Quicksort has O(n2) worst-case runtime and O(nlogn) average case runtime. However, it’s superior to merge sort in many scenarios because many factors influence an algorithm’s runtime, and, when taking them all together, quicksort wins out. In particular, the often-quoted runtime of sorting algorithms refers to the number of comparisons or the number of swaps necessary … Read more
Your first mistake is thinking that ASCII encoding and Base64 encoding are interchangeable. They are not. They are used for different purposes. When you encode text in ASCII, you start with a text string and convert it to a sequence of bytes. When you encode data in Base64, you start with a sequence of bytes … Read more
According to Pippenger [1996], when comparing a Lisp system that is purely functional (and has strict evaluation semantics, not lazy) to one that can mutate data, an algorithm written for the impure Lisp that runs in O(n) can be translated to an algorithm in the pure Lisp that runs in O(n log n) time (based … Read more
A sorting algorithm is said to be stable if two objects with equal keys appear in the same order in sorted output as they appear in the input array to be sorted. Some sorting algorithms are stable by nature like Insertion sort, Merge Sort, Bubble Sort, etc. And some sorting algorithms are not, like Heap … Read more
f ∈ O(g) says, essentially For at least one choice of a constant k > 0, you can find a constant a such that the inequality 0 <= f(x) <= k g(x) holds for all x > a. Note that O(g) is the set of all functions for which this condition holds. f ∈ o(g) … Read more
For any optimization, it’s always best to test, test, test. I would try at least sorting networks and insertion sort. If I were betting, I’d put my money on insertion sort based on past experience. Do you know anything about the input data? Some algorithms will perform better with certain kinds of data. For example, … Read more
I was presented with this problem about a year ago when it came to looking up user entered information about a oil rig in a database of miscellaneous information. The goal was to do some sort of fuzzy string search that could identify the database entry with the most common elements. Part of the research … Read more
Tarjan’s strongly connected components algorithm has O(|E| + |V|) time complexity. For other algorithms, see Strongly connected components on Wikipedia.
That heavily depends on the structure of the search tree and the number and location of solutions (aka searched-for items). If you know a solution is not far from the root of the tree, a breadth first search (BFS) might be better. If the tree is very deep and solutions are rare, depth first search … Read more
Keep 2 stacks, let’s call them inbox and outbox. Enqueue: Push the new element onto inbox Dequeue: If outbox is empty, refill it by popping each element from inbox and pushing it onto outbox Pop and return the top element from outbox Using this method, each element will be in each stack exactly once – … Read more