Implementation of Search, Insert and Delete in Treap

We strongly recommend to refer set 1 as a prerequisite of this post.
Treap (A Randomized Binary Search Tree)
In this post, implementations of search, insert and delete are discussed.
Search: 
Same as standard BST search. Priority is not considered for search. 

C++

// C function to search a given key in a given BST
TreapNode* search(TreapNode* root, int key)
{
    // Base Cases: root is null or key is present at root
    if (root == NULL || root->key == key)
       return root;

    // Key is greater than root's key
    if (root->key < key)
       return search(root->right, key);

    // Key is smaller than root's key
    return search(root->left, key);
}

Java

// Java function to search a given key in a given BST
public TreapNode search(TreapNode root, int key)
{
    // Base Cases: root is null or key is present at root
    if (root == null || root.key == key)
        return root;

    // Key is greater than root's key
    if (root.key < key)
        return search(root.right, key);

    // Key is smaller than root's key
    return search(root.left, key);
}

Python3

# Python function to search a given key in a given BST
def search(root, key):
    # Base Cases: root is None or key is present at root
    if root is None or root.key == key:
        return root

    # Key is greater than root's key
    if root.key < key:
        return search(root.right, key)

    # Key is smaller than root's key
    return search(root.left, key)

# This code is contributed by Amit Mangal.

C#

public static TreapNode search(TreapNode root, int key) {
    // Base Cases: root is null or key is present at root
    if (root == null || root.key == key) {
        return root;
    }

    // Key is greater than root's key
    if (root.key < key) {
        return search(root.right, key);
    }

    // Key is smaller than root's key
    return search(root.left, key);
}

Javascript

function search(root, key) {
  // Base Cases: root is null or key is present at root
  if (root == null || root.key === key) {
    return root;
  }

  // Key is greater than root's key
  if (root.key < key) {
    return search(root.right, key);
  }

  // Key is smaller than root's key
  return search(root.left, key);
}

Insert
1) Create new node with key equals to x and value equals to a random value.
2) Perform standard BST insert.
3) A newly inserted node gets a random priority, so Max-Heap property may be violated.. Use rotations to make sure that inserted node’s priority follows max heap property.
During insertion, we recursively traverse all ancestors of the inserted node. 
a) If new node is inserted in left subtree and root of left subtree has higher priority, perform right rotation.
b) If new node is inserted in right subtree and root of right subtree has higher priority, perform left rotation.

CPP

/* Recursive implementation of insertion in Treap */
TreapNode* insert(TreapNode* root, int key)
{
    // If root is NULL, create a new node and return it
    if (!root)
        return newNode(key);

    // If key is smaller than root
    if (key <= root->key)
    {
        // Insert in left subtree
        root->left = insert(root->left, key);

        // Fix Heap property if it is violated
        if (root->left->priority > root->priority)
            root = rightRotate(root);
    }
    else  // If key is greater
    {
        // Insert in right subtree
        root->right = insert(root->right, key);

        // Fix Heap property if it is violated
        if (root->right->priority > root->priority)
            root = leftRotate(root);
    }
    return root;
}

Java

/* Recursive implementation of insertion in Treap */
public TreapNode insert(TreapNode root, int key) {
    // If root is null, create a new node and return it
    if (root == null) {
        return newNode(key);
    }

    // If key is smaller than root
    if (key <= root.key) {
        // Insert in left subtree
        root.left = insert(root.left, key);

        // Fix Heap property if it is violated
        if (root.left.priority > root.priority) {
            root = rightRotate(root);
        }
    } else { // If key is greater
        // Insert in right subtree
        root.right = insert(root.right, key);

        // Fix Heap property if it is violated
        if (root.right.priority > root.priority) {
            root = leftRotate(root);
        }
    }
    return root;
}

Python3

# Recursive implementation of insertion in Treap
def insert(root, key):
    # If root is None, create a new node and return it
    if root is None:
        return newNode(key)

    # If key is smaller than root
    if key <= root.key:
        # Insert in left subtree
        root.left = insert(root.left, key)

        # Fix Heap property if it is violated
        if root.left.priority > root.priority:
            root = rightRotate(root)
    else: # If key is greater
        # Insert in right subtree
        root.right = insert(root.right, key)

        # Fix Heap property if it is violated
        if root.right.priority > root.priority:
            root = leftRotate(root)
    return root

