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# CSCI-1200 Homework 8 — Bidirectional Maps solved

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## Description

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In this assignment you will build a custom data structure named bidirectional_map. A bidirectional_map
is similar to an STL map, in that it stores the association between key and value data. Like a map, inserting
and erasing an association between a key and a value is completed in O(log n), where n is the number of
association pairs in the map. Also, like a map, lookup by key is O(log n), but additionally, with a bidirectional
map, lookup by value is also O(log n)!
The typical implementation of an STL map stores STL pairs of the key and value in a single binary search
tree, ordered by the keys. Our bidirectional_map will instead be stored in two distinct binary search trees,
one storing the keys and one storing the values. The associations are stored as bidirectional links between
the nodes of the two trees.
The diagram below illustrates the core structure of the bidirectional_map data structure:
1
left: right:
data: 3
left: right:
data:
2
left: right:
data:
4
left: right:
data:
5
left: right:
data:
6
left: right:
data:
Node<int,string>
Node<int,string> Node<int,string>
Node<int,string> Node<int,string> Node<int,string>
apple fig
banana
carrot
date
eggplant
left: right:
data:
left: right:
data:
left: right:
data:
left: right:
data:
left: right:
data:
left: right:
data:
Node<string,int>
Node<string,int> Node<string,int>
Node<string,int>
Node<string,int>
Node<string,int>
key_root: value_root:
size:6
bidirectional_map<string,int>
Note that the bidirectional_map is templated over two types, the key type and the value type. In this
example, the key type is STL string and the value type is int. We are currently storing 6 associations in
this structure. Note that in this initial example, the associations are “one-to-one”. This means that there
are no repeated or duplicate keys or values.
Like an STL map it is not possible to edit the key of an association, because that edit may disrupt the overall
binary search ordering property of the tree. Because the values of our bidirectional_map are also stored in
their own binary search tree, we must also prohibit editing of the values in a bidirectional_map. If the key
or the value of an association needs to be changed, that data must be removed from the tree and re-inserted.
Implementation
Your task for this homework is to implement the structure diagrammed on the previous page. We recommend
that you begin your implementation by following the structure of the ds_set class we studied and worked
with in lecture and lab. You will need to make a number of significant changes to the code, but the overall
design composed of 3 classes – Node, tree_iterator, and “manager” class (bidirectional_map) – remains
the same. Note that each class is now templated over two types rather than just one.
The provided code in main.cpp illustrates the basic functionality of the bidirectional_map class including the bidirectional_map functions: size, insert, erase, find, operator[], key_begin, key_end,
value_begin, and value_end. Study these examples carefully to deduce the expected argument and return types of the functions. The bidirectional_map has iterators over both the keys and values, which can
be incremented and decremented like regular STL iterators. Also, each iterator’s follow_link function can
be used to obtain an iterator pointing to the associated data in the other half of the structure. You will also
As this is a class with dynamically allocated memory, you will also need to implement the default constructor,
copy constructor, assignment operator, and destructor. The provided code in main.cpp does not thoroughly
test these functions, so you must write your own test cases. The homework server will compile and run your
bidirectional_map.h file with the instructor’s solution to test your implementation of these functions.
Additions/Modifications to the Core Data Structure Diagram
The Node objects illustrated in the diagram do not include parent pointers. In order to implement the
forward and backward iterators you will need to add these pointers. Alternatively, you can implement your
bidirectional_map iterators using a vector of Node pointers, as discussed in lecture.
Also, for extra credit, you can extend the structure to allow many-to-one, one-to-many, and many-to-many
key/value associations. To add this feature, each node in the structure will store an STL vector of links
to Node pointers in the other tree rather than just a single Node pointer. Examples of the non-one-to-one
interface are included in the provided code.
Performance
For this assignment we will assume that the data stored in the structure is added and removed in a mostly
random fashion and that the binary tree remains sufficiently balanced so that we may claim that the maximum
height of the tree structures is not significantly greater than log n, where n is the number of associations
stored in the structure. In lecture, we will talk about algorithms for automatically rebalancing trees (but
you do not need to implement this for the homework). In your README.txt file include the order notation
for each of the functions described above. If you complete the implementation of non-one-to-one associations
for extra credit, you will also use k = the maximum number of links in a single Node in your answers.