Blog

Problem Detail: A (now closed) question on SO made me think about the following problem: Given an arbirtary number of points (2D), draw a path that consists of straight lines between points, visits each point exactly once and does not intersect Read More …

Problem Detail: How can I sort a list of 5 integers such that in the worst case it takes 7 compares? I don’t care about how many other operations are performed. I don’t know anything particular about the integers. I’ve tried Read More …

Problem Detail: See title. And by all inputs I mean providing the functions with the same input and checking whether they give the same output for each case. EDIT If it can be reduced to Halting problem, then how? EDIT 2 Read More …

Problem Detail: I’m trying to prove that $exists L_1, L_2 : L_1$ and $L_2$ are context-free languages $land;L_1 cap L_2 = L_3$ is an undecidable language. I know that context-free languages are not closed under intersection. This means that I can Read More …

Problem Detail: In reading Uday Reddy’s answer to What is the relation between functors in SML and Category theory? Uday states Category theory doesn’t yet know how to deal with higher-order functions. Some day, it will. As I thought Category theory Read More …

Problem Detail:  $L_1$ and $L_2$ are two languages defined on the alphabet $sum$. $L_1$ is reducible to $L_2$ in polynomial time. Which of the following cannot be true? $L_1 in P$ and $L_2$ is finite $L_1 in NP$ and $L_2 Read More …

Problem Detail: I know that (1 + 0)* is the set of all bit strings; but isn’t 1* + 0* the same thing? Asked By : O.A. Answered By : Yuval Filmus The set $1^*+0^*$ is composed of two parts: $1^*$ and $0^*$. Read More …

Problem Detail: I’d like to learn something about this optimization problem: For given non-negative whole numbers $a_{i,j,k}$, find a function $f$ minimizing the expression $$max_k sum_i a_{i,f(i),k}$$ An example using a different formulation might make it clearer: You’re given a set Read More …

Problem Detail: Suppose I have a list of distinct integers. I’m looking for a data structure that will support the operations search, insert, delete and closest_pair in $O(log n)$ time. I know that a sorted array supports search, insert and delete Read More …