# This code is contributed by Amit Mangal.

C#

public TreapNode Insert(TreapNode root, int key)
{
    // If root is null, create a new node and return it
    if (root == null)
        return NewNode(key);

    // If key is smaller than root
    if (key <= root.Key)
    {
        // Insert in left subtree
        root.Left = Insert(root.Left, key);

        // Fix Heap property if it is violated
        if (root.Left.Priority > root.Priority)
            root = RightRotate(root);
    }
    else  // If key is greater
    {
        // Insert in right subtree
        root.Right = Insert(root.Right, key);

        // Fix Heap property if it is violated
        if (root.Right.Priority > root.Priority)
            root = LeftRotate(root);
    }
    return root;
}

Javascript

function insert(root, key) {
    // If root is null, create a new node and return it
    if (root == null) {
        return newNode(key);
    }

    // If key is smaller than root
    if (key <= root.key) {
        // Insert in left subtree
        root.left = insert(root.left, key);

        // Fix Heap property if it is violated
        if (root.left.priority > root.priority) {
            root = rightRotate(root);
        }
    } else { // If key is greater
        // Insert in right subtree
        root.right = insert(root.right, key);

        // Fix Heap property if it is violated
        if (root.right.priority > root.priority) {
            root = leftRotate(root);
        }
    }
    return root;
}

Delete:
The delete implementation here is slightly different from the steps discussed in previous post. 
1) If node is a leaf, delete it. 
2) If node has one child NULL and other as non-NULL, replace node with the non-empty child. 
3) If node has both children as non-NULL, find max of left and right children. 
….a) If priority of right child is greater, perform left rotation at node 
….b) If priority of left child is greater, perform right rotation at node.
The idea of step 3 is to move the node to down so that we end up with either case 1 or case 2.

CPP

/* Recursive implementation of Delete() */
TreapNode* deleteNode(TreapNode* root, int key)
{
    // Base case
    if (root == NULL) return root;

    // IF KEYS IS NOT AT ROOT
    if (key < root->key)
        root->left = deleteNode(root->left, key);
    else if (key > root->key)
        root->right = deleteNode(root->right, key);

    // IF KEY IS AT ROOT

    // If left is NULL
    else if (root->left == NULL)
    {
        TreapNode *temp = root->right;
        delete(root);
        root = temp;  // Make right child as root
    }

    // If Right is NULL
    else if (root->right == NULL)
    {
        TreapNode *temp = root->left;
        delete(root);
        root = temp;  // Make left child as root
    }

    // If key is at root and both left and right are not NULL
    else if (root->left->priority < root->right->priority)
    {
        root = leftRotate(root);
        root->left = deleteNode(root->left, key);
    }
    else
    {
        root = rightRotate(root);
        root->right = deleteNode(root->right, key);
    }

    return root;
}

Java

/* Recursive implementation of delete() */

public TreapNode deleteNode(TreapNode root, int key)
{
    // Base case
    if (root == null) {
        return root;
    }

    // IF KEY IS NOT AT ROOT
    if (key < root.key) {
        root.left = deleteNode(root.left, key);
    }
    else if (key > root.key) {
        root.right = deleteNode(root.right, key);
    }

    // IF KEY IS AT ROOT
    // If left is null
    else if (root.left == null) {
        TreapNode temp = root.right;
        root = null;
        root = temp; // Make right child as root
    }

    // If right is null
    else if (root.right == null) {
        TreapNode temp = root.left;
        root = null;
        root = temp; // Make left child as root
    }

    // If key is at root and both left and right are not
    // null
    else if (root.left.priority < root.right.priority) {
        root = leftRotate(root);
        root.left = deleteNode(root.left, key);
    }
    else {
        root = rightRotate(root);
        root.right = deleteNode(root.right, key);
    }

    return root;
}

Python3

def deleteNode(root, key):
    # Base case
    if not root:
        return root

    # IF KEYS IS NOT AT ROOT
    if key < root.key:
        root.left = deleteNode(root.left, key)
    elif key > root.key:
        root.right = deleteNode(root.right, key)

    # IF KEY IS AT ROOT
    # If left is NULL
    elif not root.left:
        temp = root.right
        del root
        root = temp  # Make right child as root

    # If Right is NULL
    elif not root.right:
        temp = root.left
        del root
        root = temp  # Make left child as root

