You cannot submit for this problem because the homework's deadline is due.

EECS 280 Project 5: Trees and Maps

Due 11:59pm Friday July 5, 2024.

Introduction

The learning goals of this project include Function Objects and Recursion. We'll reinforce learning goals from project 4: Container ADTs, Dynamic Memory, The Big Three, Linked Lists, and Iterators. You will gain experience with recursion, binary trees, templates, comparators, and the map data structure.

Here's a short description of each starter file.

File(s)	Description
BinarySearchTree.h	Starter code for BinarySearchTree.
BinarySearchTree_tests.cpp	Your BinarySearchTree unit tests.
BinarySearchTree_public_test.cpp	A small test for BinarySearchTree
BinarySearchTree_compile_check.cpp	Compile check test for BinarySearchTree
TreePrint.h	Test helper function for printing trees.
Map.h	Starter code for Map.
Map_tests.cpp	Your Map unit tests.
Map_public_test.cpp	Your Map unit tests.
Map_compile_check.cpp	Compile check test for Map.
Makefile	Helper commands for building.
unit_test_framework.h	A simple unit-testing framework.

BinarySearchTree

A binary search tree supports efficiently storing and searching for
elements.

Write implementations in BinarySearchTree.h for each _impl function. The file already contains function stubs and you should replace the assert(false) with your code. For example:

static bool empty_impl(const Node *node) {
  assert(false);  // Replace with your code
}

Run the public Binary Search Tree tests.

$ make BinarySearchTree_compile_check.exe
$ make BinarySearchTree_public_test.exe
$ ./BinarySearchTree_public_test.exe

Write tests for BinarySearchTree in BinarySearchTree_tests.cpp using the Unit Test Framework. This is ungraded, but since you won't have access to the private test cases, this is important for convincing yourself your code is correct.

$ make BinarySearchTree_tests.exe
$ ./BinarySearchTree_tests.exe

Submit BinarySearchTree.h and BinarySearchTree_tests.cpp to the autograder.

Setup

The BinarySearchTree tests should compile and run. The public tests and compile check will fail until you implement the functions. The test you write (BinarySearchTree_tests.cpp) will pass because the starter file only contains ASSERT_TRUE(true).

$ make BinarySearchTree_compile_check.exe
$ make BinarySearchTree_public_test.exe
$ ./BinarySearchTree_public_test.exe
$ make BinarySearchTree_tests.exe
$ ./BinarySearchTree_tests.exe

Template Parameters

BinarySearchTree has two template parameters:

• T - The type of elements stored within the tree.
• Compare - The type of comparator object (a functor) that should be used to determine whether one element is less than another. The default type is std::less<T>, which compares two T objects with the < operator. To compare elements in a different fashion, a custom comparator type must be specified.

No Duplicates Invariant

In the context of this project, duplicate values are NOT allowed in a
BST. This does not need to be the case, but it avoids some distracting
complications.

Sorting Invariant

A binary search tree is special in that the structure of the tree
corresponds to a sorted ordering of elements and allows efficient
searches (i.e. in logarithmic time).

Every node in a well-formed binary search tree must obey this sorting
invariant:

• It represents an empty tree (i.e. a null Node*).

- OR -

• The left subtree obeys the sorting invariant, and every element in
  the left subtree is less than the root element (i.e. this node).

  - AND -

  The right subtree obeys the sorting invariant, and the root element
  (i.e. this node) is less than every element in the right subtree.

Put briefly, go left and you'll find smaller elements. Go right and
you'll find bigger ones. See lecture for examples.

ProTip: When writing tests for check_sorting_invariant(), you can use
an iterator to break the invariant. For example:

BinarySearchTree<int> b;
b.insert(1);
b.insert(0);
// change first datum to 2, resulting in the first broken tree above
*b.begin() = 2;
ASSERT_FALSE(b.check_sorting_invariant());

Data Representation

The data representation for BinarySearchTree is a tree-like structure of
nodes similar to that described in lecture. Each Node contains an
element and pointers to left and right subtrees. The structure is
self-similar. A null pointer indicates an empty tree. You must use this
data representation. Do not add member variables to BinarySearchTree or
Node.

