathematical notations
• Describe running time of algorithm
• There are mainly three asymptotic notations:
1. Big-O notation
2. Omega notation
3. Theta notation

9. Analysis of Algorithm
It is determination of amount of time and space
Generally perform following types of analysis:
Worst case – Big Oh (MAX)
Best case - Big Omega
Average case – Big Theta
Amortized – Overall cost