#include <iostream>

using namespace std;

typedef int tree_t;
typedef int link_t;

struct treeNode {
	tree_t element;
	treeNode* left;
	treeNode* right;

	treeNode(tree_t el) {
		element = el;
		left = NULL;
		right = NULL;
	}
};

struct linkNode {
	link_t element;
	linkNode* next;

	linkNode(link_t el) {
		element = el;
		next = NULL;
	}
};

void addElement(treeNode*&, tree_t&);
void deallocateTree(treeNode*&);
void printTree(treeNode*);
void deleteFromRoot(treeNode*&, tree_t&);
void deleteRoot(treeNode*&);
void deleteLeftMost(treeNode*&, tree_t&);
int treeHeight(treeNode*);
int max(int&, int&);
bool isBalanced(treeNode*);
int abs(int&);
void rotateRight(treeNode*&);
void rotateLeft(treeNode*&);
int largestElement(treeNode*);
void createList(treeNode*, linkNode*&);
void printList(linkNode*);
void deallocateList(linkNode*&);

int main() {
	treeNode* firstTree = NULL;
	linkNode* firstList = NULL;
	tree_t newElement;
	int n;	

	cout << "Enter number of elements: ";
	cin >> n;

	for(int i = 0; i < n; ++i) {
		cin >> newElement;
		addElement(firstTree, newElement);
	}

	cout << endl << "printing tree: " << endl;
	printTree(firstTree);

	cout << endl << "head root node: " << firstTree->element << endl;
	cout << endl << "Height of tree: " << treeHeight(firstTree) << endl;
	cout << endl << "Balanced Tree: " << isBalanced(firstTree) << endl;
	cout << endl << "largest Element in tree: " << largestElement(firstTree);

	//cout << endl << "Rotate left: " << endl;
	//rotateLeft(firstTree);
	//printTree(firstTree);

	cout << endl << "Trying to balance tree: " << endl;
	rotateRight(firstTree->right);
	rotateLeft(firstTree);
	
	cout << endl << "Height of tree: " << treeHeight(firstTree) << endl;
	cout << endl << "Balanced Tree: " << isBalanced(firstTree) << endl;
	cout << endl << "New head root node: " << firstTree->element << endl;

	//cout << endl << "Rotating back right..." << endl;
	//rotateRight(firstTree);

	cout << endl << "Creating linked list: " << endl;
	createList(firstTree, firstList);
	printList(firstList);
	
	deallocateTree(firstTree);
	deallocateList(firstList);

	cout << endl << "successfully deallocated tree and list..." << endl;
	return 0;
}

void addElement(treeNode* &hdTree, tree_t &el) {
	if(hdTree == NULL) {
		treeNode* newTreeNode = new treeNode(el);
		hdTree = newTreeNode;
	} else if(el < hdTree->element) {
		addElement(hdTree->left, el);
	} else {
		addElement(hdTree->right, el);
	}
}

void deallocateTree(treeNode* &hdTree) {
	if(hdTree != NULL) {
		deallocateTree(hdTree->left);
		deallocateTree(hdTree->right);
		delete hdTree;
	}
}

void printTree(treeNode* hdTree) {
	if(hdTree != NULL) {
		printTree(hdTree->left);
		cout << hdTree->element << endl;
		printTree(hdTree->right);
	}
}

void deleteFromRoot(treeNode* &hdTree, tree_t &el) {
	if(hdTree != NULL) {
		if(hdTree->element == el) {
			deleteRoot(hdTree);
		} else if(hdTree->element > el) {
			deleteFromRoot(hdTree->left, el);
		} else {
			deleteFromRoot(hdTree->right, el);
		}
	}
}

void deleteRoot(treeNode* &hdTree) {
	treeNode* tmpPointer;
	tree_t leftMost;
	if(hdTree->right == NULL) {
		tmpPointer = hdTree->left;
		delete hdTree;
		hdTree = tmpPointer;
	} else {
		deleteLeftMost(hdTree, leftMost);
		hdTree->element = leftMost;
	}
}

void deleteLeftMost(treeNode* &hdTree, tree_t &leftMost) {
	if(hdTree->left == NULL) {
		leftMost = hdTree->element;
		deleteRoot(hdTree);
	} else {
		deleteLeftMost(hdTree->left, leftMost);
	}
}

int treeHeight(treeNode* hdTree) {
	if(hdTree == NULL) {
		return -1;
	}
	return 1 + max(treeHeight(hdTree->left), treeHeight(hdTree->right));
}

int max(int &a, int &b) {
	return (a >= b) ? a: b;
}

bool isBalanced(treeNode* hdTree) {
	int lh, rh;
	if(hdTree == NULL) {
		return true;
	}
	lh = treeHeight(hdTree->left);
	rh = treeHeight(hdTree->right);
	int diff = lh - rh;
	if(abs(diff) <= 1 && isBalanced(hdTree->left) && isBalanced(hdTree->right)) {
		return true;
	}
	return false;
}

int abs(int &a) {
	if(a > 0) {
		return a;
	}
	return (-1)*a;
}

void rotateRight(treeNode* &hdTree) {
	treeNode* tmpTree = hdTree;
	hdTree = hdTree->left;
	tmpTree->left = hdTree->right;
	hdTree->right = tmpTree;
}

void rotateLeft(treeNode* &hdTree) {
	treeNode* tmpTree = hdTree;
	hdTree = hdTree->right;
	tmpTree->right = hdTree->left;
	hdTree->left = tmpTree;
}

int largestElement(treeNode* hdTree) {
	if(hdTree->right == NULL) {
		return hdTree->element;
	}
	return largestElement(hdTree->right);
}

void createList(treeNode* hdTree, linkNode* &hdList) {
	if(hdTree != NULL) {
		createList(hdTree->left, hdList);
		linkNode* newElement = new linkNode(hdTree->element);
		newElement->next = hdList;
		hdList = newElement;
		createList(hdTree->right, hdList);
	}
}

void printList(linkNode* hdList) {
	if(hdList != NULL) {
		if(hdList->next == NULL) {
			cout << hdList->element << endl;
		} else {
			cout << hdList->element << " -> ";
		}
		printList(hdList->next);
	}
}

void deallocateList(linkNode* &hdList) {
	if(hdList != NULL) {
		linkNode* tmp = hdList->next;
		delete hdList;
		deallocateList(tmp);
	}
}