Tutorial :What is the difference between an algorithm and a function? [closed]


Are they the same thing?



A function is a block of code in a computer program.

An algorithm is an abstract concept that describes how to solve a problem.


In mathematics, a function is "a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)" (source - google.com, define:function).

In computer science, a function is a piece of code that optionally takes parameters, optionally gives a result, and optionally has a side effect (depending on the language - some languages forbid side-effects). It must have a specific machine implementation in order to execute.

The computer science term came out of the mathematical term, being the machine implementation of the mathematical concept.

An algorithm is "a precise rule (or set of rules) specifying how to solve some problem" (source - google.com, define:algorithm). An algorithm can be defined outside of computer science, and does not have a definitive machine implementation. You can "implement" it by writing it out by hand :)

The key difference here is, in computer science, an algorithm is abstract, and doesn't have a definitive machine implementation. A function is concrete, and does have a machine implementation.


An algorithm is a set of instructions.

In computer programming, a function is an implementation of an algorithm.


An algorithm is a series of steps (a process) for performing a calculation, whereas a function is the mathematical relationship between parameters and results.

A function in programming is different than the typical, mathematical meaning of function because it's a set of instructions implementing an algorithm for calculating a function.


An algorithm describes the general idea, whereas a function is an actual working implementation of that idea.


It might be almost a philosophical question, but I'de say an algorithm is the answer(or how-to) to a problem at hand where as a function does not necerally answer one problem in itself.

What you want to do normally is split your algorithm into severals function that each has their own goal, which, in the end, will achieve the problem at hand, when used together.

Ex : You want to Sort a list of numbers. The algorightm used would be for example the Merge-sort algorithm. That specific algorithm is actually composed of more than one functions, one that will split your array, another to check for equality, another to merge everything back together, and so on.


A mathematical function is the interface, or specification of the inputs and outputs of an algorithm.

An algorithm is the precise recipe that defines the steps that may implement a function.

Confusingly, computer language designers diffuse this distinction by using the concept function, func, method, etc, to talk about both concepts.

So the distinction is one of specification vs. definition.

There is also a semantic distinction: an algorithm seeks to provide a solution to a problem. It is goal-oriented. A function simply is - there is no essential teleological component.


An algorithm is the implementation of a function.

In some cases, the algorithm is trivial:

Function: Sum of two numbers. Algorithm: int sum(int x, int y){ return x+y; }

In other cases, it is not:

Function: Best chess move. Algorithm: Move bestChessMove(State gameState){ //I don't know the algorithm. }


Algorithm is a (possibly informal but necessarily precise) sequence of instructions. Function is a formal rule that associates some input w/ a specific output. Functions implement and formalize algorithms. E.g. we can formalize "go from a to b" as go(a)=b or go(x,a)=b (w/ x the one who goes), etc. According to Wikipedia,

An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function.

So you can say that "go(ing) from a to b" is an effective method for calculating go(a)=b (if you want)


An Algorithm usually refers to the method or process used to end up with the result after mathematical processing. A Function is a subroutine used to avoid writing the same code over and over again. They are different in their uses. For instance, there may be an Algorithm that is used for encrypting data, and a function for posting code to a webpage.

Here is some further reference:




A function is a symbolic representation whereare a method is the mechanical steps needed to get the answer.

Suppose this function:

f(x) = x^ 2  

Now if I tell you to count f(5000) you have to do things that this function doesn't say. Like for example how to multiply. So really these are just symbols.

But if I have a python method for example:

x = math.pow(500, 2) # or whatever it is  

Then in this case the steps themselves for each operation are totally defined (in the libraries ;) ).

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