    # If key is at root and both left and right are not NULL
    elif root.left.priority < root.right.priority:
        root = rightRotate(root)
        root.right = deleteNode(root.right, key)
    else:
        root = leftRotate(root)
        root.left = deleteNode(root.left, key)

    return root

# This code is contributed by Amit Mangal.

C#

public TreapNode DeleteNode(TreapNode root, int key)
{
    // Base case
    if (root == null) return root;

    // If key is not at root
    if (key < root.Key)
        root.Left = DeleteNode(root.Left, key);
    else if (key > root.Key)
        root.Right = DeleteNode(root.Right, key);

    // If key is at root

    // If left is null
    else if (root.Left == null)
    {
        TreapNode temp = root.Right;
        root = temp;  // Make right child as root
    }

    // If right is null
    else if (root.Right == null)
    {
        TreapNode temp = root.Left;
        root = temp;  // Make left child as root
    }

    // If key is at root and both left and right are not null
    else if (root.Left.Priority < root.Right.Priority)
    {
        root = LeftRotate(root);
        root.Left = DeleteNode(root.Left, key);
    }
    else
    {
        root = RightRotate(root);
        root.Right = DeleteNode(root.Right, key);
    }

    return root;
}

Javascript

function deleteNode(root, key) {
  // Base case
  if (root == null) return root;

  // IF KEYS IS NOT AT ROOT
  if (key < root.key) {
    root.left = deleteNode(root.left, key);
  } else if (key > root.key) {
    root.right = deleteNode(root.right, key);
  }

  // IF KEY IS AT ROOT
  else if (root.left == null) {
    let temp = root.right;
    delete root;
    root = temp;  // Make right child as root
  } else if (root.right == null) {
    let temp = root.left;
    delete root;
    root = temp;  // Make left child as root
  } else if (root.left.priority < root.right.priority) {
    root = leftRotate(root);
    root.left = deleteNode(root.left, key);
  } else {
    root = rightRotate(root);
    root.right = deleteNode(root.right, key);
  }

  return root;
}

A Complete Program to Demonstrate All Operations

CPP

// C++ program to demonstrate search, insert and delete in Treap
#include <bits/stdc++.h>
using namespace std;

// A Treap Node
struct TreapNode
{
    int key, priority;
    TreapNode *left, *right;
};

/* T1, T2 and T3 are subtrees of the tree rooted with y
  (on left side) or x (on right side)
                y                               x
               / \     Right Rotation          /  \
              x   T3   – – – – – – – >        T1   y
             / \       < - - - - - - -            / \
            T1  T2     Left Rotation            T2  T3 */

// A utility function to right rotate subtree rooted with y
// See the diagram given above.
TreapNode *rightRotate(TreapNode *y)
{
    TreapNode *x = y->left,  *T2 = x->right;

    // Perform rotation
    x->right = y;
    y->left = T2;

    // Return new root
    return x;
}

// A utility function to left rotate subtree rooted with x
// See the diagram given above.
TreapNode *leftRotate(TreapNode *x)
{
    TreapNode *y = x->right, *T2 = y->left;

    // Perform rotation
    y->left = x;
    x->right = T2;

    // Return new root
    return y;
}

/* Utility function to add a new key */
TreapNode* newNode(int key)
{
    TreapNode* temp = new TreapNode;
    temp->key = key;
    temp->priority = rand()%100;
    temp->left = temp->right = NULL;
    return temp;
}

// C function to search a given key in a given BST
TreapNode* search(TreapNode* root, int key)
{
    // Base Cases: root is null or key is present at root
    if (root == NULL || root->key == key)
       return root;

    // Key is greater than root's key
    if (root->key < key)
       return search(root->right, key);

    // Key is smaller than root's key
    return search(root->left, key);
}

/* Recursive implementation of insertion in Treap */
TreapNode* insert(TreapNode* root, int key)
{
    // If root is NULL, create a new node and return it
    if (!root)
        return newNode(key);

    // If key is smaller than root
    if (key <= root->key)
    {
        // Insert in left subtree
        root->left = insert(root->left, key);

        // Fix Heap property if it is violated
        if (root->left->priority > root->priority)
            root = rightRotate(root);
    }
    else  // If key is greater
    {
        // Insert in right subtree
        root->right = insert(root->right, key);

