In this lab, you will be implemeting the ADT called BinarySearchTree. This data stucture will provide us with an alternative to vectors and linked lists when it comes to storing a list of data values.
Exercise 1: Implement the BinarySearchTree ADT in a file BinarySearchTree.h exactly as shown below. As always, make an effort to copy mindfully, trying to understand the purpose of each line of code as you go along.
// BinarySearchTree.h
// afater Mark A. Weiss, Chapter 4
// KV replaced exceptions with assert statements;
// we are writing <typename C> to indicate that the template type must be // “comparable”, i.e., have defined <, > and == operators;
#ifndef BINARY_SEARCH_TREE_H
#define BINARY_SEARCH_TREE_H
#include <cassert> #include <algorithm> using namespace std;
template <typename C> class BinarySearchTree
{ public:
BinarySearchTree( ) : root{ nullptr }
{
}
BinarySearchTree( const BinarySearchTree & rhs ) : root{ nullptr }
{
root = clone( rhs.root );
}
BinarySearchTree( BinarySearchTree && rhs ) : root{ rhs.root }
{
rhs.root = nullptr;
}
~BinarySearchTree( )
{
makeEmpty();
}
BinarySearchTree & operator=( const BinarySearchTree & rhs )
{
BinarySearchTree copy = rhs; std::swap( *this, copy ); return *this;
}
BinarySearchTree & operator=( BinarySearchTree && rhs )
{
std::swap( root, rhs.root ); return *this;
}
const C & findMin( ) const
{
assert(!isEmpty());
return findMin( root )->element;
}
const C & findMax( ) const
{ assert(!isEmpty());
return findMax( root )->element;
} bool contains( const C & x ) const
{
return contains( x, root );
}
bool isEmpty( ) const
{
return root == nullptr;
}
void printTree( ostream & out = cout ) const
{
if( isEmpty( ) )
out << “Empty tree” << endl; else
printTree( root, out );
}
void makeEmpty( )
{
makeEmpty( root );
}
void insert( const C & x )
{
insert( x, root );
}
void insert( C && x )
{
insert( std::move( x ), root );
}
void remove( const C & x )
{
remove( x, root );
}
private:
struct BinaryNode
{
C element;
BinaryNode *left;
BinaryNode *right;
BinaryNode( const C & theElement, BinaryNode *lt, BinaryNode *rt )
: element{ theElement }, left{ lt }, right{ rt } { }
BinaryNode( C && theElement, BinaryNode *lt, BinaryNode *rt )
: element{ std::move( theElement ) }, left{ lt }, right{ rt } { } };
BinaryNode *root;
// Internal method to insert into a subtree.
// x is the item to insert.
// t is the node that roots the subtree.
// Set the new root of the subtree.
void insert( const C & x, BinaryNode * & t )
{
if( t == nullptr )
t = new BinaryNode{ x, nullptr, nullptr }; else if( x < t->element ) insert( x, t->left ); else if( t->element < x ) insert( x, t->right ); else
; // Duplicate; do nothing
}
// Internal method to insert into a subtree.
// x is the item to insert.
// t is the node that roots the subtree.
// Set the new root of the subtree.
void insert( C && x, BinaryNode * & t )
{
if( t == nullptr )
t = new BinaryNode{ std::move( x ), nullptr, nullptr }; else if( x < t->element ) insert( std::move( x ), t->left ); else if( t->element < x ) insert( std::move( x ), t->right ); else
; // Duplicate; do nothing
}
// Internal method to remove from a subtree.
// x is the item to remove.
// t is the node that roots the subtree.
// Set the new root of the subtree.
void remove( const C & x, BinaryNode * & t )
{
if( t == nullptr )
return; // Item not found; do nothing if( x < t->element ) remove( x, t->left ); else if( t->element < x ) remove( x, t->right );
else if( t->left != nullptr && t->right != nullptr ) // Two children
{
t->element = findMin( t->right )->element; remove( t->element, t->right );
} else
{
BinaryNode *oldNode = t;
t = ( t->left != nullptr ) ? t->left : t->right; delete oldNode;
}
}
// Internal method to find the smallest item in a subtree t.
// Return node containing the smallest item.
BinaryNode * findMin( BinaryNode *t ) const
{
if( t == nullptr ) return nullptr; if( t->left == nullptr ) return t;
return findMin( t->left );
}
// Internal method to find the largest item in a subtree t. // Return node containing the largest item.
BinaryNode * findMax( BinaryNode *t ) const
{
if( t != nullptr ) while( t->right != nullptr ) t = t->right; return t;
}
// Internal method to test if an item is in a subtree.
// x is item to search for.
// t is the node that roots the subtree.
bool contains( const C & x, BinaryNode *t ) const
{
if( t == nullptr ) return false; else if( x < t->element ) return contains( x, t->left ); else if( t->element < x ) return contains( x, t->right ); else
return true; // Match
} void makeEmpty( BinaryNode * & t )
{
if( t != nullptr )
{
makeEmpty( t->left ); makeEmpty( t->right ); delete t;
}
t = nullptr;
}
void printTree( BinaryNode *t, ostream & out ) const
{
if( t != nullptr )
{
printTree( t->left, out ); out << t->element << endl; printTree( t->right, out );
}
}
BinaryNode * clone( BinaryNode *t ) const
{
if( t == nullptr ) return nullptr; else
return new BinaryNode{ t->element,
clone( t->left ), clone( t->right ) };
}
}; #endif
Exercise 2: Program your own file BinarySearchTreeMain.cpp in which your main() function will test the new data structure. Declare an instance of BinarySearchTree (short: BST) suitable to hold integer values. Then enter a random sequence of 25 integer values into the data structure (your values should NOT be in sorted order).
Use the print_Tree () member function in order to print out the values of the BST structure – What do you notice?
Next, remove 5 values from your BST and save them in a vector (use your own Vector.h or STL <vector>). Print out the reduced BST.
Exercise 3: Next add the following member function do your BinarySearchTree class:
Under public:
void printInternal()
{
print_Internal(root,0);
}
Under private:
void printInternal(BinaryNode* t, int offset)
{
if (t == nullptr) return;
for(int i = 1; i ≤ offset; i++) cout “..” cout t->element endl; printInternal(t->left, offset + 1); printInternal(t->right, offset + 1);
}
Go back to your program BinarySearchTreeMain.cpp and change printTree to printInternal.
Compile and run your program, and see what you get.
Next, insert the 5 value that have been removed back into the BST. Print the new BST with printInternal. How does this printed BST compare with the BST that the program printed before the removal of 5 values? Same? Different? Explanation?
Credit for this lab: (1) Sign up on the signup sheet. (2) Portal submission of your best effort for Exercises 1 and 2, 3 optional. Wednesday group submits by Friday 11:59pm; Monday group submits by Wednesday 11:59pm.
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