sol6 - CS 170 Algorithms Fall 2014 David Wagner Soln 6 1(20 pts Fundamental concepts Decide whether each of the following claims is correct or not If it

sol6 - CS 170 Algorithms Fall 2014 David Wagner Soln 6 1(20...

This preview shows page 1 - 3 out of 12 pages.

CS 170 Algorithms Fall 2014 David Wagner Soln 6 1. (20 pts.)Fundamental conceptsDecide whether each of the following claims is correct or not. If it is correct, write “True” and then providea short proof (one or two sentences should be enough).If it is incorrect, write “False” and provide acounterexample (please make your counterexample as small as possible, for the readers’ sake).(a) LetGbe a dag and suppose the verticesv1,...,vnare in topologically sorted order. If there is an edge(vi,vj)inG, then we are guaranteed thati<j. (b) LetGbe a dag and suppose the verticesv1,...,vnare in topologically sorted order. If there is a pathfromvitovjinG, then we are guaranteed thati<j. (c) LetG= (V,E)be a directed graph. If there is an edge(u,v)inG, thenuandvmust be in the samestrongly connected component. (d) LetG= (V,E)be a directed graph. IfsVis a source andtVis a sink, then there is a path fromstot. CS 170, Fall 2014, Soln 6 1
Image of page 1
(e) LetG= (V,E)be a directed graph where every vertex has at most three outgoing edges. Then everyvertex has at most three incoming edges. (f) LetG= (V,E)be a dag. Then there are at most|V|2possible ways to order the vertices so they are intopologically sorted order.
Image of page 2
Image of page 3

You've reached the end of your free preview.

Want to read all 12 pages?

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture