The Function T(n)

What is?

T(n) is a function that represents the amount of a resource (usually time) needed to run an algorithm that processes an input of size n. Its purpose is to evaluate the efficiency and scalability of an algorithm.

Why Determine T(n):

• Measure performance: Understand how the algorithm’s resource consumption grows as the input size increases.
• Compare algorithms: Compare different algorithms to choose the most efficient one.
• Predict scalability: Estimate how well the algorithm performs with larger inputs.
• Optimize solutions: Identify and improve resource-intensive parts of the algorithm.

How Determine T(n):

Steps to Determine T(n):

• Identify the parameter that defines the problem size (n).
• Assign an abstract cost to each line of code.
• Determine how many times each line is executed.
• Calculate T(n) based on these executions.

Apply simplifications to make T(n) easier to interpret.

• Simplifications Used:
• Abstract costs for operations.
• Grouping of constants.
• Ignoring lower-order terms.

Ignoring the coefficient of the highest-order term. In short, T(n) helps us analyze, compare, and optimize algorithms by understanding their resource consumption.