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 BSTTreapNode* 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 BSTdef 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. |
Java
// Java function to search a given key in a given BSTpublic 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);} |
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;} |
Python3
# Recursive implementation of insertion in Treapdef 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. |
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;} |
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;} |
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. |
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 Nodestruct 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 BSTTreapNode* 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 treevoid 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 functionsint 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;} |
Python3
import random# A Treap Nodeclass 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 ydef 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 rootdef 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 BSTdef 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 treedef 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 functionsif __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. |
Java
/*package whatever //do not write package name here */import java.util.*;// A Treap Nodeclass 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"); }} |
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.
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