Public Member Functions and Iterator Interface

The public member functions and iterator interface for
BinarySearchTree are already implemented in the starter code. DO NOT
modify the code for any of these functions. They delegate the work to
private, static implementation functions, which you will write.

Implementation Functions

The core of the implementation for BinarySearchTree is a collection of
private, static member functions that operate on tree-like structures of
nodes. You are responsible for writing the implementation of several of
these functions.

To disambiguate these implementation functions from the public interface
functions, we have used names ending with _impl. (This is not
strictly necessary, because the compiler can differentiate them based on
the Node* parameter.)

There are a few keys to thinking about the implementation of these
functions:

• The functions have no idea that such a thing as the BinarySearchTree class exists, and they shouldn't. A "tree" is not a class, but simply a tree-shaped structure of Nodes. The parameter node points to the root of these nodes.
• A recursive implementation depends on the idea of similar subproblems, so a "subtree" is just as much a tree as the "whole tree". That means you shouldn't need to think about "where you came from" in your implementation.
• Every function should have a base case! Start by writing this part.
• You only need to think about one "level" of recursion at a time. Avoid thinking about the contents of subtrees and take the recursive leap of faith.

We've structured the starter code so that the first bullet point above
is actually enforced by the language. Because they are static member
functions, they do not have access to a receiver object (i.e. there's no
this pointer). That means it's actually impossible for these functions
to try to do something bad with the BinarySearchTree object (e.g. trying
to access the root member variable).

Instead, the implementation functions are called from the regular member
functions to perform specific operations on the underlying nodes and
tree structure, and are passed only a pointer to the root Node of the
tree/subtree they should work with.

The empty_impl function must run in constant time. It must must be able
to determine and return its result immediately, without using either
iteration or recursion. The rest of the implementation functions must be
recursive. There are additional requirements on the kind of recursion
that must be used for some functions. See comments in the starter code
for details. Iteration (i.e. using loops) is not allowed in any of the
_impl functions.

Using the Comparator

The _impl functions that need to compare data take in a comparator
parameter called less. Make sure to use less rather than the < operator
to compare elements!

The insert_impl Function

The key to properly maintaining the sorting invariant lies in the
implementation of the insert_impl function - this is essentially where
the tree is built, and this function will make or break the whole ADT.
Your insert_impl function should follow this procedure:

1. Handle an originally empty tree as a special case.
2. Insert the element into the appropriate place in the tree, keeping in mind the sorting invariant. You'll need to compare elements for this, and to do so make sure to use the less comparator passed in as a parameter.
3. Use the recursive leap of faith and call insert_impl itself on the left or right subtree. Hint: You do need to use the return value of the recursive call. (Why?)

Important: When recursively inserting an item into the left or right
subtree, be sure to replace the old left or right pointer of the current
node with the result from the recursive call. This is essential, because
in some cases the old tree structure (i.e. the nodes pointed to by the
old left or right pointer) is not reused. Specifically, if the subtree
is empty, the only way to get the current node to "know" about the newly
allocated node is to use the pointer returned from the recursive call.

Technicality: In some cases, the tree structure may become unbalanced
(i.e. too many nodes on one side of the tree, causing it to be much deeper
than necessary) and prevent efficient operation for large trees. You
don't have to worry about this.

Testing

Pro-tip: When writing tests for functions that return a size_t (which is an unsigned integer type), compare against an unsigned literal. For example:

BinarySearchTree<int> b;
ASSERT_EQUAL(b.height(), 0u);

Map

Write a map abstract data type (ADT). Map is an associative container, and works just like std::map.

Write implementations at the end of Map.h for the functions declared at the beginning of Map.h. The most important functions are find, insert, and the [] operator.

Your implementations should not require much code. Reuse the functionality provided by BinarySearchTree.

Run the public Map tests.

$ make Map_compile_check.exe
$ make Map_public_test.exe
$ ./Map_public_test.exe

Write tests for Map in Map_tests.cpp using the Unit Test Framework. While you should write your own tests for Map to ensure that your implementation is correct, you will not be graded on these test cases.

$ make Map_tests.exe
$ ./Map_tests.exe

Submit Map.h to the autograder. Don't forget to include the code you finished earlier, BinarySearchTree.h and BinarySearchTree_tests.cpp.

