Generally, a program is only an algorithm if it stops eventually. First, understand that there is no good formal definition of "algorithm" at the time of writing. The key word here is "formal".
What we know is that whatever an "algorithm" is, it sits somewhere between "mathematical function" and "computer program". A mathematical function is formal notion of a mapping from inputs to outputs. So, for example, "sort" is a mapping between a sequence of orderable items and a sequence of orderable items of the same type, which maps each sequence to its ordered sequence. This function could be implemented using different algorithms e. Each algorithm, in turn, could be implemented using different programs even given the same programming language.
So the best handle that we have on what an "algorithm" is, is that it's some kind of equivalence class on programs, where two programs are equivalent if they do "essentially the same thing". Any two programs which implement the same algorithm must compute the same function, but the converse is not true. Similarly, there is an equivalence class between algorithms, where two algorithms are equivalent if they compute the same mathematical function.
There are some obvious things that we should include. For example, two programs are essentially the same if they differ only by variable renamings. Most models of programming languages have native notions of "equivalence" e. Whatever equivalence relation we pick, this gives us some structure. Algorithms form a category by virtue of the fact that they are the quotient category of programs.
Some interesting equivalence relations are known to give rise to interesting categorical structures; for example, the category of primitive recursive algorithms is a universal object in the category of categories. Whenever you see interesting structure like that, you know that this line of enquiry will probably be useful.
Ultimately, the difference is one of perspective. A program is a program: a sequence of statements in some language, perhaps a programming language or machine-level instructions. Algorithms are usually described at a higher level than machine instructions or programming language statements but just how high a level is rather flexible.
As you say, an algorithm is something like "a process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer. Usually, though, we speak of programs implementing algorithms. Usually, when describing an algorithm, we avoid the low-level detail of exactly how things are implemented, assuming that a competent programmer would be able to implement it in the langauge of their choosing. Algorithms in the Turing-complete mindset are usually specified by input and output.
Real programs do more; they. These things are usually not considered in algorithms or theory of computation, but are essential for most programs. A program therefore does not even need to solve a problem. I'm sure we can all think of several programs that have caused more problems than they've solved. A program can be an implementation of many algorithms, or an algorithm can be implemented by patching together many programs.
A program can even contain no algorithms. For example, the empty program which simply exits, or perhaps even a Hello World, could be considered a program with no algorithm. Since an algorithm solves a specific problem, it is focused on a specific whole concept.
An algorithm therefore provides abstract steps for processing one set of related information into a different set of derived information. A program does not require its constituents to be at all conceptually related. For example, a program can have an easter egg, but a thing properly called an algorithm should not. You can have a virus or trojan lurking in a program, but not in an algorithm. The closest an algorithm can get to this would be something like a backdoor in an encryption algorithm, where the planned flaw is part of the information relationship established by the algorithm.
And lastly, a program, as it is short for a computer program, tautologically requires a computer. An algorithm does not. If I systematically separate the shirts, pants, and socks from my laundry before putting them away, this is an algorithm.
It deals with related inputs and outputs, can be described in a flow chart, and has calculable consequences in terms of efficiency for example, the number of clothing pieces which must be compared to find matching socks. An algorithm is a concept or idea. It is a formal approach for solving a problem.
Algorithms can be expressed, or implemented, in a variety of programming language usually, almost any language can implement any algorithm.
For some examples you should read through the Sorting Algorithms in Wikipedia. A computer program is a specific sequence of instructions in a specific programming language.
A program may contain the implementation of many algorithms. The result from 3. The next digit in 52 is 2. Since this is the last digit 17 is the final answer. If you continue the division you will find the fractional part. Let's go a step higher and continue with some more complex algorithm examples. Given is the array prices with elements prices[]. The problem consists of two parts. For part 1 we iterate through the whole array, starting with index 0.
This is the same as multiplying it by 0. The last note here — we use short version of the multiply-assign operator:. The last of the algorithm examples will be more branched. Check prime number. Find the factorial of a number. Print the Fibonacci sequence.
Check leap year. DSA Introduction What is an algorithm? Related Topics Merge Sort Algorithm. What is an Algorithm? Each step in the algorithm should be clear and unambiguous.
Algorithms should be most effective among many different ways to solve a problem. An algorithm shouldn't include computer code. Instead, the algorithm should be written in such a way that it can be used in different programming languages. Algorithm Examples Algorithm to add two numbers Algorithm to find the largest among three numbers Algorithm to find all the roots of the quadratic equation Algorithm to find the factorial Algorithm to check prime number Algorithm of Fibonacci series Algorithm 1: Add two numbers entered by the user Step 1: Start Step 2: Declare variables num1, num2 and sum.
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