The purpose of the Big-O notation is to find what is the dominant factor in the asymptotic behavior of a function as the value tends towards the infinity. As we walk through the function domain, some factors become more important than others. Imagine f(n) = n^3+n^2. As n goes to infinity, n^2 becomes less and … Read more
This seems to be a question of mislead, because I happened to read that book just now. This part of text in the book is a typo! Here is the context: =================================================================== Question: What is the running time of this code? 1 public String makeSentence(String[] words) { 2 StringBuffer sentence = new StringBuffer(); 3 for … Read more
Big-O is an upper bound. Big-Theta is a tight bound, i.e. upper and lower bound. When people only worry about what’s the worst that can happen, big-O is sufficient; i.e. it says that “it can’t get much worse than this”. The tighter the bound the better, of course, but a tight bound isn’t always easy … Read more
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 much slower an algorithm will get (approximately) if you double the number of items processed, or how much faster it will get … Read more
map, set, multimap, and multiset These are implemented using a red-black tree, a type of balanced binary search tree. They have the following asymptotic run times: Insertion: O(log n) Lookup: O(log n) Deletion: O(log n) hash_map, hash_set, hash_multimap, and hash_multiset These are implemented using hash tables. They have the following runtimes: Insertion: O(1) expected, O(n) … Read more
Also take a look at related sorts too: pigeonhole sort or counting sort, as well as radix sort as mentioned by Pukku.
about the version field UPDATE1: In my memory, a lot of (maybe all?) collections in BCL have the field version. First, about foreach: according to this msdn link The foreach statement repeats a group of embedded statements for each element in an array or an object collection. The foreach statement is used to iterate through the collection to get … Read more
Is there anything in the JavaScript guaranteeing that the values are looked up in O(1) time? No. JavaScript does not give any complexity guarantees whatsoever, except for ES6 collections. I know the access operator [] gives a seasoned programmer the impression that he’s dealing with an O(1) lookup structure Yes you are, this is a … Read more
The theoretical answers from everyone else are all neat, but let’s be pragmatic. ActionScript provides the tools you need so that you don’t even have to write a loop in this case! First, note that Math.min() and Math.max() can take any number of arguments. Also, it’s important to understand the apply() method available to Function … Read more
It sounds like what you are asking for is an extention of the Halting Problem. I do not believe that such a thing is possible, even in theory. Just answering the question “Will this line of code ever run?” would be very difficult if not impossible to do in the general case. Edited to add: … Read more