Today I'm gonna code a relatively simple and efficient data structure, treap. Basically treap is like a improved Binary Search Tree(BST). Although BST gives lg(n) time performance on searching and inserting the values but it has a drawback which makes it most of the times impractical. BST could reshape itself in linked list on certain values. To overcome this problem many solutions have been provided like AVL trees, RB(Red-Black) trees, 2-3-4 trees and so on. These trees maintains the height to lg(n) which assures the lg(n) performance.
Treap also does the same but in much simple manner. Treap = "Tree" + "Heap". If you've already coded a BST and a heap, treap must be a piece of cake for you. Treap is built on the idea of "Randomized BST". Here randomized means the input for BST is randomly distributed. It doesn't follow any predefined rule. In practice we don't have control over input data so we add the randomness in BST in form the heap priority. Treap nodes have two things, key and priority. Key is used for inserting values exactly as in BST while priority is maintained as in heap. Formally, key of left child should be less than or equal to right child and priority of parent node should be greater than its child nodes.
Here I've implemented only insert() and delete(). They works as follows:
Insertion : Insertion in treap works exactly as in BST with the addition that we've to maintain the heap property of nodes. For maintaining the priority in nodes there are two methods, rotateLeft() and rotateRight()
Deletion : Deletion works in opposite way of insertion. We first locate the node to be deleted and then float it down till it become leaf node and the eventually clip it.
Treap also does the same but in much simple manner. Treap = "Tree" + "Heap". If you've already coded a BST and a heap, treap must be a piece of cake for you. Treap is built on the idea of "Randomized BST". Here randomized means the input for BST is randomly distributed. It doesn't follow any predefined rule. In practice we don't have control over input data so we add the randomness in BST in form the heap priority. Treap nodes have two things, key and priority. Key is used for inserting values exactly as in BST while priority is maintained as in heap. Formally, key of left child should be less than or equal to right child and priority of parent node should be greater than its child nodes.
Here I've implemented only insert() and delete(). They works as follows:
Insertion : Insertion in treap works exactly as in BST with the addition that we've to maintain the heap property of nodes. For maintaining the priority in nodes there are two methods, rotateLeft() and rotateRight()
Deletion : Deletion works in opposite way of insertion. We first locate the node to be deleted and then float it down till it become leaf node and the eventually clip it.
Here's the implementation in Java
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.Random;
class Treap{
// Nodes in treap
class Node{
private int key, priority;
Node left, right;
Node( int k){
this.key = k;
// this.hashCode() is for uniqueness
this.priority = this.hashCode();
left = right = null;
}
}
Node root;
Treap(){root = null;} // Constructor
public void insert (int key){
root = insert (root, key);
}
private Node insert (Node dummy, int val){
if (dummy == null){
return new Node(val);
}
else if (val < dummy.key){
dummy.left = insert(dummy.left, val);
if (dummy.left.priority > dummy.priority){
dummy = rotateRight(dummy);
}
}
else if (val > dummy.key){
dummy.right = insert(dummy.right, val);
if (dummy.right.priority > dummy.priority){
dummy = rotateLeft(dummy);
}
}
return dummy;
}
private Node rotateRight (Node dummy){
Node tmp = dummy.left;
dummy.left = tmp.right;
tmp.right = dummy;
return tmp;
}
private Node rotateLeft (Node dummy){
Node tmp = dummy.right;
dummy.right = tmp.left;
tmp.left = dummy;
return tmp;
}
public void printTreap(){
// in-order traversal as in BinarySearchTree
print(root);
}
private void print(Node n){
if (n == null)
return ;
else {
print (n.left);
System.out.print (n.key+" ");
print (n.right);
}
}
private boolean findNode (Node dummy, int query){
while (dummy != null){
if (query == dummy.key){
return true;
}
if (query < dummy.key)
dummy = dummy.left;
else dummy = dummy.right;
}
return false;
}
public void deleteNode(int key){
// findNode returns true if node exists otherwise false
if (findNode(root, key))
root = remove (root, key);
else System.out.println ("There's no such key in treap.");
}
private Node remove (Node dummy, int val){
if (val < dummy.key) // to locate the node
dummy.left = remove(dummy.left, val);
else if (val > dummy.key) // to locate the node
dummy.right = remove(dummy.right, val);
else { // node found
if ((dummy.left == null && dummy.right == null)||
dummy == null ) return null; //clip the leaf node
// make sure both children exists
else if (dummy.left != null && dummy.right != null){
if (dummy.left.priority > dummy.right.priority){
dummy = rotateRight (dummy);
dummy.right = remove (dummy.right, val);
}
else {
dummy = rotateLeft (dummy);
dummy.left = remove (dummy.left, val);
}
}
else if (dummy.left == null){ // node only having right child
dummy = rotateLeft (dummy);
dummy.left = remove (dummy.left, val);
}
else if (dummy.right == null){ // node only having left child
dummy = rotateRight (dummy);
dummy.right = remove (dummy.right, val);
}
}
return dummy;
}
}
class testDrive{
public static void main (String [] S)throws IOException{
Treap t = new Treap();
Random gen = new Random();
for (int i=1;i<10;i++){
int value = gen.nextInt(100);
// insert values in treap
t.insert(value);
}
System.out.println("Content of treap");
t.printTreap();
System.out.println();
int num;
BufferedReader br = new BufferedReader (new InputStreamReader(System.in));
// to test the deletion in treap
for (int i=0;i<9;i++){
num = Integer.parseInt(br.readLine());
t.deleteNode(num);
t.printTreap();
System.out.println();
}
}
}
