complexity-theory

In .NET 4.0+, a class SortedSet<T> has a method called GetViewBetween(l, r) , which returns an interface view on a tree part containing all the values between the two specified. Given that SortedSet<T> is implemented as a red-black tree, I naturally expect it to run in O(log N) time. The similar method in C++ is std::set::lower_bound/upper_bound , in Java it's TreeSet.headSet/tailSet , and they are logarithmic. However, that is not true. The following code runs in 32 sec, whereas the equivalent O(log N) version of GetViewBetween would make this code run in 1-2 sec. var s = new SortedSet<int>()

This question already has an answer here: What is a plain English explanation of “Big O” notation? 39 answers What is Big O notation? Do you use it? I missed this university class I guess :D Does anyone use it and give some real life examples of where they used it? See also: Big-O for Eight Year Olds? Big O, how do you calculate/approximate it? Did you apply computational complexity theory in real life? Mecki One important thing most people forget when talking about Big-O, thus I feel the need to mention that: You cannot use Big-O to compare the speed of two algorithms. Big-O only says how

There is an array of size n and the elements contained in the array are between 1 and n-1 such that each element occurs once and just one element occurs more than once. We need to find this element. Though this is a very FAQ, I still haven't found a proper answer. Most suggestions are that I should add up all the elements in the array and then subtract from it the sum of all the indices, but this won't work if the number of elements is very large. It will overflow. There have also been suggestions regarding the use of XOR gate dup = dup ^ arr[i] ^ i , which are not clear to me. I have come up