Discrete Math Chapter 7: Computation.

For-loop

A for-loop specifies the number of iterations in advance, via the beginning and ending index values.

Pseudocode

A language in between written English and a computer language. Steps are formatted carefully as indented lists so as to convey the structure of the approach. The steps themselves are expressed in brief English phrases or mathematical symbols.

Algorithm

A step-by-step method for solving a problem

While-loop

A while-loop iterates an unknown number of times, ending when a certain condition becomes false.

Polynomial Time

An algorithm is called efficient if its running time is O(nk) for some fixed constant k.

Asymptotic Notation

Asymptotic notation is a mathematical framework to classify functions according to their rate of growth. Asymptotic notation applies to any function whose domain is the set of natural numbers and whose target is the set of positive real numbers. The classification using Oh, Ω, and Θ notation covered here ignores constant factors and low order terms.

Iteration

Each repetition in a for-loop is called an iteration.

Computational Complexity

The amount of a particular resource used by an algorithm.

Space Complexity

The amount of memory used by an algorithm.

Asymptotic Time Complexity

The asymptotic time complexity of an algorithm characterizes the asymptotic growth of the algorithm's time complexity function f(n).

Input Size

The terms in which time and space efficiency are measured.

Time Complexity

The time an algorithm requires to run. The time complexity of an algorithm is defined by a function f: N → N such that f(n) is the maximum number of atomic operations performed by the algorithm on any input of size n.

Worst-case Complexity

The worst-case analysis determines the running time of the algorithm on the input that takes the longest time.

Constant Factors

Values that are fixed and do not change as the variable gets larger.