In this post first we will understand what are AVL Trees and then we write a program to implement AVL Trees in C++.
What is AVL Tree:
An AVL treeis another balanced binary search tree. Named after their inventors, Adelson-Velskii and Landis, they were the first dynamically balanced trees to be proposed. Like red-black trees, they are not perfectly balanced, but pairs of sub-trees differ in height by at most 1, maintaining an O(logn) search time. Addition and deletion operations also take O(logn) time.
Definition of an AVL tree:
An AVL tree is a binary search tree which has the following properties:
- The sub-trees of every node differ in height by at most one.
- Every sub-tree is an AVL tree.
Now we have got an idea of it, let’s write the source code to implement AVL Tree.
C++ program to implement AVL Tree:
// Program to implement AVL Trees
#include<iostream>
#include<cstdio>
#include<sstream>
#include<algorithm>
#define pow2(n) (1 << (n))
using namespace std;
// Node Declaration
struct avl_node
{
int data;
struct avl_node *left;
struct avl_node *right;
}*root;
// Class Declaration
class avlTree
{
public:
int height(avl_node *);
int diff(avl_node *);
avl_node *rr_rotation(avl_node *);
avl_node *ll_rotation(avl_node *);
avl_node *lr_rotation(avl_node *);
avl_node *rl_rotation(avl_node *);
avl_node* balance(avl_node *);
avl_node* insert(avl_node *, int );
void display(avl_node *, int);
void inorder(avl_node *);
void preorder(avl_node *);
void postorder(avl_node *);
avlTree()
{
root = NULL;
}
};
int main()
{
int choice, item;
avlTree avl;
while (1)
{
cout<<"\n---------------------"<<endl;
cout<<"AVL Tree Implementation"<<endl;
cout<<"\n---------------------"<<endl;
cout<<"1.Insert Element into the tree"<<endl;
cout<<"2.Display Balanced AVL Tree"<<endl;
cout<<"3.InOrder traversal"<<endl;
cout<<"4.PreOrder traversal"<<endl;
cout<<"5.PostOrder traversal"<<endl;
cout<<"6.Exit"<<endl;
cout<<"Enter your Choice: ";
cin>>choice;
switch(choice)
{
case 1:
cout<<"Enter value to be inserted: ";
cin>>item;
root = avl.insert(root, item);
break;
case 2:
if (root == NULL)
{
cout<<"Tree is Empty"<<endl;
continue;
}
cout<<"Balanced AVL Tree:"<<endl;
avl.display(root, 1);
break;
case 3:
cout<<"Inorder Traversal:"<<endl;
avl.inorder(root);
cout<<endl;
break;
case 4:
cout<<"Preorder Traversal:"<<endl;
avl.preorder(root);
cout<<endl;
break;
case 5:
cout<<"Postorder Traversal:"<<endl;
avl.postorder(root);
cout<<endl;
break;
case 6:
exit(1);
break;
default:
cout<<"Wrong Choice"<<endl;
}
}
return 0;
}
// Height of AVL Tree
int avlTree::height(avl_node *temp)
{
int h = 0;
if (temp != NULL)
{
int l_height = height (temp->left);
int r_height = height (temp->right);
int max_height = max (l_height, r_height);
h = max_height + 1;
}
return h;
}
// Height Difference
int avlTree::diff(avl_node *temp)
{
int l_height = height (temp->left);
int r_height = height (temp->right);
int b_factor= l_height - r_height;
return b_factor;
}
// Right- Right Rotation
avl_node *avlTree::rr_rotation(avl_node *parent)
{
avl_node *temp;
temp = parent->right;
parent->right = temp->left;
temp->left = parent;
return temp;
}
// Left- Left Rotation
avl_node *avlTree::ll_rotation(avl_node *parent)
{
avl_node *temp;
temp = parent->left;
parent->left = temp->right;
temp->right = parent;
return temp;
}
// Left - Right Rotation
avl_node *avlTree::lr_rotation(avl_node *parent)
{
avl_node *temp;
temp = parent->left;
parent->left = rr_rotation (temp);
return ll_rotation (parent);
}
// Right- Left Rotation
avl_node *avlTree::rl_rotation(avl_node *parent)
{
avl_node *temp;
temp = parent->right;
parent->right = ll_rotation (temp);
return rr_rotation (parent);
}
// Balancing AVL Tree
avl_node *avlTree::balance(avl_node *temp)
{
int bal_factor = diff (temp);
