Mathematical Induction

Mathematical Induction

It is a method of proof used in mathematics to establish the truth of an infinite sequence of statements.

Base Case, Inductive Step

Mathematical Induction consists of what?

Base Case

It verifies that the statement holds for the initial value. this step confirms that the statement is true for the first element in the sequence.

Inductive Step

It assumes that the statement holds for some arbitrary positive integer k.

Induction Hypothesis

What do you call this assumption?

Assuming that the statement holds for some arbitrary positive integer k.

Principle of Mathematical Induction

If both the base case and the inductive step are successfully proven, then the statement is true for all positive integers n.

Proof by Induction in Computer Science

A mathematical technique used to prove statements when dealing with recursively defined objects such as trees, expressions, and more.

Correctness, speed, resources, processors, developer effort

What are the Algorithm Analysis Criteria?

the process of determining how processing time increases the size of the problem increases

What is the Running Time Analysis?

Rate at which the running time increases as a function of input.

What is a Rate of Growth?

Express the running time of a given algorithm as a function of the input size f(n)

How to compare algorithms?

Constant

Name: 1

Logarithmic

Name: logn

Linear

Name: n

Linear Logarithmic

Name: n(logn)

Quadratic

Name: n²

Cubic

Name: n³

Exponential

Name: 2^n

Constant, Logarithmic, Linear, Linear Logarithmic, Quadratic, Cubic, Exponential

What are the different types of time complexity?