#include<iostream> using namespace std; class TNode { public: int val; TNode(){}
ID: 3699435 • Letter: #
Question
#include<iostream>
using namespace std;
class TNode
{
public:
int val;
TNode(){}
TNode(int v){val = v;}
TNode * left;
TNode * right;
TNode * parent;
};
class BTree
{
public:
//constructors and destructor
BTree();
BTree(TNode *r);// initialize BTree with the root r. r is the only node.
BTree(const BTree & t); // copy constructor
BTree(const int *p, const int n);// similar to the copy constructor, but your input is of the array form.
// input is given an array that denotes a tree that uses up to n slots. The size of the tree is not given directly as input.
// the array is pointed by p and has size n, where p[0] is used to store the empty symbol.
//the function converts the array representation into a linked-list representation, i.e. BTree
~BTree();
int size;
TNode *root;
TNode * convertpos(int position);// find the pointer where the position points to
void add2left(TNode newnode, TNode *p); // you should new a node that copies newnode and then add to left of p
void add2right(TNode newnode, TNode *p);
void add2left(TNode newnode, int position);
void add2right(TNode newnode, int position);
void add2left(BTree newsubtree, int position); // you should create a separate new tree that copies
//newsubtree and then add to left of p
void add2right(BTree newsubtree, int position);
void removeleaf(int position); // should check if position is leaf
void removeleaf(TNode *p);
void swapnodes(TNode *n1, TNode *n2);//swap-the-values is fine
int * Toarray(int &n);// convert the BT into the array form. Determine what n should be, and new an array of size n+1, and store the empty symbol at array[0]. Convert the BT into the array form and retrun the array pointer. The size of the array will be given to the variable n.
void print_pre_order();// print the node as you traverse according to the order.
void print_in_order();
void print_post_order();
bool isValidBST(); // return whether this BT is a valid BST
};
bool isValidBT(const int *p, const int n);
//Determine whether the array forms a valid BT.
// the input format is the same as the above
int main()
{
return 0;
}
You are given a clas TNode that contains one integer value, and three pointers one to the parent, one to the left child, and one to the right chikd. You need to complete the class "BTree and two other functions specified in the cpp file. Task 1: Write a function isValidBT that given inputs as a binary tree in the array form, and outputs whether the array forms a correet binary tree. The inputs contain a pointer p to an array, and an integer n denoting the number of slots used in the array representation. Here the array has size n, and we use po to store the empty symbol for the binary tree as discussed in the lass. For this representation, the tree has size n 1 Task 2: Implement the constructors (default and copy) of BTree, and the destructor. You need to make sure that the copy constructor makes a separate copy of the list In addition to the nml copy constructor, here we ask you to implement a special "copy constructor" that takes input a binary tree of the array form. The inputs have the same format as Task 1, and you need to copy the binary tree, and convert the array form/to the pointer-based Task 3: Implement the function convertpos that takes input an integer position, and returns the TNode pointer that points to the position-th ode in the tree. We discussed about how to do this in the class. Task 4: Implement the add2left, add2right functions. The functionalities are just as the names Here you need to consider how to handle different input of positions, ie. places that you want to add the node/tree to. You need to consider whether the position is available to add a new node. Task 5: Write the removeleaf function. You need to first check whether the input is a leaf or not. If that is a leaf, then remove it. Otherwise do nothing. Task 6: Write a function Toarray that converts the BTree into the array form. You can start by determining the size to the reference n, and new an array of size n. Then you need to produce the correct array according to your BTree. Task 7: Write swapnodes and the three tree traversal algorithms. For the traversal algorithm, you can just print the notes according to the order. Here you just need to swap the values for the swapnodes. This task should be very simple. Write a function isValidBST that checks whether the binary tree is a valid binary search Task 8: tree Task 9: Test the above tasks.Explanation / Answer
#include<iostream>
#include<string>
using namespace std;
bool isValidBT(const int *p, const int n);
class TNode
{
public:
int val;
TNode() {}
TNode(int v) { val = v; }
TNode * left;
TNode * right;
TNode * parent;
};
class BTree
{
public:
BTree();
BTree(TNode *r);// initialize BTree with the root r. r is the only node.
BTree(const BTree & t); // copy constructor
BTree(const int *p, const int n);// similar to the copy constructor, but your input is of the array form.
TNode * convertpos(int position);// find the pointer where the position points to
void add2left(TNode *newnode, TNode *p);
void add2right(TNode *newnode, TNode *p);
void add2left(TNode *newnode, int position);
void add2right(TNode *newnode, int position);
void add2left(BTree &newsubtree, int position);
void add2right(BTree &newsubtree, int position);
void addNode(TNode *newnode);
void removeleaf(int position);
void removeleaf(TNode *p);
void swapnodes(TNode *n1, TNode *n2);//swap-the-values is fine
int * Toarray(int &n);// convert the BT into the array form. Write the size to n, and new an array of size n+1. Retrun the array
void print_pre_order();// print the node as you traverse according to the order.