        // Fix Heap property if it is violated
        if (root->right->priority > root->priority)
            root = leftRotate(root);
    }
    return root;
}

/* Recursive implementation of Delete() */
TreapNode* deleteNode(TreapNode* root, int key)
{
    if (root == NULL)
        return root;

    if (key < root->key)
        root->left = deleteNode(root->left, key);
    else if (key > root->key)
        root->right = deleteNode(root->right, key);

    // IF KEY IS AT ROOT

    // If left is NULL
    else if (root->left == NULL)
    {
        TreapNode *temp = root->right;
        delete(root);
        root = temp;  // Make right child as root
    }

    // If Right is NULL
    else if (root->right == NULL)
    {
        TreapNode *temp = root->left;
        delete(root);
        root = temp;  // Make left child as root
    }

    // If key is at root and both left and right are not NULL
    else if (root->left->priority < root->right->priority)
    {
        root = leftRotate(root);
        root->left = deleteNode(root->left, key);
    }
    else
    {
        root = rightRotate(root);
        root->right = deleteNode(root->right, key);
    }

    return root;
}

// A utility function to print tree
void inorder(TreapNode* root)
{
    if (root)
    {
        inorder(root->left);
        cout << "key: "<< root->key << " | priority: %d "
            << root->priority;
        if (root->left)
            cout << " | left child: " << root->left->key;
        if (root->right)
            cout << " | right child: " << root->right->key;
        cout << endl;
        inorder(root->right);
    }
}


// Driver Program to test above functions
int main()
{
    srand(time(NULL));

    struct TreapNode *root = NULL;
    root = insert(root, 50);
    root = insert(root, 30);
    root = insert(root, 20);
    root = insert(root, 40);
    root = insert(root, 70);
    root = insert(root, 60);
    root = insert(root, 80);

    cout << "Inorder traversal of the given tree \n";
    inorder(root);

    cout << "\nDelete 20\n";
    root = deleteNode(root, 20);
    cout << "Inorder traversal of the modified tree \n";
    inorder(root);

    cout << "\nDelete 30\n";
    root = deleteNode(root, 30);
    cout << "Inorder traversal of the modified tree \n";
    inorder(root);

    cout << "\nDelete 50\n";
    root = deleteNode(root, 50);
    cout << "Inorder traversal of the modified tree \n";
    inorder(root);

    TreapNode *res = search(root, 50);
    (res == NULL)? cout << "\n50 Not Found ":
                   cout << "\n50 found";

    return 0;
}

Java

/*package whatever //do not write package name here */

import java.util.*;
// A Treap Node
class TreapNode
{
    int key,priority;
    TreapNode left,right;

}
/* T1, T2 and T3 are subtrees of the tree rooted with y
  (on left side) or x (on right side)
                y                               x
               / \     Right Rotation          /  \
              x   T3   – – – – – – – >        T1   y
             / \       < - - - - - - -            / \
            T1  T2     Left Rotation            T2  T3 */

// A utility function to right rotate subtree rooted with y
// See the diagram given above.
class Main
{
    public static TreapNode rightRotate(TreapNode y) {
        TreapNode x = y.left;
        TreapNode T2 = x.right;

        // Perform rotation
        x.right = y;
        y.left = T2;

        // Return new root
        return x;
    }

    // A utility function to left rotate subtree rooted with x
// See the diagram given above.
    public static TreapNode leftRotate(TreapNode x) {
        TreapNode y = x.right;
        TreapNode T2 = y.left;

        // Perform rotation
        y.left = x;
        x.right = T2;

        // Return new root
        return y;
    }

    /* Utility function to add a new key */
    public static TreapNode newNode(int key) {
        TreapNode temp = new TreapNode();
        temp.key = key;
        temp.priority = (int)(Math.random() * 100);
        temp.left = temp.right = null;
        return temp;
    }
    /* Recursive implementation of insertion in Treap */
    public static TreapNode insert(TreapNode root, int key) {
        // If root is null, create a new node and return it
        if (root == null) {
            return newNode(key);
        }

        // If key is smaller than root
        if (key <= root.key) {
            // Insert in left subtree
            root.left = insert(root.left, key);

            // Fix Heap property if it is violated
            if (root.left.priority > root.priority) {
                root = rightRotate(root);
            }
        } else { // If key is greater
            // Insert in right subtree
            root.right = insert(root.right, key);

