Homework Soursewrite a method to generate AVL tree of height h wth fewest n
write a method to generate AVL tree of height h wth fewest nodes and what is the running time of your method
Solution
class Node {
int key, height;
Node left, right;
Node(int d) {
key = d;
height = 1;
}
}
class AVLTree {
static Node root;
// A utility function to get height of the tree
int height(Node N) {
if (N == null) {
return 0;
}
return N.height;
}
// A utility function to get maximum of two integers
int max(int a, int b) {
return (a > b) ? a : b;
}
// A utility function to right rotate subtree rooted with y
// See the diagram given above.
Node rightRotate(Node y) {
Node x = y.left;
Node T2 = x.right;
// Perform rotation
x.right = y;
y.left = T2;
// Update heights
y.height = max(height(y.left), height(y.right)) + 1;
x.height = max(height(x.left), height(x.right)) + 1;
// Return new root
return x;
}
// A utility function to left rotate subtree rooted with x
// See the diagram given above.
Node leftRotate(Node x) {
Node y = x.right;
Node T2 = y.left;
// Perform rotation
y.left = x;
x.right = T2;
// Update heights
x.height = max(height(x.left), height(x.right)) + 1;
y.height = max(height(y.left), height(y.right)) + 1;
// Return new root
return y;
}
// Get Balance factor of node N
int getBalance(Node N) {
if (N == null) {
return 0;
}
return height(N.left) - height(N.right);
}
Node insert(Node node, int key) {
/* 1. Perform the normal BST rotation */
if (node == null) {
return (new Node(key));
}
if (key < node.key) {
node.left = insert(node.left, key);
} else {
node.right = insert(node.right, key);
}
/* 2. Update height of this ancestor node */
node.height = max(height(node.left), height(node.right)) + 1;
/* 3. Get the balance factor of this ancestor node to check whether
this node became unbalanced */
int balance = getBalance(node);
// If this node becomes unbalanced, then there are 4 cases
// Left Left Case
if (balance > 1 && key < node.left.key) {
return rightRotate(node);
}
// Right Right Case
if (balance < -1 && key > node.right.key) {
return leftRotate(node);
}
// Left Right Case
if (balance > 1 && key > node.left.key) {
node.left = leftRotate(node.left);
return rightRotate(node);
}
// Right Left Case
if (balance < -1 && key < node.right.key) {
node.right = rightRotate(node.right);
return leftRotate(node);
}
/* return the (unchanged) node pointer */
return node;
}
// A utility function to print preorder traversal of the tree.
// The function also prints height of every node
void preOrder(Node node) {
if (node != null) {
System.out.print(node.key + \" \");
preOrder(node.left);
preOrder(node.right);
}
}
public static void main(String[] args) {
AVLTree tree = new AVLTree();
/* Constructing a tree with random values */
root = tree.insert(root, 10);
root = tree.insert(root, 20);
root = tree.insert(root, 30);
root = tree.insert(root, 40);
root = tree.insert(root, 50);
root = tree.insert(root, 25);
System.out.println(\"The preorder traversal of constructed tree is : \");
tree.preOrder(root);
}
}
The running time of this method is O(h).
