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AVLTree.cpp
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AVLTree.cpp
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/*
* AVLTree.cpp
* Copyright (C) 2022 qingyun <[email protected]>
*
* Distributed under terms of the MIT license.
*/
#include <iostream>
#include <algorithm>
using namespace std;
// data structure that represents a node in the tree
struct Node {
int data; // holds the key
Node *parent; // pointer to the parent
Node *left; // pointer to left child
Node *right; // pointer to right child
int bf; // balance factor of the node
};
// class AVLTree implements the operations in AVL tree
class AVLTree {
private:
Node* root;
// initializes the nodes with appropirate values
// all the pointers are set to point to the null pointer
void initializeNode(Node* node, int key) {
node->data = key;
node->parent = nullptr;
node->left = nullptr;
node->right = nullptr;
node->bf = 0;
}
void preOrderHelper(Node* node) {
if (node != nullptr) {
cout<<node->data<<" ";
preOrderHelper(node->left);
preOrderHelper(node->right);
}
}
void inOrderHelper(Node* node) {
if (node != nullptr) {
inOrderHelper(node->left);
cout<<node->data<<" ";
inOrderHelper(node->right);
}
}
void postOrderHelper(Node* node) {
if (node != nullptr) {
postOrderHelper(node->left);
postOrderHelper(node->right);
cout<<node->data<<" ";
}
}
Node* searchTreeHelper(Node* node, int key) {
if (node == nullptr || key == node->data) {
return node;
}
if (key < node->data) {
return searchTreeHelper(node->left, key);
}
return searchTreeHelper(node->right, key);
}
Node* deleteNodeHelper(Node* node, int key) {
// search the key
if (node == nullptr) return node;
else if (key < node->data) node->left = deleteNodeHelper(node->left, key);
else if (key > node->data) node->right = deleteNodeHelper(node->right, key);
else {
// the key has been found, now delete it
// case 1: node is a leaf node
if (node->left == nullptr && node->right == nullptr) {
delete node;
node = nullptr;
}
// case 2: node has only one child
else if (node->left == nullptr) {
Node* temp = node;
node = node->right;
delete temp;
}
else if (node->right == nullptr) {
Node* temp = node;
node = node->left;
delete temp;
}
// case 3: has both children
else {
Node* temp = minimum(node->right);
node->data = temp->data;
node->right = deleteNodeHelper(node->right, temp->data);
}
}
// Write the update balance logic here
// YOUR CODE HERE
return node;
}
// update the balance factor the node
void updateBalance(Node* node) {
if (node->bf < -1 || node->bf > 1) {
rebalance(node);
return;
}
if (node->parent != nullptr) {
if (node == node->parent->left) {
node->parent->bf -= 1;
}
if (node == node->parent->right) {
node->parent->bf += 1;
}
if (node->parent->bf != 0) {
updateBalance(node->parent);
}
}
}
// rebalance the tree
void rebalance(Node* node) {
if (node->bf > 0) {
if (node->right->bf < 0) {
rightRotate(node->right);
leftRotate(node);
} else {
leftRotate(node);
}
} else if (node->bf < 0) {
if (node->left->bf > 0) {
leftRotate(node->left);
rightRotate(node);
} else {
rightRotate(node);
}
}
}
void printHelper(Node* root, string indent, bool last) {
// print the tree structure on the screen
if (root != nullptr) {
cout<<indent;
if (last) {
cout<<"R----";
indent += " ";
} else {
cout<<"L----";
indent += "| ";
}
cout<<root->data<<"( BF = "<<root->bf<<")"<<endl;
printHelper(root->left, indent, false);
printHelper(root->right, indent, true);
}
}
public:
AVLTree() {
root = nullptr;
}
// Pre-Order traversal
// Node->Left Subtree->Right Subtree
void preorder() {
preOrderHelper(this->root);
}
// In-Order traversal
// Left Subtree -> Node -> Right Subtree
void inorder() {
inOrderHelper(this->root);
}
// Post-Order traversal
// Left Subtree -> Right Subtree -> Node
void postorder() {
postOrderHelper(this->root);
}
// search the tree for the key k
// and return the corresponding node
Node* searchTree(int k) {
return searchTreeHelper(this->root, k);
}
// find the node with the minimum key
Node* minimum(Node* node) {
while (node->left != nullptr) {
node = node->left;
}
return node;
}
// find the node with the maximum key
Node* maximum(Node* node) {
while (node->right != nullptr) {
node = node->right;
}
return node;
}
// find the successor of a given node
Node* successor(Node* x) {
// if the right subtree is not null,
// the successor is the leftmost node in the
// right subtree
if (x->right != nullptr) {
return minimum(x->right);
}
// else it is the lowest ancestor of x whose
// left child is also an ancestor of x.
Node* y = x->parent;
while (y != nullptr && x == y->right) {
x = y;
y = y->parent;
}
return y;
}
// find the predecessor of a given node
Node* predecessor(Node* x) {
// if the left subtree is not null,
// the predecessor is the rightmost node in the
// left subtree
if (x->left != nullptr) {
return maximum(x->left);
}
Node* y = x->parent;
while (y != nullptr && x == y->left) {
x = y;
y = y->parent;
}
return y;
}
// rotate left at node x
void leftRotate(Node* x) {
Node* y = x->right;
x->right = y->left;
if (y->left != nullptr) {
y->left->parent = x;
}
y->parent = x->parent;
if (x->parent == nullptr) {
this->root = y;
} else if (x == x->parent->left) {
x->parent->left = y;
} else {
x->parent->right = y;
}
y->left = x;
x->parent = y;
// update the balance factor
x->bf = x->bf - 1 - max(0, y->bf);
y->bf = y->bf - 1 + min(0, x->bf);
}
// rotate right at node x
void rightRotate(Node* x) {
Node* y = x->left;
x->left = y->right;
if (y->right != nullptr) {
y->right->parent = x;
}
y->parent = x->parent;
if (x->parent == nullptr) {
this->root = y;
} else if (x == x->parent->right) {
x->parent->right = y;
} else {
x->parent->left = y;
}
y->right = x;
x->parent = y;
// update the balance factor
x->bf = x->bf + 1 - min(0, y->bf);
y->bf = y->bf + 1 + max(0, x->bf);
}
// insert the key to the tree in its appropriate position
void insert(int key) {
// PART 1: Ordinary BST insert
Node* node = new Node;
node->parent = nullptr;
node->left = nullptr;
node->right = nullptr;
node->data = key;
node->bf = 0;
Node* y = nullptr;
Node* x = this->root;
while (x != nullptr) {
y = x;
if (node->data < x->data) {
x = x->left;
} else {
x = x->right;
}
}
// y is parent of x
node->parent = y;
if (y == nullptr) {
root = node;
} else if (node->data < y->data) {
y->left = node;
} else {
y->right = node;
}
// PART 2: re-balance the node if necessary
updateBalance(node);
}
Node* getRoot(){
return this->root;
}
// delete the node from the tree
Node* deleteNode(int data) {
Node* deletedNode = deleteNodeHelper(this->root, data);
return deletedNode;
}
// print the tree structure on the screen
void prettyPrint() {
printHelper(this->root, "", true);
}
};
int main() {
AVLTree bst;
// bst.createSampleTree1();
bst.insert(50);
bst.insert(30);
bst.insert(70);
bst.insert(23);
bst.prettyPrint();
return 0;
}