            // Fix Heap property if it is violated
            if (root.right.priority > root.priority) {
                root = leftRotate(root);
            }
        }
        return root;
    }
    /* Recursive implementation of Delete() */
    public static TreapNode deleteNode(TreapNode root, int key) {
        if (root == null)
            return root;

        if (key < root.key)
            root.left = deleteNode(root.left, key);
        else if (key > root.key)
            root.right = deleteNode(root.right, key);

        // IF KEY IS AT ROOT

        // If left is NULL
        else if (root.left == null)
        {
            TreapNode temp = root.right;
            root = temp;  // Make right child as root
        }
        // If Right is NULL
        else if (root.right == null)
        {
            TreapNode temp = root.left;
            root = temp;  // Make left child as root
        }
        // If key is at root and both left and right are not NULL
        else if (root.left.priority < root.right.priority)
        {
            root = leftRotate(root);
            root.left = deleteNode(root.left, key);
        }
        else
        {
            root = rightRotate(root);
            root.right = deleteNode(root.right, key);
        }

        return root;
    }
    // Java function to search a given key in a given BST
    public static TreapNode search(TreapNode root, int key)
    {
        // Base Cases: root is null or key is present at root
        if (root == null || root.key == key)
            return root;

        // Key is greater than root's key
        if (root.key < key)
            return search(root.right, key);

        // Key is smaller than root's key
        return search(root.left, key);
    }
    static void inorder(TreapNode root)
    {
        if (root != null)
        {
            inorder(root.left);
            System.out.print("key: " + root.key + " | priority: " + root.priority);
            if (root.left != null)
                System.out.print(" | left child: " + root.left.key);
            if (root.right != null)
                System.out.print(" | right child: " + root.right.key);
            System.out.println();
            inorder(root.right);
        }
    }

    // Driver Program to test above functions
    public static void main(String[] args)
    {
        Random rand = new Random();

        TreapNode root = null;
        root = insert(root, 50);
        root = insert(root, 30);
        root = insert(root, 20);
        root = insert(root, 40);
        root = insert(root, 70);
        root = insert(root, 60);
        root = insert(root, 80);

        System.out.println("Inorder traversal of the given tree:");
        inorder(root);

        System.out.println("\nDelete 20");
        root = deleteNode(root, 20);
        System.out.println("Inorder traversal of the modified tree:");
        inorder(root);

        System.out.println("\nDelete 30");
        root = deleteNode(root, 30);
        System.out.println("Inorder traversal of the modified tree:");
        inorder(root);

        System.out.println("\nDelete 50");
        root = deleteNode(root, 50);
        System.out.println("Inorder traversal of the modified tree:");
        inorder(root);

        TreapNode res = search(root, 50);
        System.out.println(res == null ? "\n50 Not Found" : "\n50 found");
    }

}

Python3

import random

# A Treap Node
class TreapNode:
    def __init__(self, key):
        self.key = key
        self.priority = random.randint(0, 99)
        self.left = None
        self.right = None

# T1, T2 and T3 are subtrees of the tree rooted with y
#  (on left side) or x (on right side)
#                y                               x
#               / \     Right Rotation          /  \
#              x   T3   – – – – – – – >        T1   y
#             / \       < - - - - - - -            / \
#            T1  T2     Left Rotation            T2  T3 */

# A utility function to right rotate subtree rooted with y
# See the diagram given above.

def rightRotate(y):
    x = y.left
    T2 = x.right

    # Perform rotation
    x.right = y
    y.left = T2

    # Return new root
    return x

def leftRotate(x):
    y = x.right
    T2 = y.left

    # Perform rotation
    y.left = x
    x.right = T2

    # Return new root
    return y

def insert(root, key):
    # If root is None, create a new node and return it
    if not root:
        return TreapNode(key)

    # If key is smaller than root
    if key <= root.key:
        # Insert in left subtree
        root.left = insert(root.left, key)

        # Fix Heap property if it is violated
        if root.left.priority > root.priority:
            root = rightRotate(root)
    else:
        # Insert in right subtree
        root.right = insert(root.right, key)

