Rohan and his friends kept track of which cities they visited on their Euro trip on a map with 2k cities and k edges, where 2 cities have an edge between them if the group took a direct mode of transportation between them. Rohan noticed that their map had no isolated cities. Show that their map has exactly k connected components (groups of cities all connected via direct mode of transportation)

All businesses want to keep their customers happy. To do that, many companies assign a certain amount of time to each customer to optimize the business. The alternative would be to hire more employees, which would lead to higher costs.  This problem requires you to simulate how authorities optimize the number of cashiers at the entrance of a toll bridge to make sure drivers are satisfied. Make the following assumptions: There is one cashier per line. The line works as a queue with no cars cutting the line or leaving it. One car arrives at the entrance every 10 seconds.  It takes 90 seconds (1.5 minutes) to process the payment, starting from the moment a cashier is available. Assume there is no pause between cars.  Written in java, Your Tasks:  Design class CarInLine, with the following specifications: The class has two instance variables: arrivalTime and DepartureTime, stored as integers. Define a constructor that accepts an integer as an argument representing the arrival time, in…

We want to tile an n × 1 strip with 1 × 1 tiles that are GREEN (G), BLUE (B), and RED (R), 2 × 1PURPLE (P) and 2 × 1 ORANGE (O) tiles. GREEN, BLUE and PURPLE tiles cannot be next to each other, and there should be no two PURPLE or three BLUE or GREEN tiles in a row (for ex., GGOBR is allowed, but GGGOBR,GROPP and PBOBR are not). Give a formula for the number of such tilings. Your solution must include a recurrence equation (with initial conditions!), and a full justification. You do not need to solve it.

Consider the following edge-weighted digraph with 8 vertices and 13 edges. V->W weight A->E 1 A->B B->C C->F 4 C->D D->G F->E 39 23 F->B 26 F->A 16 G->F G->C 40 34 H->D 95 H->G 17 Here is a graphical representation of the same edge-weighted digraph: (A) -3---->(B) -39-->(D) 16 95 (E)- -23- (F). 40 (G) (H) Suppose that you run the Bellman-Ford algorithm to compute the shortest paths from H to every other vertex. What is the distTo[] array immediately after the end of three passes of the algorithm (pass 1, 2, and 3)? Each pass consists of relaxing the 13 edges in the order given above. Here is the distTo[] array before the beginning of pass 1: v A B CDE F H. distTo(v] Answer Your answer should be a sequence of 8 integers, separated by whitespace,

ii)Detail the four abstraction layers that make up TCP/IP. ii) Provide a scenario in which two computers share a video file via an unencrypted ftp connection using a weak TCP three-way handshake.

A weighted, directed graph is a suitable representation to represent the daily airline route flown by a small airline. The airline have the following daily flights: - Three flights from Cape Town to Johannesburg, - Two flights from Johannesburg to Cape Town. - Four flights from Johannesburg to Durban. - Three flights from Durban to Johannesburg. - One flight from Johannesburg to George. - One flight from George to Johannesburg. Draw the graph and answer the questions that follow. Upload your drawing in question 3 of this part. Draw a graph that represents this problem and upload your drawing.