Problem Detail: Exercise 2.3-7 from “Introduction to Algorithms” by Cormen et al. Third Edition, states: Describe a O(n lg n)-time algorithm that, given a set S of n integers and another integer x, determines whether of not there exist two elements Read More …
Author: ignougroup
[Solved]: Why choose D* over Dijkstra?
Problem Detail: I understand the basis of A* as being a derivative of Dijkstra, however, I recently found out about D*. From Wikipedia, I can understand the algorithm. What I do not understand is why I would use D* over Dijkstra. Read More …
[Solved]: Understanding definition of NP
Problem Detail: In my lecture notes, the definition of the class NP is given as: A language $L$ is in the class NP, if there exists a turing machine $M$ and polynomials $T$ and $p$ such that: For every input $x$, Read More …
[Solved]: Convert a CFG into CNF
Problem Detail: I’m still new to CFG and CNF and have trouble sometimes understanding the concepts. I’m trying to convert this CFG into Chomsky Normal Form: G: S -> aSbS | bSaS | epsilon I think the language generates all strings Read More …
[Solved]: Vertex cover of a graph by removing leaf-vertices from a DFS tree
Problem Detail: Question taken from “The Algorithm Design Manual” by Steven S. Skiena, 1997. A vertex cover of a graph $G=(V,E)$ is a subset of vertices $V’subseteq V$ such that every edge $ein E$ contains at least one vertex from $V′$. Read More …
[Solved]: Typical file structure
Problem Detail: Short version The question & answers relate to the following topics: File as a collection of records vs. file as a stream of bytes Sequential File Distinction between file data and metadata Transfer of metadata along with the Read More …
[Solved]: Proof: Sum of weights of paths in a network
Problem Detail: I was given problem 6.7 out of the book “Networks: An Introduction” as a question. The problem is defined as follows: Consider the set of all paths from node $s$ to node $t$ on an undirected network with adjacency Read More …
[Solved]: Problem with derivative of sigmoid activation function
Problem Detail: I’m following Jeff heatons book ‘Introduction to Neural Networks with Java’. To get node deltas, we need to calculate $f'(sum)$. In the very first row for Training Element #1, we need to compute $f'(1.13) cdot 0.25$ which Heaton evaluates Read More …
[Solved]: Has this model of random directed graphs been studied?
Problem Detail: Youtube recently added a feature called autoplay, where each clip is assigned a (presumably related) clip that follows it. This, in effect, defines a directed graph on the set of youtube clips, where each vertex has outdegree 1. The Read More …
[Solved]: Knight’s tour from all starting positions
Problem Detail: Is it true that for all $ngeq 5$, there is a knight’s tour of an $ntimes n$ chessboard beginning at every square? For example, is it correct, that there is no solution for a $5times5$ board, with start position Read More …