Professor Gaedel has written a program that he claims implements Dijkstra’s algorithm. The program produces v. dv. d and v.πv.π for each vertex v∈Vv∈V . Give an O(V+E)O(V+E) time algorithm to check the output of the professor’s program. It should determine whether the dd and ππ attributes match those of some shortest-paths tree. You may assume that all edge weights are nonnegative.

Which of the following statements best describes it careers?

The volume v and paper surface area a of a conical paper cup are given by where r is the radius of the base of the cone and h is the height of the cone. a. by eliminating h, obtain the expression for a as a function of r and v. b. create a user-de ned function that accepts r as the only argument and computes a for a given value of v. declare v to be global within the function. c. for v ! 10 in.3 , use the function with the fminbnd function to compute the value of r that minimizes the area a. what is the corresponding value of the height h? investigate the sensitivity of the solution by plotting v versus r. how much can r vary about its optimal value before the area increases 10 percent above its minimum value?

This chapter lists many ways in which becoming computer literate is beneficial. think about what your life will be like once you’re started in your career. what areas of computing will be most important for you to understand? how would an understanding of computer hardware and software you in working from home, working with groups in other countries and contributing your talents.