        # Fix Heap property if it is violated
        if root.right.priority > root.priority:
            root = leftRotate(root)
    return root

def deleteNode(root, key):
    if not root:
        return root

    if key < root.key:
        root.left = deleteNode(root.left, key)
    elif key > root.key:
        root.right = deleteNode(root.right, key)
    else:
        # IF KEY IS AT ROOT

        # If left is None
        if not root.left:
            temp = root.right
            root = None
            return temp

        # If right is None
        elif not root.right:
            temp = root.left
            root = None
            return temp

        # If key is at root and both left and right are not None
        elif root.left.priority < root.right.priority:
            root = leftRotate(root)
            root.left = deleteNode(root.left, key)
        else:
            root = rightRotate(root)
            root.right = deleteNode(root.right, key)

    return root

# A utility function to search a given key in a given BST
def search(root, key):
    # Base Cases: root is None or key is present at root
    if not root or root.key == key:
        return root

    # Key is greater than root's key
    if root.key < key:
        return search(root.right, key)

    # Key is smaller than root's key
    return search(root.left, key)

# A utility function to print tree
def inorder(root):
    if root:
        inorder(root.left)
        print("key:", root.key, "| priority:", root.priority, end="")
        if root.left:
            print(" | left child:", root.left.key, end="")
        if root.right:
            print(" | right child:", root.right.key, end="")
        print()
        inorder(root.right)

# Driver Program to test above functions
if __name__ == '__main__':
    random.seed(0)

    root = None
    root = insert(root, 50)
    root = insert(root, 30)
    root = insert(root, 20)
    root = insert(root, 40)
    root = insert(root, 70)
    root = insert(root, 60)
    root = insert(root, 80)

    print("Inorder traversal of the given tree")
    inorder(root)

    print("\nDelete 20")
    root = deleteNode(root, 20)
    print("Inorder traversal of the modified tree")
    inorder(root)

    print("\nDelete 30")
    root = deleteNode(root, 30)
    print("Inorder traversal of the modified tree")
    inorder(root)

    print("\nDelete 50")
    root = deleteNode(root, 50)
    print("Inorder traversal of the modified tree")
    inorder(root)

    res = search(root, 50)
    if res is None:
        print("50 Not Found")
    else:
        print("50 found")

# This code is contributed by Amit Mangal.

C#

using System;

// A Treap Node
class TreapNode
{
public int key, priority;
public TreapNode left, right;
}
/* T1, T2 and T3 are subtrees of the tree rooted with y
  (on left side) or x (on right side)
                y                               x
               / \     Right Rotation          /  \
              x   T3   – – – – – – – >        T1   y
             / \       < - - - - - - -            / \
            T1  T2     Left Rotation            T2  T3 */

// A utility function to right rotate subtree rooted with y
// See the diagram given above.
class Program
{
static Random rand = new Random();

  // A utility function to right rotate subtree
static TreapNode rightRotate(TreapNode y)
{
    TreapNode x = y.left;
    TreapNode T2 = x.right;
    // Perform rotation
    x.right = y;
    y.left = T2;
    return x;
}


    // A utility function to left rotate subtree rooted with x
// See the diagram given above.
static TreapNode leftRotate(TreapNode x)
{
    TreapNode y = x.right;
    TreapNode T2 = y.left;
  // Perform rotation
    y.left = x;
    x.right = T2;
    return y;
}

  /* Utility function to add a new key */
static TreapNode newNode(int key)
{
    TreapNode temp = new TreapNode();
    temp.key = key;
    temp.priority = rand.Next(100);
    temp.left = temp.right = null;
    return temp;
}

   /* Recursive implementation of insertion in Treap */
static TreapNode insert(TreapNode root, int key)
{
     // If root is null, create a new node and return it
    if (root == null)
    {
        return newNode(key);
    }
     // If key is smaller than root
    if (key <= root.key)
    {
        root.left = insert(root.left, key);

       // Fix Heap property if it is violated
        if (root.left.priority > root.priority)
        {
            root = rightRotate(root);
        }
    }
    else
    {// If key is greater
      // Insert in right subtree
        root.right = insert(root.right, key);
      // Fix Heap property if it is violated
      if (root.right.priority > root.priority)
        {
            root = leftRotate(root);
        }
    }
    return root;
}

   /* Recursive implementation of Delete() */
static TreapNode deleteNode(TreapNode root, int key)
{
    if (root == null)
    {
        return root;
    }
    if (key < root.key)
    {
        root.left = deleteNode(root.left, key);
    }
    else if (key > root.key)
    {
        root.right = deleteNode(root.right, key);
    }
    // IF KEY IS AT ROOT

