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AVL Tree Deletion.cpp
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AVL Tree Deletion.cpp
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//{ Driver Code Starts
//
#include <bits/stdc++.h>
using namespace std;
struct Node
{
int data, height;
Node *left, *right;
Node(int x)
{
data = x;
height = 1;
left = right = NULL;
}
};
int setHeights(Node* n)
{
if(!n) return 0;
n->height = 1 + max( setHeights(n->left) , setHeights(n->right) );
return n->height;
}
Node* buildTree(string str)
{
// Corner Case
if(str.length() == 0 || str[0] == 'N')
return NULL;
// Creating vector of strings from input
// string after spliting by space
vector<string> ip;
istringstream iss(str);
for(string str; iss >> str; )
ip.push_back(str);
// Create the root of the tree
Node* root = new Node(stoi(ip[0]));
// Push the root to the queue
queue<Node*> queue;
queue.push(root);
// Starting from the second element
int i = 1;
while(!queue.empty() && i < ip.size()) {
// Get and remove the front of the queue
Node* currNode = queue.front();
queue.pop();
// Get the current node's value from the string
string currVal = ip[i];
// If the left child is not null
if(currVal != "N") {
// Create the left child for the current node
currNode->left = new Node(stoi(currVal));
// Push it to the queue
queue.push(currNode->left);
}
// For the right child
i++;
if(i >= ip.size())
break;
currVal = ip[i];
// If the right child is not null
if(currVal != "N") {
// Create the right child for the current node
currNode->right = new Node(stoi(currVal));
// Push it to the queue
queue.push(currNode->right);
}
i++;
}
setHeights(root);
return root;
}
bool isBST(Node *n, int lower, int upper)
{
if(!n) return 1;
if( n->data <= lower || n->data >= upper ) return 0;
return isBST(n->left, lower, n->data) && isBST(n->right, n->data, upper) ;
}
pair<int,bool> isBalanced(Node* n)
{
if(!n) return pair<int,bool> (0,1);
pair<int,bool> l = isBalanced(n->left);
pair<int,bool> r = isBalanced(n->right);
if( abs(l.first - r.first) > 1 ) return pair<int,bool> (0,0);
return pair<int,bool> ( 1 + max(l.first , r.first) , l.second && r.second );
}
bool isBalancedBST(Node* root)
{
if( !isBST(root, INT_MIN, INT_MAX) )
cout<< "BST voilated, inorder traversal : ";
else if ( ! isBalanced(root).second )
cout<< "Unbalanced BST, inorder traversal : ";
else return 1;
return 0;
}
void printInorder(Node* n)
{
if(!n) return;
printInorder(n->left);
cout<< n->data << " ";
printInorder(n->right);
}
struct Node* deleteNode(struct Node* root, int data);
int main()
{
int t;
cin>>t;
getchar();
while(t--)
{
string s;
getline(cin,s);
Node* root = buildTree(s);
int n;
cin>> n;
int ip[n];
for(int i=0; i<n; i++)
cin>> ip[i];
for(int i=0; i<n; i++)
{
root = deleteNode(root, ip[i]);
if( !isBalancedBST(root) )
break;
}
if(root==NULL)
cout<<"null";
else
printInorder(root);
cout<< endl;
getline(cin,s); // to deal with newline char
}
return 1;
}
// } Driver Code Ends
/* Node is as follows:
struct Node
{
int data, height;
Node *left, *right;
Node(int x)
{
data = x;
height = 1;
left = right = NULL;
}
};
*/
int height(Node* root) {
if (root == NULL) {
return 0;
}
return root->height;
}
int getBalanceFactor(Node* n) {
if (n == NULL) {
return 0;
}
return height(n->left) - height(n->right);
}
Node* leftRotate(Node* root) {
Node* newMid = root->right;
Node* temp = newMid->left;
// rotation
newMid->left = root;
root->right = temp;
// updating height
root->height = max(height(root->left), height(root->right)) + 1;
newMid->height = max(height(newMid->left), height(newMid->right)) + 1;
// return new root after rotation
return newMid;
}
Node* rightRotate(Node* root) {
Node* newMid = root->left;
Node* temp = newMid->right;
// rotation
newMid->right = root;
root->left = temp;
// updating height
root->height = max(height(root->left), height(root->right)) + 1;
newMid->height = max(height(newMid->left), height(newMid->right)) + 1;
// return new root after rotation
return newMid;
}
Node* inorderSucc(Node* root) {
Node* curr = root;
while (curr && curr->left != NULL) {
curr = curr->left;
}
return curr;
}
Node* deleteAVL(Node* root, int val) {
// Normal BST deletion
if (root == NULL) {
return NULL;
}
if (val < root->data) {
root->left = deleteAVL(root->left, val);
} else if (val > root->data) {
root->right = deleteAVL(root->right, val);
} else {
// Node has no child
if (root->left == NULL and root->right == NULL) {
return NULL;
}
// Node with only one child or no child
else if (root->left == NULL) {
struct Node* temp = root->right;
free(root);
return temp;
} else if (root->right == NULL) {
struct Node* temp = root->left;
free(root);
return temp;
}
// Node with two children: Get the inorder successor
// (smallest in the right subtree)
Node* temp = inorderSucc(root->right);
// Copy the inorder successor's content to this Node
root->data = temp->data;
// Delete the inorder successor
root->right = deleteAVL(root->right, temp->data);
}
if (root == NULL) {
return root;
}
// 2. Update height of ancestor Node
root->height = max(height(root->left), height(root->right)) + 1;
// 3. Get the balance factor of the ancestor
int balance = getBalanceFactor(root);
// if balanced then simply return
if (balance <= 1 && balance >= -1) {
return root;
}
// if current Node is unbalanced, then
// check for 4 cases
// Left Left case
if (balance > 1 && getBalanceFactor(root->left) >= 0) {
return rightRotate(root);
}
// Left Right Case
if (balance > 1 && getBalanceFactor(root->left) < 0) {
root->left = leftRotate(root->left);
return rightRotate(root);
}
// Right Right Case
if (balance < -1 && getBalanceFactor(root->right) <= 0) {
return leftRotate(root);
}
// Right Left Case
if (balance < -1 && getBalanceFactor(root->right) > 0) {
root->right = rightRotate(root->right);
return leftRotate(root);
}
}
Node* deleteNode(Node* root, int data) {
return deleteAVL(root, data);
}