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For this assignment, you are to augment your code from Assignment 2 to solve the minimal Vertex Cover problem for the input graph. Your approach is based on a polynomial time reduction to CNF- SAT, and use of a SAT solver. The following are the steps you should take for this assignment.SAT SolverWe will be using MiniSat SAT solver available at agurfinkel/ *****(隐私)MiniSat provides a CMake build system. You can compile it using the usual sequence:cd PROJECT mkdir build cd build cmake ../ makeThe build process creates an executable minisat and a library libminisat.a. You will need link against the library in your assignment.Create a polynomial reduction of the decision version of VERTEX COVER to CNF-SAT. We have discussed the reduction in class. It is also available under the name a4 encoding.pdf on LEARN. You are allowed to use your own reduction provided it is sound and polynomial-time. Implement the reduction and use minisat as a library to solve the minimum VERTEX COVER problem for the graphs that are input to your program (as in Assignment 2).As soon as you get an input graph via the ’V’ and ’E’ specification you should compute a minimum-sized Vertex Cover, and immediately output it. The output should just be a sequence of vertices in increasing order separated by one space each. You can use qsort(3) or std::sort for sorting.Assuming that your executable is called ece650-a4, the following is a sample run of your program:$ ./ece650-a4
V 5
E { 0,4 , 4,1 , 0,3 , 3,4 , 3,2 , 1,3 } 3 4The lines starting with V and E are the inputs to your program, and the last line is the output. Note that the minimum-sized vertex cover is not necessarily unique. You need to output just one of them.MarkingWe will try different graph inputs and check what vertex cover you output. We will only test your program with syntactically and semantically correct inputs.0Marking script for compile/make etc. fails: automatic 00Your program runs, awaits input and does not crash on input: + 200Passes Test Case 1: + 250Passes Test Case 2: + 250Passes Test Case 3: + 250Programming style: + 5CMakeAs discussed below under “Submission Instructions”, you should use a CMakeLists.txt file to build your project. We will build your project using the following sequence: 
cd PROJECT mkdir build cd build cmake ../ 
where PROJECT is the top level directory of your submission. If your code is not compiled from scratch (i.e., from the C++ sources), you get an automatic 0.