The city of San Juan commissions you to design a new bus system for Old San Juan which has n stops numbered 1; 2; : : : ; n on the North-bound route (lets ignore the South-bound route). Commuters may begin their journey at any stop i and end at any other stop j > i. There are some obvious options: (a) You can have a bus run from the southern-most point to the northern- most point as a traditional busline might run. The system would be cheap because it only requires n segments for the entire system. However, a person traveling from stop i = 0 to stop j = n must travel through all n segments. This system will be slow for that person. (b) You can have a special express bus run from every point to every other destination. No person will every wait through any unnecessary segments no matter where they start and end. However, this system requires (n2) segments and will be expensive. Use a divide-and-conquer technique to design a bus system that uses (n log n) route segments and which requires a person to wait through at most 1 extra segment when going from any i to any j (as long as i j, i. e., we only consider North-bound routes for simplicity, and all buses run North). In other words, a commuter can travel from any i to any j by using at most 2 segments.(a) For the base cases n = 1; 2, design a system using at most 1 route.(b) For n > 2 we will use divide-and-conquer. Assume that we already put in place routes connecting the rst n=2 stops and routes connect- ing the last n=2 stops so that if i and j both belong to the same half, we can get from i to j in at most 2 segments. Show how to add O(n) additional routes so that if i is in the rst half and j is in the second half we can get from i to j in 2 segments.(c) Write the recurrence for the number of routes your solution use and solve it using the master theorem.

In this lab, you complete a prewritten c++ program for a carpenter who creates personalized house signs. the program is supposed to compute the price of any sign a customer orders, based on the following facts: the charge for all signs is a minimum of $35.00. the first five letters or numbers are included in the minimum charge; there is a $4 charge for each additional character. if the sign is made of oak, add $20.00. no charge is added for pine. black or white characters are included in the minimum charge; there is an additional $15 charge for gold-leaf lettering. instructions ensure the file named housesign. cppis open in the code editor. you need to declare variables for the following, and initialize them where specified: a variable for the cost of the sign initialized to 0.00 (charge). a variable for the number of characters initialized to 8 (numchars). a variable for the color of the characters initialized to "gold" (color). a variable for the wood type initialized to "oak" (woodtype). write the rest of the program using assignment statements and ifstatements as appropriate. the output statements are written for you. execute the program by clicking the run button. your output should be: the charge for this sign is $82. this is the code, // housesign. cpp - this program calculates prices for custom made signs. #include #include using namespace std; int main() { // this is the work done in the housekeeping() function // declare and initialize variables here // charge for this sign // color of characters in sign // number of characters in sign // type of wood // this is the work done in the detailloop() function // write assignment and if statements here // this is the work done in the endofjob() function // output charge for this sign cout < < "the charge for this sign is $" < < charge < < endl; return(0); }

Discuss the ways in which electronic information associated with payments is addressed in terms of security. include encryption, secure sockets layers, and secure electronic transactions in your discussion. are there any other ways that consumers and businesses can keep their payment information secure in an electronic commerce environment? do you feel that your information is safe when conducting electronic business? why or why not?

What is the digital revolution and how did it change society? what are the benefits of digital media?