Problem Detail: I have no idea how I managed to get this far in life without ever really grasping this but as it happens I’m still very confused on the concept of a hash function. I did some googling/wikipedia-ing, and here’s Read More …
Category: Uncategorized
[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 …
[Solved]: How can GIF compression be lossless if the maximum # of colors is 256?
Problem Detail: I’m reading “Computer Science Made Simple” by V. Anton Spraul, and in the chapter about Graphics, he describes GIF files as follows: A GIF file uses lossless compression to store an image with a maximum of 256 different colors. Read More …
