Category: Uncategorized

Problem Detail: The subset-sum problem is a classic NP-complete problem: Given a list of numbers $L$ and a target $k$, is there a subset of numbers from $L$ that sums to $k$? A student asked me if this variant of the Read More …

Problem Detail: Is there a data structure to keep a list of elements (not necessarily sorted) that performs the Access (by index) and Insert operations in a reasonable asymptotic time? When I say “reasonable time”, I mean that it should be Read More …

Problem Detail: If P does equal NP, will it still be possible do design a cryptosystem where the optimal cryptanalysis algorithm takes, say, the square of the time taken up by the legitimate encryption and decryption algorithms? Do any such algorithms Read More …

Problem Detail: I want to prove that any polynomial of degree $k$ is in $Theta(n^k)$. The coefficient of $n^k$, $a_{k}$, is positive. I know I need $0 leq c_{1}n^k leq a_{k}n^k + … + a_{0} leq c_{2}n^k$ for all $n geq Read More …

Problem Detail: Directly from Wikipedia, a set of vertices $X subseteq V(G)$ of a graph $G$ is independent if and only if its complement $V(G) setminus X$ is a vertex cover. Does this imply that the complement of the independent set Read More …

Problem Detail: This is a problem from a past contest at topcoder : Problem. Its solution is given here : Solution [Scroll Down to Penguin Emperor] I am unable to understand how the section with subheading “Combinations are associative” works. What Read More …

Problem Detail: This is a basic question, but I’m thinking that $O(m+n)$ is the same as $O(max(m,n))$, since the larger term should dominate as we go to infinity? Also, that would be different from $O(min(m,n))$. Is that right? I keep seeing Read More …

Problem Detail: I have trouble understanding Turing’s halting problem. His proof assumes that there exists a magical machine $H$ which could determine whether a computer would halt or loop forever for a given input. Then we attach another machine that reverses Read More …

Problem Detail: A true/false question: If a DFA $M$ contains a self-loop on some state $q$, then $M$ must accept an infinite language. The answer is “false”. I’ve read this question, but I’m still wondering why $M$ does not necessarily accept Read More …

Problem Detail: A multi-user, multi-processing operating system cannot be implemented on hardware that does not support Address translation DMA for disk transfer At least two modes of CPU execution (privileged and non-privileged) Demand paging My attempt: Somewhere it explain as : Read More …