void print_in_order();
void print_post_order();
private:
int size;
TNode *root;
void copy(TNode * orgRoot, TNode * newRoot);
void pInOrder(TNode * root);
void pPreOrder(TNode * root);
void pPostOrder(TNode * root);
};
BTree::BTree()
{
root = 0;
size = 0;
}
BTree::BTree(TNode *r)
{
root = r;
r->parent = 0;
r->left = 0;
r->right = 0;
size = 1;
}
BTree::BTree(const BTree &t)
{
root = new TNode(t.root->val);
copy(t.root, root);
}
BTree::BTree(const int *p, const int n)
{
if (isValidBT(p, n))
{
for (int i = 1; i < n + 1; i++)
{
if (p[i] != p[0])
{
if ((size + 1) % 2 != 0) add2right(new TNode(p[i]), i);
else add2left(new TNode(p[i]), i);
}
}
}
}
TNode * BTree::convertpos(int position)
{
if (position <= 1)
{
return root;
}
TNode* temp;
if (position & 1)
{
temp = (convertpos(position >> 1))->right;
}
else
{
temp = (convertpos(position >> 1))->left;
}
if (temp == 0) throw (string)"location does not exist";
return temp;
}
void BTree::add2left(TNode *newnode, TNode *p)
{
if (p == 0)
{
root = newnode;
newnode->parent = p;
size++;
}
else if (p->left == 0)
{
p->left = newnode;
newnode->parent = p;
size++;
}
else throw (string)"Location already full.";
}
void BTree::add2right(TNode *newnode, TNode *p)
{
if (p == 0)
{
root = newnode;
newnode->parent = p;
size++;
}
else if (p->right == 0)
{
p->right = newnode;
newnode->parent = p;
size++;
}
else throw (string)"Location already full.";
}
void BTree::add2left(TNode *newnode, int position)
{
add2left(newnode, convertpos((position/2)));
}
void BTree::add2right(TNode *newnode, int position)
{
add2right(newnode, convertpos((position/2)));
}
void BTree::add2left(BTree &newsubtree, int position)
{
BTree temp = newsubtree;
add2left(temp.root, position);
size += (temp.size) - 1;
}
void BTree::add2right(BTree &newsubtree, int position)
{
BTree temp = newsubtree;
add2right(temp.root, position);
size += (temp.size) - 1;
}
void BTree::copy(TNode * orgRoot, TNode * newRoot)
{
if (orgRoot->left != 0)
{
add2left(new TNode(orgRoot->left->val), newRoot);
copy(orgRoot->left, newRoot->left);
}
if (orgRoot->right != 0)
{
add2right(new TNode(orgRoot->right->val), newRoot);
copy(orgRoot->right, newRoot->right);
}
}
void BTree::print_in_order()
{
pInOrder(root);
cout << endl;
}
void BTree::pInOrder(TNode * root)
{
if (root->left != 0)
{
pInOrder(root->left);
}
cout << root->val<< " ";
if (root->right != 0)
{
pInOrder(root->right);
}
}
void BTree::addNode(TNode *newnode)
{
if ((size+1) % 2 != 0) add2right(newnode, size+1);
else add2left(newnode, size+1);
}
void BTree::print_pre_order()
{
pPreOrder(root);
cout << endl;
}
void BTree::pPreOrder(TNode * root)
{
cout << root->val << " ";
if (root->left != 0)
{
pPreOrder(root->left);
}
if (root->right != 0)
{
pPreOrder(root->right);
}
}
void BTree::print_post_order()
{
pPostOrder(root);
cout << endl;
}
void BTree::pPostOrder(TNode * root)
{
if (root->left != 0)
{
pPostOrder(root->left);
}
if (root->right != 0)
{
pPostOrder(root->right);
}
cout << root->val << " ";
}
void BTree::removeleaf(int position)
{
removeleaf(convertpos(position));
}
void BTree::removeleaf(TNode *p)
{
if (p->left == 0 && p->right == 0)
{
if (p->parent->left == p)
{
p->parent->left = 0;
}
else if (p->parent->right == p)
{
p->parent->right = 0;
}
delete p;
}
size--;
}
void BTree::swapnodes(TNode *n1, TNode *n2)
{
int temp = n1->val;
n1->val = n2->val;
n2->val = temp;
}
int * BTree::Toarray(int &n)
{
n = 1;
int i = 1, j = 1;
while(i<size)
{
try
{
convertpos(i)->val;
i++;
}
catch (...){}
j++;
}
int * p = new int[j];
for (int x = 1; x <= j; x++)
{
try
{
p[x] = convertpos(x)->val;
}
catch (...)
{
p[x] = -1;
}
n++;
}
p[0] = -1;
return p;
}
bool isValidBT(const int *p, const int n)
{
for (int i = 2; i < n + 1; i++)
{
if (p[i] != p[0] && p[i/2]==p[0])
{
return false;
}
}
return true;
}
int main()
{
try {
BTree T1;
BTree T2;
for (int i = 1; i <= 5; i++)
{
TNode* temp = new TNode(i);
T1.addNode(temp);
}
for (int i = 6; i <= 10; i++)
{
TNode* temp = new TNode(i);
T2.addNode(temp);
}
T1.print_in_order();
T2.print_in_order();
T1.add2left(T2, 6);
T1.print_in_order();
T2.print_in_order();
T2.removeleaf(4);
T1.removeleaf(12);
T1.print_post_order();
T2.print_post_order();
T1.print_pre_order();
T2.print_pre_order();
int * ar = new int[10];
ar[0] = -1; ar[1] = 1; ar[2] = 2; ar[3] = -1; ar[4] = 4; ar[5] = 5; ar[6] = -1; ar[7] = -1;
cout << isValidBT(ar, 6)<<endl;
BTree T3(ar, 6);
T3.print_in_order();
ar[6] = 6;
cout << isValidBT(ar, 6) << endl;
int size;
int * p = T2.Toarray(size);
for (int i = 0; i < size; i++)
{
cout << p[i] << " ";
}
}
catch (string s)
{
cout << s << endl;
}
return 0;
}
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