MUST USE THE BINARY TREE DEFINITION AS LISTED BELOW. #include <queue> #include <
ID: 3772857 • Letter: M
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MUST USE THE BINARY TREE DEFINITION AS LISTED BELOW.
#include <queue>
#include <stack>
#ifndef BINARY_SEARCH_TREE
#define BINARY_SEARCH_TREE
using namespace std;
template<class T>
class Stack : public stack<T> {
public:
T pop() {
T tmp = stack <T>::top();
stack<T>::pop();
return tmp;
}
};
template<class T>
class Queue : public queue<T> {
public:
T dequeue() {
T tmp = queue<T>::front();
queue<T>::pop();
return tmp;
}
void enqueue(const T& el) {
push(el);
}
};
template<class T> class BST;
template<class T>
class BSTNode {
public:
BSTNode() {
left = right = 0;
}
BSTNode(const T& e, BSTNode<T> *l = 0, BSTNode<T> *r = 0) {
el = e; left = l; right = r;
}
T el;
BSTNode<T> *left, *right;
};
template<class T>
class BST {
public:
BST() {
root = 0;
}
~BST() {
clear();
}
void clear() {
clear(root);
root = 0;
}
bool isEmpty() const {
return root == 0;
}
void preorder() {
preorder(root);
}
void inorder() {
inorder(root);
}
void postorder() {
postorder(root);
}
void insert(const T& el);
void recursiveInsert(const T& el) {
recursiveInsert(root,el);
}
T* search(const T& el) const {
return search(root,el);
}
T* recursiveSearch(const T& el) const {
return recursiveSearch(root,el);
}
void deleteByCopying(BSTNode<T>*&);
void findAndDeleteByCopying(const T&);
void deleteByMerging(BSTNode<T>*&);
void findAndDeleteByMerging(const T&);
void iterativePreorder();
void iterativeInorder();
void iterativePostorder();
void breadthFirst();
void MorrisPreorder();
void MorrisInorder();
void MorrisPostorder();
void balance(T*,int,int);
protected:
BSTNode<T>* root;
void clear(BSTNode<T>*);
void recursiveInsert(BSTNode<T>*&, const T&);
T* search(BSTNode<T>*, const T&) const;
T* recursiveSearch(BSTNode<T>*, const T&) const;
void preorder(BSTNode<T>*);
void inorder(BSTNode<T>*);
void postorder(BSTNode<T>*);
virtual void visit(BSTNode<T> *p) {
cout << p->el << ' ';
}
};
template<class T>
void BST<T>::clear(BSTNode<T> *p) {
if (p != 0) {
clear(p->left);
clear(p->right);
delete p;
}
}
template<class T>
void BST<T>::insert(const T& el) {
BSTNode<T> *p = root, *prev = 0;
while (p != 0) { // find a place for inserting new node;
prev = p;
if (el < p->el)
p = p->left;
else p = p->right;
}
if (root == 0) // tree is empty;
root = new BSTNode<T>(el);
else if (el < prev->el)
prev->left = new BSTNode<T>(el);
else prev->right = new BSTNode<T>(el);
}
template<class T>
void BST<T>::recursiveInsert(BSTNode<T>*& p, const T& el) {
if (p == 0)
p = new BSTNode<T>(el);
else if (el < p->el)
recursiveInsert(p->left, el);
else recursiveInsert(p->right,el);
}
template<class T>
T* BST<T>::search(BSTNode<T>* p, const T& el) const {
while (p != 0)
if (el == p->el)
return &p->el;
else if (el < p->el)
p = p->left;
else p = p->right;
return 0;
}
template<class T>
T* BST<T>::recursiveSearch(BSTNode<T>* p, const T& el) const {
if (p != 0)
if (el == p->el)
return &p->el;
else if (el < p->el)
return recursiveSearch(p->left,el);
else return recursiveSearch(p->right,el);
else return 0;
}
template<class T>
void BST<T>::inorder(BSTNode<T> *p) {
if (p != 0) {
inorder(p->left);
visit(p);
inorder(p->right);
}
}
template<class T>
void BST<T>::preorder(BSTNode<T> *p) {
if (p != 0) {
visit(p);
preorder(p->left);
preorder(p->right);
}
}
template<class T>
void BST<T>::postorder(BSTNode<T>* p) {
if (p != 0) {
postorder(p->left);
postorder(p->right);
visit(p);
}
}
template<class T>
void BST<T>::deleteByCopying(BSTNode<T>*& node) {
BSTNode<T> *previous, *tmp = node;
if (node->right == 0)
node = node->left;
else if (node->left == 0 )
node = node->right;
else {
tmp = node->left ;
previous = node;
while (tmp->right != 0) {
previous = tmp;
tmp = tmp->right;
}
node->el = tmp->el;
if (previous == node)
previous->left = tmp->left;
else previous->right = tmp->left; // 4.