Setup

Edit Map.h, adding a function stub for every function prototype in Map. Here are a few examples to get you started. We're using K, V, and C as shorthands for Key_type, Value_type, and Key_compare.

bool Map<K, V, C>::empty() const {
  assert(false);
}

template <typename K, typename V, typename C>
typename Map<K, V, C>::Iterator Map<K, V, C>::find(const K& k) const {
  assert(false);
}

template <typename K, typename V, typename C>
V& Map<K, V, C>::operator[](const K& k) {
  assert(false);
}

template <typename K, typename V, typename C>
std::pair<typename Map<K, V, C>::Iterator, bool> Map<K, V, C>::insert(const Pair_type &val) {
  assert(false);
}

Now you should be able to compile and run the Map unit tests. The public tests will fail until you implement the functions.

$ make Map_compile_check.exe
$ make Map_public_test.exe
$ ./Map_public_test.exe

Map Examples

A map is an associative container. It stores two types, key and value. Our map works just like std::map.

Map<string, double> words;
std::map<string, double> words;

One way to use a map is a lot like an array.

words["hello"] = 1;

Maps store a std::pair type, which "glues" one key to one value. The computer science term is Tuple, a fixed-size heterogeneous container.

pair<string, double> tuple;
tuple.first = "world";
tuple.second = 2;
words.insert(tuple);

Here's a more compact way to insert a pair.

words.insert({"pi", 3.14159});

The range-for loop makes it easier to iterate over a map.

for (const auto &kv : words) {
  const auto &word = kv.first; //key
  auto number = kv.second; //value
  cout << word << " " << number << endl;
}

You can check if a key is in the map. The find() function returns an iterator.

auto found_it = words.find("pi");
if (found_it != words.end()) {
  const auto &word = (*found_it).first; //key
  auto number = (*found_it).second; //value
  cout << "found " << word << " " << number << endl;
}

When using the [] notation, an element not found is automatically created. If the value type of the map is numeric, it will always be 0 by default.

cout << "bleh: " << words["bleh"] << endl;

Building on the BST

The operation of a map is quite similar to that of a BST. The additional
consideration for a map is that we want to store key-value pairs instead
of single elements, but also have any comparisons (e.g. for searching)
only depend on the key and be able to freely change the stored values
without messing up the BST sorting invariant. We can employ the has-a
pattern using a BinarySearchTree as the data representation for Map:

• BST template parameter: T

  Instantiate with: Pair_type

  We've provided a using declaration in the starter code for Pair_type:

  using Pair_type = std::pair<Key_type, Value_type>;

  std::pair is basically like a struct that stores two objects together.
  Key_type and Value_type are whatever template parameters were used to
  instantiate Map.

• BST template parameter: Compare

  Instantiate with: PairComp

  You'll need to define your own comparator by declaring a functor
  type called PairComp (or whatever you want to call it) in your
  Map class. The overloaded () operator should accept two objects of
  Pair_type and return whether the key of the LHS is less than the
  key of the RHS (according to Key_compare).

Finally, we can even reuse the iterators from the BST class, since the
interface we want (based on std::map) calls for iterators to yield a
key-value pair when dereferenced. Since the element type T of the BST is
our Pair_type, BST iterators will yield pairs and will work just fine.
We've provided this using declaration with the starter code to make
Map::Iterator simply an alias for iterators from the corresponding BST:

using Iterator = typename BinarySearchTree<Pair_type, PairComp>::Iterator;

Submission and Grading

Submit these files to the autograder:
- BinarySearchTree.h
- Map.h

This project will be autograded for correctness and programming style.

Testing

Run all the unit tests and system tests. This includes the public tests we provided and the unit tests that you wrote.

$ make test

Pro-tip: Run commands in parallel with make -j.

$ make -j4 test

Requirements and Restrictions

Do not modify the BinarySearchTree or Map public interfaces or use any part of the STL except for containers in your BinarySearchTree and Map implementations.

Make sure you use recursion for all the BST _impl functions.

Acknowledgments

Andrew DeOrio and James Juett wrote the original project and specification. Amir Kamil contributed to code structure, style, and implementation details. This project was developed for EECS 280, Fall 2016 at the University of Michigan.