Problem Detail: For Prim’s and Kruskal’s Algorithm there are many implementations which will give different running times. However suppose our implementation of Prim’s algorithm has runtime $O(|E| + |V|cdot log(|V|))$ and Kruskals’s algorithm has runtime $O(|E|cdot log(|V|))$. What is the base Read More …
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Shortest non intersecting path for a graph embedded in a euclidean plane (2D)
Problem Detail: What algorithm would you use to find the shortest path of a graph, which is embedded in an euclidean plane, such that the path should not contain any self-intersections (in the embedding)? For example, in the graph below, you Read More …
Do any decision problems exist outside NP and NP-Hard?
Problem Detail: This question asks about NP-hard problems that are not NP-complete. I’m wondering if there exist any decision problems that are neither NP nor NP-hard. In order to be in NP, problems have to have a verifier that runs in Read More …
Average Time Complexity of Two Nested Loops
Problem Detail: Recently I have had this question in one of my interviews. You have 1 Million sorted integer, you have a value of $x$, compare each pair in this array and if the addition of two pair is less or Read More …
Greedy algorithms tutorial
Problem Detail: Could anyone point me to simple tutorial on greedy algorithm for Minimum Spanning tree – Kruskal’s and Prims’ Method I am looking for a tutorial which does not include all the mathematical notation explains algorithm along with the analysis Read More …
Microsoft Singularity : why closed
Problem Detail: I’m talking about this one research project: but MS closed it in 2008. I’ve read many articles about it, about high perfomance (30+% faster against tradinional monolithic kernels), much more secure etc. So it should be really a revolution Read More …
Does a never-halting machine always loop?
Problem Detail: A Turing machine that returns to a previously encountered state with its read/write head on the same cell of the exact same tape will be caught in a loop. Such a machine doesn’t halt. Can someone give an example Read More …
The difference between a bit and a Qubit
Problem Detail: Ok, I have done a lot of research on Quantum computers. I understand that they are possibly the future of computers and may be commonplace in approximately 30-50 years time. I know that a Binary is either 0 or Read More …
Turing machine and language decidability
Problem Detail: The document I am reading is here: Turing Machines Before getting into the question, here is the notation used on the picture: Here $Delta$ denotes the blank and R, L and S denote move the head right, left and Read More …
Iterative binary search analysis
Problem Detail: I’m a little bit confused about the analysis of binary search. In almost every paper, the writer assumes that the array size $n$ is always $2^k$. Well I truly understand that the time complexity becomes $log(n)$ (worst case) under Read More …
