Introduce a little anarchy, upset the established order and everything becomes chaos. Youll work hard to run bat-signal, adios uhuhhhaahahahah…

1 Description

Hi, there. Im Commissioner Gordon. First of all, thank you all for helping me to collect the Bat-Signal. But I have bad news. Just when we were assembling the last part of Bat-Signal, a piece of card is dropped from the machine. On the back of the card, the note above was written. When we tried to run Bat-Signal later, we understood what the note meant. Joker had sabotaged all cables of Bat-Signal and set up a setting. Now, we are in this situation: we have lots of cables, and ports just as much as the cables. Each cable produces a different voltage when connected to a different port. To run Bat-Signal we need the maximum voltage and each cable must be connected to one port. Finally, we have only one chance of trying

So, we are looking for fast programmers who can calculate the maximum voltage in this setting, therefore we prepared some test cases.

I believe that this will be the last game of Joker. Lets light up the sky!

2 Solution Guidelines

Let us share what we figured out until now in order to find a fast solution.

• This problem is solvable with a minimum-cost maximum-flow (MCMF) modeling approach and we expect you to model the test cases accordingly. We are aware that MCMF might be unfamiliar to you, but an excellent programmer is the one who finds a way through in the darkness!
• For MCMF modeling, you will need cost and capacities on each edge. Determine them wisely to find the maximum voltage.
• When the modeling is complete, you will find the algorithm for MCMF problems. The algorithm needs to find negative cycles and you are free to use the code and explanation in this link.

3 Input & Output

Your code must read the name of the input and output files from the command line. We will run your code as follows:

• g++ *.cpp *.h -std=c++11 -o project4
• ./project4 inputFile outputFile

If you do not use any .h file. Your code will be compiled as follows: g++ *.cpp -std=c++11

-o project4

Make sure that your final submission compiles and runs with these commands

3.1 Input

Each input file contains several test cases and each test case consists of a matrix that specifies the output voltage when a cable is plugged into a port. The format of the input file is as follows:

• The first line contains an integer T, that denotes the number of test cases in this input file.
• The next line contains another integer N which is the number of cables (and ports) in the next test case.
• The subsequent N lines denote an N N integer matrix V , in which V_ij is the output voltage when the cable i is plugged into port j.
• The rest of the lines denote other test cases, where each has the same format: an integer N and an N N integer matrix V .

Table 1: Sample input and output files

• In all input files, 1 T 30,1 N 150,1 V_ij 2000.

An example input file is displayed in Table 1 and Figure 1 illustrates the two test cases in the sample input with graphs.

3.2 Output

The output file is expected to contain the maximum voltage to run Bat-Signal for each test case in the input file in a separate line. The correct output file for the sample input is provided in Table 1.

In the first test case, we have two cables and two ports. To obtain the maximum voltage, we match the first cable with the second port (8V), the second cable with the first port (3V), totaling 11V. Note that we matched each cable with a single port and all of the cables and ports are matched.

In the second test case, we connect cable 1 to port 3 (6V), cable 2 to port 2 (6V), and cable 3 to port 1 (5V) and obtain the maximum voltage which is equal to 17 V. Remark that an alternative matching with the same output voltage is also possible but we are interested only in the maximum voltage.