To answer your question, if you have a traversal algorithm for traversing the list which allocate a single pointer to do so, the traversal algorithms is considered to be of O(1) space complexity. Additionally, let’s say that traversal algorithm needs not 1 but 1000 pointers, the space complexity is still considered to be O(1). However, … Read more
Complexity A Quicksort starts by partitioning the input into two chunks: it chooses a “pivot” value, and partitions the input into those less than the pivot value and those larger than the pivot value (and, of course, any equal to the pivot value have go into one or the other, of course, but for a … Read more
Yes, nested loops are one way to quickly get a big O notation. Typically (but not always) one loop nested in another will cause O(n²). Think about it, the inner loop is executed i times, for each value of i. The outer loop is executed n times. thus you see a pattern of execution like … Read more
I’ve only scanned through the paper, but here’s a rough summary of how it all hangs together. From page 86 of the paper. … polynomial time algorithms succeed by successively “breaking up” the problem into smaller subproblems that are joined to each other through conditional independence. Consequently, polynomial time algorithms cannot solve problems in regimes … Read more
In C++11 it is required that for any standard container the .size() operation must be complete in “constant” complexity (O(1)). (Table 96 — Container requirements). Previously in C++03 .size() should have constant complexity, but is not required (see Is std::string size() a O(1) operation?). The change in standard is introduced by n2923: Specifying the complexity … Read more
Good question. Actually, I always show these 3 pictures: n = [0; 10] n = [0; 100] n = [0; 1000] So, O(N*log(N)) is far better than O(N^2). It is much closer to O(N) than to O(N^2). But your O(N^2) algorithm is faster for N < 100 in real life. There are a lot of … Read more
This is one of the most popular outlines: Regular Expression Matching Can Be Simple And Fast . Running a DFA-compiled regular expression against a string is indeed O(n), but can require up to O(2^m) construction time/space (where m = regular expression size).
See Time Complexity. The python dict is a hashmap, its worst case is therefore O(n) if the hash function is bad and results in a lot of collisions. However that is a very rare case where every item added has the same hash and so is added to the same chain which for a major … Read more
To state it different: Having a (complex) query with JOINs, SUBSELECTs, UNIONs is it possible (or not) to reduce it to a simpler, equivalent SQL statement, which is producing the same result, by using some transformation rules? This answer was written in 2009. Some of the query optimization tricks described here are obsolete by now, … Read more
Abuse of notation or not, polylog(n) does mean “some polynomial in log(n)”, just as “poly(n)” can mean “some polynomial in n”. So O(polylog(n)) means “O((log n)k) for some k”. (See Wikipedia: Polylogarithmic, or, to see it in context, Prof. Scott Aaronson’s blog: My Favorite Growth Rates.) The point is that just as we often don’t … Read more