Problem Detail: Suppose that someone found an algorithm A for a NP problem (that is not NP-complete) that uses an algorithm B for PSPACE-complete or #P-complete problem during execution. (Remaining part of the algorithm takes polynomial time.) Then suppose there is Read More …
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[Solved]: Can OR be “undone”?
Problem Detail: Suppose that $Z = X vee Y$, where $X$, $Y$ and $Z$ are 96-bit binary numbers. If I’m given the values of $Z$ and $Y$, is it possible to work out what $X$ is? I know this is possible with XOR but Read More …
[Solved]: Books to get prepared before self studying Artificial Intelligence
Problem Detail: I want to study Artificial Intelligence from Artificial Intelligence: A Modern Approach by Russell and Norvig, in the mid-year vacation. I want to get prepared before diving into the book so I decided to review some relevant subjects like Read More …
[Solved]: What are the state-of-the-art algorithms for pathfinding on a continuous map of the Earth?
Problem Detail: Suppose I have got a solar-powered autonomous surface vessel somewhere in the fjords of Norway, supplied with a fairly recent set of maps, a GPS receiver, and no means of downlinking detailed commands from me. This vessel has to Read More …
[Solved]: What is the overhead of Virtual Memory?
Problem Detail: What is the price paid for the vast virtual address space provided to programmers for their applications? Or in other words, what is the overhead due to virtual memory? Is there any other overhead from implementing virtual memory, beyond Read More …
[Solved]: Show that every grammar for an inherently ambiguous CFL has infinitely many ambiguities
Problem Detail: Prove that if a CFL $L$ is inherently ambiguous, then for any grammar $G$ with $L(G) = L$, there are infinitely many strings in $L$ that have (at least) 2 different derivations in $G$. Here’s a sketch of Read More …
[Solved]: Is there a general-case sweep line algorithm for line segment intersection?
Problem Detail: I’m looking for a sweep line algorithm for finding all intersections in a set of line segments that doesn’t necessarily respects the general position constraint of Bentley-Ottman’s algorithm (taken from Wikipedia): No two line segment endpoints or crossings have Read More …
[Solved]: Shortest paths in weighted graphs, and minimum spanning trees
Problem Detail: I stuck in one challenging question, I read on my notes. An undirected, weighted, connected graph $G$, (with no negative weights and with all weights distinct) is given. We know that, in this graph, the shortest path between any Read More …
[Solved]: Number of possible programs in a language
Problem Detail: Is the number of possible programs usually finite or infinite? I’m playing with the idea of generating all possible programs for a language – is that even a finite number or must we be more specific, finite RAM etc? Read More …
[Solved]: Why does merging two sorted arrays take 2N – 1 comparisons?
Problem Detail: A friend of mine asked me a question on how to prove that merging two sorted arrays requires at least 2N – 1 comparisons Prove that merging two sorted arrays of N items requires at least 2N-1 comparisons. /* Read More …
