complexity-theory

The question of whether P=NP is perhaps the most famous in all of Computer Science. What does it mean? And why is it so interesting? Oh, and for extra credit, please post a proof of the statement's truth or falsehood. :) P stands for polynomial time. NP stands for non-deterministic polynomial time. Definitions: Polynomial time means that the complexity of the algorithm is O(n^k), where n is the size of your data (e. g. number of elements in a list to be sorted), and k is a constant. Complexity is time measured in the number of operations it would take, as a function of the number of data items

What is the computational complexity of the n-dimensional FFT with m points along each dimension? For a 1D FFT it's O(m log m) . For a 2D FFT you have to do m x 1D FFTs in each axis so that's O(2 m^2 log m) = O(m^2 log m) . It's too early in the morning here to get my head round n >= 3 but I'm guessing it's probably: O(m^n log m) 来源： https://stackoverflow.com/questions/6514861/computational-complexity-of-the-fft-in-n-dimensions

The quicksort algorithm has an average time complexity of O(n*log(n)) and a worst case complexity of O(n^2). Assuming some variant of Hoare’s quicksort algorithm, what kinds of input will cause the quicksort algorithm to exhibit worst case complexity? Please state any assumptions relating to implementation details regarding the specific quicksort algorithm such as pivot selection, etc. or if it's sourced from a commonly available library such as libc. Some reading: A Killer Adversary for Quicksort Quicksort Is Optimal Engineering a Sort Function Introspective Sorting and Selection Algorithms

I was studying the merge-sort subject that I ran into this concept that the number of comparisons in merge-sort (in the worst-case, and according to Wikipedia ) equals (n ⌈lg n⌉ - 2 ⌈lg n⌉ + 1); in fact it's between (n lg n - n + 1) and (n lg n + n + O(lg n)). The problem is that I cannot figure out what these complexities try to say. I know O(nlogn) is the complexity of merge-sort but the number of comparisons? Why to count comparisons There are basically two operations to any sorting algorithm: comparing data and moving data. In many cases, comparing will be more expensive than moving. Think

Can anyone think of a linear time algorithm for determining a majority element in a list of elements? The algorithm should use O(1) space. If n is the size of the list, a majority element is an element that occurs at least ceil(n / 2) times. [Input] 1, 2, 1, 1, 3, 2 [Output] 1 [Editor Note] This question has a technical mistake. I preferred to leave it so as not to spoil the wording of the accepted answer, which corrects the mistake and discusses why. Please check the accepted answer. I would guess that the Boyer-Moore algorithm (as linked to by nunes and described by cldy in other answers) is

When dealing with small projects, what do you feel is the break even point for storing data in simple text files, hash tables, etc., versus using a real database? For small projects with simple data management requirements, a real database is unnecessary complexity and violates YAGNI. However, at some point the complexity of a database is obviously worth it. What are some signs that your problem is too complex for simple ad-hoc techniques and needs a real database? Note: To people used to enterprise environments, this will probably sound like a weird question. However, my problem domain is