Aug 24, 2015 · The typical examples are ones that deal with binary search. For example, a binary search algorithm is usually O(log n). If you have a binary search tree, lookup, insert and delete are all O(log n) complexity. Any situation where you continually partition the space will often involve a log n component.

Apr 20, 2016 · I see where most readings online derive that the Big-Oh notation of a Binary Search is O(log(n)), but doesn't this assume a balanced tree? What if the tree is completely unbalanced (i.e. similar to a linked list). In this case the height of the tree is not log(n) it is n. Binary Search doesn't assume a tree at all. Binary Search assumes a data ...

No, O(log n) + O(log n) is not O(n). It is still O(log n). When we have a big-O formula multiplied by a constant, it is equivalent to the value without the multiplied constant. So: O(k * g) = O(g) where k is a constant, non-zero factor and g is a bounding function.

Sep 14, 2015 · The complexity of merge sort is O(nlog(n)) and NOT O(log(n)). Merge sort is a divide and conquer algorithm. Think of it in terms of 3 steps: The divide step computes the midpoint of each of the sub-arrays. Each of this step just takes O(1) time. The conquer step recursively sorts two subarrays of n/2 (for even n) elements each.

Apr 2, 2016 · Since Hashlife runs the Game of Life which is Turing complete, it can run any Turing-computable program. If the complexity for all programs run through Hashlife would be reduced by log(n), that would for example get the (NP-complete) SAT problem (where the best known implementations have O(2^n)) run in O(n).

Jul 18, 2015 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Dec 19, 2018 · Congratulations, you have re-invented counting sort! (I'm not being sarcastic, things independently being re-invented multiple times is a good thing, it shows that it is a natural and good way to solve problems.)

The big O notation is defined as a set: So contains all functions that are - starting from some arbitrary large point - always smaller than g.

3-6. [5] Describe how to modify any balanced tree data structure such that search, insert, delete, minimum, and maximum still take O(log n) time each, but successor and predecessor now take O(1) time each. Which operations have to be modified to support this? Solution: Maintain extra pointers to the successor and predecessor.

Sep 8, 2015 · That depends on the context, but typically, m and n are the sizes of two separate parts of the dataset, or two separate properties of the dataset, for example, filling a m×n array.