What is the difference between polynomial time and exponential time?

O(n^2) is polynomial time. The polynomial is f(n) = n^2. On the other hand, O(2^n) is exponential time, where the exponential function implied is f(n) = 2^n. The difference is whether the function of n places n in the base of an exponentiation, or in the exponent itself.

What is exponential time complexity?

Exponential Time complexity denotes an algorithm whose growth doubles with each additon to the input data set. If you know of other exponential growth patterns, this works in much the same way. The time complexity starts off very shallow, rising at an ever-increasing rate until the end.

What is the time complexity of polynomial?

An algorithm is said to have polynomial time complexity if its worst-case running time Tworst(n) for an input of size n is upper bounded by a polynomial p(n) for large enough n≥n0. For example, if an algorithm’s worst-case running time is Tworst(n)∈O(2n4+5n3+6) then the algorithm has polynomial time complexity.

What is Linearithmic time complexity?

Linearithmic time ( O(n log n) ) is the Muddy Mudskipper of time complexities—the worst of the best (although, less grizzled and duplicitous). It is a moderate complexity that floats around linear time ( O(n) ) until input reaches advanced size.

Which of the following is an example of polynomial time complexity?

Some examples of polynomial time algorithms: The selection sort sorting algorithm on n integers performs operations for some constant A. Thus it runs in time and is a polynomial time algorithm.

Is log n polynomial time?

Yes, O(nlogn) is polynomial time. From http://mathworld.wolfram.com/PolynomialTime.html, An algorithm is said to be solvable in polynomial time if the number of steps required to complete the algorithm for a given input is O(n^m) for some nonnegative integer m, where n is the complexity of the input.

What does Linearithmic mean?

Filters. (computer science, of a procedure) Taking up to time proportional to n log(n) to run on inputs of size n. adjective.

What are the different types of time complexity?

There are different types of time complexities, so let’s check the most basic ones.

• Constant Time Complexity: O(1)
• Linear Time Complexity: O(n)
• Logarithmic Time Complexity: O(log n)
• Quadratic Time Complexity: O(n²)
• Exponential Time Complexity: O(2^n)

What is the exponential time complexity of a problem?

Similarly the exponential time complexity ( Θ (a^N) for some constant a > 1) means that if you increase that size of the problem just by 1, you need a times more operations.

Is there a sub-expoential algorithm with running time 2n O(1)?

If by subexpoential you mean 2 n o ( 1), then a conjecture in complexity theory called ETH (Exponential Time Hypothesis) implies that no N P -hard problem can have an algorithm with running-time 2 n o ( 1). Note that this class is closed under composition with polynomials.

Is there such a thing as a subexponential polynomial with no ETH?

The situation is similar to the previous one. It is closed under polynomials so no N P -hard problem can be solved in this time without violating ETH. If by subexponential you mean 2 O ( n ϵ) for some ϵ < 1 then the answer is yes, there are provably such problems.

What is the difference between exponential and subexponential functions?

As the name indicates, “subexponential” means slower than exponential. By exponential we usually mean functions in class 2 Θ ( n), or in the nicer class 2 n Θ ( 1) (which is closed under composition with polynomials). Subexponetial should be close to these but smaller.