        // If left is NULL
    else if (root.left == null)
    {
        TreapNode temp = root.right;
        root = temp; // Make right child as root
    }
          // If right is NULL
    else if (root.right == null)
    {
        TreapNode temp = root.left;
        root = temp;  // Make left child as root
    }
     // If key is at root and both left and right are not NULL
    else if (root.left.priority < root.right.priority)
    {
        root = leftRotate(root);
        root.left = deleteNode(root.left, key);
    }
    else
    {
        root = rightRotate(root);
        root.right = deleteNode(root.right, key);
    }
    return root;
}

  // Function to search a given key in a given BST
static TreapNode search(TreapNode root, int key)
{
    // Base Cases: root is null or key is present at root
    if (root == null || root.key == key)
    {
        return root;
    }
   // Key is greater than root's key
    if (root.key < key)
    {
        return search(root.right, key);
    }
   // Key is smaller than root's key
    return search(root.left, key);
}

  // A utility function to print tree
static void inorder(TreapNode root)
{
    if (root != null)
    {
        inorder(root.left);
        Console.Write("key: " + root.key + " | priority: " + root.priority);
        if (root.left != null)
        {
            Console.Write(" | left child: " + root.left.key);
        }
        if (root.right != null)
        {
            Console.Write(" | right child: " + root.right.key);
        }
        Console.WriteLine();
        inorder(root.right);
    }
}

 // Driver Code
static void Main(string[] args)
{
    TreapNode root = null;
        root = insert(root, 50);
        root = insert(root, 30);
        root = insert(root, 20);
        root = insert(root, 40);
        root = insert(root, 70);
        root = insert(root, 60);
        root = insert(root, 80);

        Console.WriteLine("Inorder traversal of the given tree:");
        inorder(root);
        Console.WriteLine("\nDelete 20");
        root = deleteNode(root, 20);
        Console.WriteLine("Inorder traversal of the modified tree:");
        inorder(root);
        Console.WriteLine("\nDelete 30");
        root = deleteNode(root, 30);
        Console.WriteLine("Inorder traversal of the modified tree:");
        inorder(root);
        Console.WriteLine("\nDelete 50");
        root = deleteNode(root, 50);
        Console.WriteLine("Inorder traversal of the modified tree:");
        inorder(root);
        TreapNode res = search(root, 50);
        Console.WriteLine(res == null ? "\n50 Not Found" : "\n50 found");
    }
};

Javascript

// A Treap Node
class TreapNode {
    constructor(key) {
        this.key = key;
        this.priority = Math.floor(Math.random() * 100);
        this.left = null;
        this.right = null;
    }
}

/* T1, T2, and T3 are subtrees of the tree rooted with y
  (on the left side) or x (on the right side)
                y                               x
               / \     Right Rotation          /  \
              x   T3   – – – – – – – >        T1   y
             / \       < - - - - - - -            / \
            T1  T2     Left Rotation            T2  T3 */

// A utility function to right rotate subtree rooted with y
// See the diagram given above.
function rightRotate(y) {
    let x = y.left;
    let T2 = x.right;

    // Perform rotation
    x.right = y;
    y.left = T2;

    // Return new root
    return x;
}

// A utility function to left rotate subtree rooted with x
// See the diagram given above.
function leftRotate(x) {
    let y = x.right;
    let T2 = y.left;

    // Perform rotation
    y.left = x;
    x.right = T2;

    // Return new root
    return y;
}

/* Utility function to add a new key */
function newNode(key) {
    let temp = new TreapNode(key);
    return temp;
}

// JavaScript implementation of search in a given Treap
function search(root, key) {
    // Base Cases: root is null or key is present at root
    if (root === null || root.key === key)
        return root;

    // Key is greater than root's key
    if (root.key < key)
        return search(root.right, key);

    // Key is smaller than root's key
    return search(root.left, key);
}

/* Recursive implementation of insertion in Treap */
function insert(root, key) {
    // If root is null, create a new node and return it
    if (!root)
        return newNode(key);

    // If key is smaller than root
    if (key <= root.key) {
        // Insert in the left subtree
        root.left = insert(root.left, key);

