Blog

Problem Detail: Suppose $A$ is a sorted array with $n$ elements. I want to know whether we can determine if there are majority elements in $A$ with time complexity $O(1)$. Recall that a majority element of $A$ is an element which Read More …

Problem Detail: Assume that we choose randomly $k$ distinct numbers $N_1$, $dots$, $N_k$ in ${1, dots, k}$ and we have a file of $k$ parts. We have these two cases : We read (or write) sequentially from part $1$ to part Read More …

Problem Detail: This question is about geometric theorem proving and is inspired by this Math.SE post. Currently, Euclidean-geometric theorem provers, as referred to in the post, use coordinate geometry to convert a geometry problem into a set of algebraic equations. Why Read More …

Problem Detail: Let $phi$ be a 3-CNF formula over variables $x_1,x_2,ldots,x_n$. Every variable $x_i$, $i in [n]$, occurs equally many times as a positive literal and as a negative literal in $phi$. Is it NP-complete to decide the satisfiability of such Read More …

Problem Detail: I found this problem while I was reading an ACM problem and it is about dynamic programming. The problem says that you have a square matrix $ntimes n$ filled with 1’s or 0’s, like this: $$begin{bmatrix} 1 &1 &1 Read More …

Problem Detail: Take a number i. You need to split it in two pieces as many times as necessary so that all splits are less than or equal to j. How does one obtain this with the minimum number of splits? Read More …

Problem Detail: I’ve googled this problem somewhat pretty extensively, and all the relevant literature understandably deals with 2-d or 3-d cases, rather than the n-d case. EDIT: Yes, ℝn. I’ve done many searches combining terms like union, intersection, volume, convex hulls, Read More …

Problem Detail: It’s known that the following language, the so-called acceptance problem is undecidable: $A_{TM} = {langle M,wrangle,vert,Mtext{ is a TM which accepts }w}$ The proof is by contradiction: Assume there is a TM $H$ which decides $A_{TM}$. Let $D$ be Read More …

Problem Detail: I want to prove that grammar $$ begin{cases} S’rightarrow S Srightarrow aSb ~|~ A Arightarrow bA~|~b end{cases} $$ isn’t $LR(1)$. I’ve constructed parser table and got Shift-Reduce conflict. I want to prove that without parser table, using another $LR(1)$ Read More …

Problem Detail: I always thought that TSP currently requires time exponential in the number of cities to solve. How, then, has Concorde optimally solved a TSP instance with 85,900 cities?!? Is this a typo? Is the base of the exponential 1.0000000000000001 Read More …