}
delete tmp; // 5.
}
// findAndDeleteByCopying() searches the tree to locate the node containing
// el. If the node is located, the function DeleteByCopying() is called.
template<class T>
void BST<T>::findAndDeleteByCopying(const T& el) {
BSTNode<T> *p = root, *prev = 0;
while (p != 0 && !(p->el == el)) {
prev = p;
if (el < p->el)
p = p->left;
else p = p->right;
}
if (p != 0 && p->el == el)
if (p == root)
deleteByCopying(root);
else if (prev->left == p)
deleteByCopying(prev->left);
else deleteByCopying(prev->right);
else if (root != 0)
cout << "el " << el << " is not in the tree ";
else cout << "the tree is empty ";
}
template<class T>
void BST<T>::deleteByMerging(BSTNode<T>*& node) {
BSTNode<T> *tmp = node;
if (node != 0) {
if (!node->right) // node has no right child: its left
node = node->left; // child (if any) is attached to its parent;
else if (node->left == 0) // node has no left child: its right
node = node->right; // child is attached to its parent;
else { // be ready for merging subtrees;
tmp = node->left; // 1. move left
while (tmp->right != 0)// 2. and then right as far as possible;
tmp = tmp->right;
tmp->right = // 3. establish the link between the
node->right; // the rightmost node of the left
// subtree and the right subtree;
tmp = node; // 4.
node = node->left; // 5.
}
delete tmp; // 6.
}
}
template<class T>
void BST<T>::findAndDeleteByMerging(const T& el) {
BSTNode<T> *node = root, *prev = 0;
while (node != 0) {
if (node->el == el)
break;
prev = node;
if (el < node->el)
node = node->left;
else node = node->right;
}
if (node != 0 && node->el == el)
if (node == root)
deleteByMerging(root);
else if (prev->left == node)
deleteByMerging(prev->left);
else deleteByMerging(prev->right);
else if (root != 0)
cout << "el " << el << " is not in the tree ";
else cout << "the tree is empty ";
}
template<class T>
void BST<T>::iterativePreorder() {
Stack<BSTNode<T>*> travStack;
BSTNode<T> *p = root;
if (p != 0) {
travStack.push(p);
while (!travStack.empty()) {
p = travStack.pop();
visit(p);
if (p->right != 0)
travStack.push(p->right);
if (p->left != 0) // left child pushed after right
travStack.push(p->left); // to be on the top of the stack;
}
}
}
template<class T>
void BST<T>::iterativeInorder() {
Stack<BSTNode<T>*> travStack;
BSTNode<T> *p = root;
while (p != 0) {
while (p != 0) { // stack the right child (if any)
if (p->right) // and the node itself when going
travStack.push(p->right); // to the left;
travStack.push(p);
p = p->left;
}
p = travStack.pop(); // pop a node with no left child
while (!travStack.empty() && p->right == 0) { // visit it and all nodes
visit(p); // with no right child;
p = travStack.pop();
}
visit(p); // visit also the first node with
if (!travStack.empty()) // a right child (if any);
p = travStack.pop();
else p = 0;
}
}
template<class T>
void BST<T>::iterativePostorder() {
Stack<BSTNode<T>*> travStack;
BSTNode<T>* p = root, *q = root;
while (p != 0) {
for ( ; p->left != 0; p = p->left)
travStack.push(p);
while (p->right == 0 || p->right == q) {
visit(p);
q = p;
if (travStack.empty())
return;
p = travStack.pop();
}
travStack.push(p);
p = p->right;
}
}
template<class T>
void BST<T>::breadthFirst() {
Queue<BSTNode<T>*> queue;
BSTNode<T> *p = root;
if (p != 0) {
queue.enqueue(p);
while (!queue.empty()) {
p = queue.dequeue();
visit(p);
if (p->left != 0)
queue.enqueue(p->left);
if (p->right != 0)
queue.enqueue(p->right);
}
}
}
template<class T>
void BST<T>::MorrisInorder() {
BSTNode<T> *p = root, *tmp;
while (p != 0)
if (p->left == 0) {
visit(p);
p = p->right;
}
else {
tmp = p->left;
while (tmp->right != 0 &&// go to the rightmost node of
tmp->right != p) // the left subtree or
tmp = tmp->right; // to the temporary parent of p;
if (tmp->right == 0) { // if 'true' rightmost node was