        // Fix Heap property if it is violated
        if (root.left.priority > root.priority)
            root = rightRotate(root);
    } else { // If key is greater
        // Insert in the right subtree
        root.right = insert(root.right, key);

        // Fix Heap property if it is violated
        if (root.right.priority > root.priority)
            root = leftRotate(root);
    }
    return root;
}

/* Recursive implementation of Delete() */
function deleteNode(root, key) {
    if (root === null)
        return root;

    if (key < root.key)
        root.left = deleteNode(root.left, key);
    else if (key > root.key)
        root.right = deleteNode(root.right, key);

    // IF KEY IS AT ROOT

    // If left is NULL
    else if (root.left === null) {
        let temp = root.right;
        root = temp; // Make the right child the root
    }
    // If Right is NULL
    else if (root.right === null) {
        let temp = root.left;
        root = temp; // Make the left child the root
    }
    // If the key is at the root, and both left and right are not NULL
    else if (root.left.priority < root.right.priority) {
        root = leftRotate(root);
        root.left = deleteNode(root.left, key);
    } else {
        root = rightRotate(root);
        root.right = deleteNode(root.right, key);
    }

    return root;
}

// A utility function to print tree
function inorder(root) {
    if (root) {
        inorder(root.left);
        console.log(`key: ${root.key} | priority: ${root.priority}`);
        if (root.left)
            console.log(` | left child: ${root.left.key}`);
        if (root.right)
            console.log(` | right child: ${root.right.key}`);
        console.log();
        inorder(root.right);
    }
}

// Driver Program to test above functions
function main() {
    let root = null;
    root = insert(root, 50);
    root = insert(root, 30);
    root = insert(root, 20);
    root = insert(root, 40);
    root = insert(root, 70);
    root = insert(root, 60);
    root = insert(root, 80);

    console.log("Inorder traversal of the given tree");
    inorder(root);

    console.log("\nDelete 20");
    root = deleteNode(root, 20);
    console.log("Inorder traversal of the modified tree");
    inorder(root);

    console.log("\nDelete 30");
    root = deleteNode(root, 30);
    console.log("Inorder traversal of the modified tree");
    inorder(root);

    console.log("\nDelete 50");
    root = deleteNode(root, 50);
    console.log("Inorder traversal of the modified tree");
    inorder(root);

    let res = search(root, 50);
    console.log(res === null ? "\n50 Not Found" : "\n50 found");
}

main();

// Contributed by siddhesh

Output

...eft child: 20 | right child: 40
key: 40 | priority: %d 87 | right child: 60
key: 50 | priority: %d 46
key: 60 | priority: %d 62 | left child: 50 | right child: 80
key: 70 | priority: %d 10
key: 80 | priority: %d 57 | left child: 70

Delete 20
Inorder traversal of the modified tree 
key: 30 | priority: %d 92 | right child: 40
key: 40 | priority: %d 87 | right child: 60
key: 50 | priority: %d 46
key: 60 | priority: %d 62 | left child: 50 | right child: 80
key: 70 | priority: %d 10
key: 80 | priority: %d 57 | left child: 70

Delete 30
Inorder traversal of the modified tree 
key: 40 | priority: %d 87 | right child: 60
key: 50 | priority: %d 46
key: 60 | priority: %d 62 | left child: 50 | right child: 80
key: 70 | priority: %d 10
key: 80 | priority: %d 57 | left child: 70

Delete 50
Inorder traversal of the modified tree 
key: 40 | priority: %d 87 | right child: 60
key: 60 | priority: %d 62 | right child: 80
key: 70 | priority: %d 10
key: 80 | priority: %d 57 | left child: 70

50 Not Found 

Explanation of the above output:

Every node is written as key(priority)

The above code constructs below tree
  20(92)
     \
     50(73)
     /     \
  30(48)   60(55) 
     \        \
  40(21)     70(50)
                \
                80(44)   


After deleteNode(20)
     50(73)
     /     \
  30(48)   60(55) 
     \        \
  40(21)     70(50)
                \
                80(44)   
 

After deleteNode(30)
     50(73)
     /     \
  40(21)   60(55) 
             \
             70(50)
               \
               80(44)   
 

After deleteNode(50)
     60(55)
     /     \
  40(21)  70(50)  
             \
            80(44)   

Thanks to Jai Goyal for providing an initial implementation. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.