if (bal_factor > 1)
{
if (diff (temp->left) > 0)
temp = ll_rotation (temp);
else
temp = lr_rotation (temp);
}
else if (bal_factor < -1)
{
if (diff (temp->right) > 0)
temp = rl_rotation (temp);
else
temp = rr_rotation (temp);
}
return temp;
}
// Insert Element into the tree
avl_node *avlTree::insert(avl_node *root, int value)
{
if (root == NULL)
{
root = new avl_node;
root->data = value;
root->left = NULL;
root->right = NULL;
return root;
}
else if (value < root->data)
{
root->left = insert(root->left, value);
root = balance (root);
}
else if (value >= root->data)
{
root->right = insert(root->right, value);
root = balance (root);
}
return root;
}
// Display AVL Tree
void avlTree::display(avl_node *ptr, int level)
{
int i;
if (ptr!=NULL)
{
display(ptr->right, level + 1);
printf("n");
if (ptr == root)
cout<<"Root -> ";
for (i = 0; i < level && ptr != root; i++)
cout<<" ";
cout<<ptr->data;
display(ptr->left, level + 1);
}
}
// Inorder Traversal of AVL Tree
void avlTree::inorder(avl_node *tree)
{
if (tree == NULL)
return;
inorder (tree->left);
cout<<tree->data<<" ";
inorder (tree->right);
}
// Preorder Traversal of AVL Tree
void avlTree::preorder(avl_node *tree)
{
if (tree == NULL)
return;
cout<<tree->data<<" ";
preorder (tree->left);
preorder (tree->right);
}
// Postorder Traversal of AVL Tree
void avlTree::postorder(avl_node *tree)
{
if (tree == NULL)
return;
postorder ( tree ->left );
postorder ( tree ->right );
cout<<tree->data<<" ";
}OUTPUT:
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 2
Tree is Empty
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 1
Enter value to be inserted: 8
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 2
Balanced AVL Tree:
Root -> 8
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 1
Enter value to be inserted: 5
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 2
Balanced AVL Tree:
Root -> 8
5
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 1
Enter value to be inserted: 4
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 2
Balanced AVL Tree:
8
Root -> 5
4
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 1
Enter value to be inserted: 11
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 2
Balanced AVL Tree:
11
8
Root -> 5
4
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 1
Enter value to be inserted: 15
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 2
Balanced AVL Tree:
15
11
8
Root -> 5
4
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 1
Enter value to be inserted: 3
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 2
Balanced AVL Tree:
15
11
8
Root -> 5
4
3
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 1
Enter value to be inserted: 6
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 2
Balanced AVL Tree:
15
11
8
6
Root -> 5
4
3
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 1
Enter value to be inserted: 2
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 2
Balanced AVL Tree:
15
11
8
6
Root -> 5
4
3
2
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 4
Preorder Traversal:
5 3 2 4 11 8 6 15
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 5
Postorder Traversal:
2 4 3 6 8 15 11 5
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 3
Inorder Traversal:
2 3 4 5 6 8 11 15
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 2
Balanced AVL Tree:
15
11
8
6
Root -> 5
4
3
2
---------------------
AVL Tree Implementation
---------------------
1.Insert Element into the tree
2.Display Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
Enter your Choice: 6
------------------Comment below in case you want to discuss more about the C++ program to implement AVL Trees.
The height is recalculated recursively at each insertion, so it’s not O(log(N)) …