Problem Detail: Say I want to compute a covnex hull of given points on the plane. I would like to write an algorithm, that only compares the points and doesn’t do any arithmetic operations. Wikipedia states, that: The standard $Omega(n log Read More …
Author: ignougroup
[Solved]: Feedback polynomial of 7-bit Linear Feedback Shift Register
Problem Detail: My friend gave me a question to solve. The question he asked me was: the following sequence has been generated by a 7-bit linear feedback shift register. He asked me to find the feedback polynomial. I went through some Read More …
[Solved]: Algorithm for fastest division below threshold
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 …
[Solved]: Problem contest with matrix and DP
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 …
[Solved]: 3-SAT where variables occur equally many times as a positive literal and as a negative literal
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 …
[Solved]: Automated geometric theorem-proving using synthetic methods
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 …
[Solved]: Comparing random access and sequential access
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 …
[Solved]: Lower bound for finding majority element in a sorted array
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 …
[Solved]: Will floating point code return the same arithmetical results on two different computers?
Problem Detail: Say I am using boost or the built-in float or double mathematical libraries of my C++ compiler. I distribute the program. Will the execution of my C++ program on different machines given different floating point results given that the Read More …
[Solved]: Why don’t modern SAT solvers use the notion of a “watched clause”, in the same way they use the notion of a “watched literal”?
Problem Detail: Modern SAT solvers use the notion of “watched literals”: when a value is chosen for a literal $l$, the solver only checks whether that falsifies clauses with $l$ in them if $l$ is one of the watched literals in Read More …