tmp->right = p; // reached, make it a temporary
p = p->left; // parent of the current root,
}
else { // else a temporary parent has been
visit(p); // found; visit node p and then cut
tmp->right = 0; // the right pointer of the current
p = p->right; // parent, whereby it ceases to be
} // a parent;
}
}
template<class T>
void BST<T>::MorrisPreorder() {
BSTNode<T> *p = root, *tmp;
while (p != 0) {
if (p->left == 0) {
visit(p);
p = p->right;
}
else {
tmp = p->left;
while (tmp->right != 0 &&// go to the rightmost node of
tmp->right != p) // the left subtree or
tmp = tmp->right; // to the temporary parent of p;
if (tmp->right == 0) { // if 'true' rightmost node was
visit(p); // reached, visit the root and
tmp->right = p; // make the rightmost node a temporary
p = p->left; // parent of the current root,
}
else { // else a temporary parent has been
tmp->right = 0; // found; cut the right pointer of
p = p->right; // the current parent, whereby it ceases
} // to be a parent;
}
}
}
template<class T>
void BST<T>::MorrisPostorder() {
BSTNode<T> *p = new BSTNode<T>(), *tmp, *q, *r, *s;
p->left = root;
while (p != 0)
if (p->left == 0)
p = p->right;
else {
tmp = p->left;
while (tmp->right != 0 &&// go to the rightmost node of
tmp->right != p) // the left subtree or
tmp = tmp->right; // to the temporary parent of p;
if (tmp->right == 0) { // if 'true' rightmost node was
tmp->right = p; // reached, make it a temporary
p = p->left; // parent of the current root,
}
else { // else a temporary parent has been found;
// process nodes between p->left (included) and p (excluded)
// extended to the right in modified tree in reverse order;
// the first loop descends this chain of nodes and reverses
// right pointers; the second loop goes back, visits nodes,
// and reverses right pointers again to restore the pointers
// to their original setting;
for (q = p->left, r = q->right, s = r->right;
r != p; q = r, r = s, s = s->right)
r->right = q;
for (s = q->right; q != p->left;
q->right = r, r = q, q = s, s = s->right)
visit(q);
visit(p->left); // visit node p->left and then cut
tmp->right = 0; // the right pointer of the current
p = p->right; // parent, whereby it ceases to be
} // a parent;
}
}
template<class T>
void BST<T>::balance (T data[], int first, int last) {
if (first <= last) {
int middle = (first + last)/2;
insert(data[middle]);
balance(data,first,middle-1);
balance(data,middle+1,last);
}
}
#endif
Explanation / Answer
Cpp PART:
The following program creates a mirror image of a tree:
#include<iostream>
using namespace std;
typedef struct tree_node {
int value;
struct tree_node *left, *right;
}node;
// create a new node
node *getNewNode(int value) {
node *new_node = new node;
new_node->value = value;
new_node->left = NULL;
new_node->right = NULL;
return new_node;
}
// create the tree
node *createTree() {
node *root = getNewNode(31);
root->left = getNewNode(16);
root->right = getNewNode(45);
root->left->left = getNewNode(7);
root->left->right = getNewNode(24);
root->left->right->left = getNewNode(19);
root->left->right->right = getNewNode(29);
return root;
}
// Inorder traversal of a tree
void inorderTraversal(node *ptr) {
if(ptr == NULL)
return;
else {
inorderTraversal(ptr->left);
cout<<ptr->value<<" ";
inorderTraversal(ptr->right);
}
}
// create mirror tree
node* mirror(node* root) {
node* m_root = NULL;
if(!root) return NULL;
m_root = getNewNode(root->value);
m_root->left = mirror(root->right);
m_root->right = mirror(root->left);
return m_root;
}
// main
int main() {
node *root = createTree();
cout<<" Inorder traversal before conversion ";
inorderTraversal(root);
node *m_root = mirror(root);
cout<<" Inorder traversal after conversion ";
inorderTraversal(m_root);
cout<<endl;
return 0;
}
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