Fun with classes Solution

union- nd




A C++ class, like a class in Python, is an object that contains both data and functions (sometimes called member functions or methods). In this project you will implement a union- nd class using union-by-size.

You should base your C++ implementation on the Python implementation in union find.py.




You are to complete the implementation of the union nd class de ned in the le union find.hpp.




You should not modify the class de nition in union find.hpp. Your code should be placed




in a le named union find.cpp, the skeleton of which is provided to you.







the union- nd structure




Union- nd with path compression and union-by-size is presented in union find.py. When merging two trees, we attach the smaller tree to the larger tree. This limits the growth of the trees. In addition, when executing a nd operation, we attach all nodes on our search path directly to the root. This also attens the trees representing the connected components.







The implementation is rather elegant. There is an vector s with one entry for every node. If s[p] 0, then s[p] is the index of the next node we should visit on the way to the root of the component. If s[p] < 0, then we have arrived at a root of a connected component. In addition, the absolute value of the value stored in a root is the number of nodes in the component. The latter is updated in the union operation.




what you are to do




Here is what you are to implement.




nd(const long int &p) This returns the component that contains p and applies path compression as it does so.



2. onion(const long int &p, const long int &q)1 This adds an edge (connection) between p and q using union-by-size.




In the case of a tie, where the trees containing p and q are the same size, the tree containing q should be attached to the tree containing p.




Your onion() will also need to increment the tree size (stored as a negative num-ber in the root) as needed. It should also decrement the number of components (num components) as components are combined.







Do not make any changes to union find.hpp! I will be using the original version of this le, and if your code depends on changes you make in the API, your code will probably fail in testing!







1We cannot use the name union since that is a reserved keyword in C and C++.



what to turn in, and how




Inside your cs303 git repository you should create a new directory named union find. This will be the folder for this project. You should add and commit the your union find.cpp to the repository.







This is the tree structure your repository cs303 should have when you are done. Leaves are les and all the other nodes are directories:










cs303












hello


world
array
sorting
union


find












array.cpp
sort.hpp
















main.cpp










hello.cpp
main.cpp
union


find.cpp
valgrind.txt










valgrind.txt
















array.cpp.gcov


































I will pull your code from gitlab.com (make sure you shared cs303 with me!) to grade.




grading




No credit will be given for




code that does not compile and link, code that opens any les,




code that includes an active main(),




code that writes any output (so be sure to disable any debugging output).




Here are things that will have a negative e ect on your grade, more or less in decreasing order of severity.




Your program crashes during testing. Code that is incorrect.




Code that appears to work but nevertheless has memory access errors. Memory leaks.




Code that is unnecessarily ine cient.