diff --git a/src/main/java/com/thealgorithms/datastructures/trees/Treap.java b/src/main/java/com/thealgorithms/datastructures/trees/Treap.java new file mode 100644 index 000000000000..68c713f50640 --- /dev/null +++ b/src/main/java/com/thealgorithms/datastructures/trees/Treap.java @@ -0,0 +1,329 @@ +package com.thealgorithms.datastructures.trees; + +import java.util.Random; + +/** + * Treap -> Tree + Heap + * Also called as cartesian tree + * + * @see + * + */ + +public class Treap { + + static class TreapNode { + /** + * TreapNode class defines the individual nodes in the Treap + * + * value -> holds the value of the node. + * Binary Search Tree is built based on value. + * + * priority -> holds the priority of the node. + * Heaps are maintained based on priority. + * It is randomly assigned + * + * size -> holds the size of the subtree with current node as root + * + * left -> holds the left subtree + * right -> holds the right subtree + */ + public int value; + private int priority, size; + public TreapNode left, right; + + public TreapNode(int value, int priority) { + this.value = value; + this.priority = priority; + this.size = 1; + this.left = this.right = null; + } + + /** + * updateSize -> updates the subtree size of the current node + */ + private void updateSize() { + this.size = 1; + if (this.left != null) this.size += this.left.size; + if (this.right != null) this.size += this.right.size; + } + } + + /** + * root -> holds the root node in the Treap + * random -> to generate random priority for the nodes in the Treap + */ + private TreapNode root; + private Random random = new Random(); + + /** + * Constructors + * + * Treap() -> create an empty Treap + * Treap(int[] nodeValues) -> add the elements given in the array to the Treap + */ + public Treap() { + this.root = null; + } + + /** + * merges two Treaps left and right into a single Treap + * + * @param left left Treap + * @param right right Treap + * @return root of merged Treap + */ + private TreapNode merge(TreapNode left, TreapNode right) { + if (left == null) return right; + if (right == null) return left; + + if (left.priority > right.priority) { + left.right = merge(left.right, right); + left.updateSize(); + return left; + } else { + right.left = merge(left, right.left); + right.updateSize(); + return right; + } + } + + /** + * split the Treap into two Treaps where left Treap has nodes <= key and right Treap has nodes > key + * + * @param node root node to be split + * @param key key to compare the nodes + * @return TreapNode array of size 2. + * TreapNode[0] contains the root of left Treap after split + * TreapNode[1] contains the root of right Treap after split + */ + private TreapNode[] split(TreapNode node, int key) { + if (node == null) { + return new TreapNode[] {null, null}; + } + + TreapNode[] result; + + if (node.value <= key) { + result = split(node.right, key); + node.right = result[0]; + node.updateSize(); + result[0] = node; + } else { + result = split(node.left, key); + node.left = result[1]; + node.updateSize(); + result[1] = node; + } + + return result; + } + + /** + * insert a node into the Treap + * + * @param value value to be inserted into the Treap + * @return root of the Treap where the value is inserted + */ + public TreapNode insert(int value) { + if (root == null) { + root = new TreapNode(value, random.nextInt()); + return root; + } + + TreapNode[] splitted = split(root, value); + + TreapNode node = new TreapNode(value, random.nextInt()); + + TreapNode tempMerged = merge(splitted[0], node); + tempMerged.updateSize(); + + TreapNode merged = merge(tempMerged, splitted[1]); + merged.updateSize(); + + root = merged; + + return root; + } + + /** + * delete a value from root if present + * + * @param value value to be deleted from the Treap + * @return root of the Treap where delete has been performed + */ + public TreapNode delete(int value) { + root = deleteNode(root, value); + return root; + } + + private TreapNode deleteNode(TreapNode root, int value) { + if (root == null) return null; + + if (value < root.value) { + root.left = deleteNode(root.left, value); + } else if (value > root.value) { + root.right = deleteNode(root.right, value); + } else { + root = merge(root.left, root.right); + } + + if (root != null) root.updateSize(); + return root; + } + + /** + * print inorder traversal of the Treap + */ + public void inOrder() { + System.out.print("{"); + printInorder(root); + System.out.print("}"); + } + + private void printInorder(TreapNode root) { + if (root == null) return; + printInorder(root.left); + System.out.print(root.value + ","); + printInorder(root.right); + } + + /** + * print preOrder traversal of the Treap + */ + public void preOrder() { + System.out.print("{"); + printPreOrder(root); + System.out.print("}"); + } + + private void printPreOrder(TreapNode root) { + if (root == null) return; + System.out.print(root.value + ","); + printPreOrder(root.left); + printPreOrder(root.right); + } + + /** + * print postOrder traversal of the Treap + */ + public void postOrder() { + System.out.print("{"); + printPostOrder(root); + System.out.print("}"); + } + + private void printPostOrder(TreapNode root) { + if (root == null) return; + printPostOrder(root.left); + printPostOrder(root.right); + System.out.print(root.value + ","); + } + + /** + * Search a value in the Treap + * + * @param value value to be searched for + * @return node containing the value + * null if not found + */ + public TreapNode search(int value) { + return searchVal(root, value); + } + + private TreapNode searchVal(TreapNode root, int value) { + if (root == null) return null; + + if (root.value == value) + return root; + else if (root.value < value) + return searchVal(root.right, value); + else + return searchVal(root.left, value); + } + + /** + * find the lowerBound of a value in the Treap + * + * @param value value for which lowerBound is to be found + * @return node which is the lowerBound of the value passed + */ + public TreapNode lowerBound(int value) { + TreapNode lowerBoundNode = null; + TreapNode current = root; + + while (current != null) { + if (current.value >= value) { + lowerBoundNode = current; + current = current.left; + } else + current = current.right; + } + + return lowerBoundNode; + } + + /** + * find the upperBound of a value in the Treap + * + * @param value value for which upperBound is to be found + * @return node which is the upperBound of the value passed + */ + public TreapNode upperBound(int value) { + TreapNode upperBoundNode = null; + TreapNode current = root; + + while (current != null) { + if (current.value > value) { + upperBoundNode = current; + current = current.left; + } else + current = current.right; + } + + return upperBoundNode; + } + + /** + * returns size of the Treap + */ + public int size() { + if (root == null) return 0; + return root.size; + } + + /** + * returns if Treap is empty + */ + public boolean isEmpty() { + return root == null; + } + + /** + * returns root node of the Treap + */ + public TreapNode getRoot() { + return root; + } + + /** + * returns left node of the TreapNode + */ + public TreapNode getLeft(TreapNode node) { + return node.left; + } + + /** + * returns the right node of the TreapNode + */ + public TreapNode getRight(TreapNode node) { + return node.right; + } + + /** + * prints the value, priority, size of the subtree of the TreapNode, left TreapNode and right TreapNode of the node + */ + public String toString(TreapNode node) { + return "{value : " + node.value + ", priority : " + node.priority + ", subTreeSize = " + node.size + ", left = " + node.left + ", right = " + node.right + "}"; + } +} diff --git a/src/test/java/com/thealgorithms/datastructures/trees/TreapTest.java b/src/test/java/com/thealgorithms/datastructures/trees/TreapTest.java new file mode 100644 index 000000000000..dbd169c06481 --- /dev/null +++ b/src/test/java/com/thealgorithms/datastructures/trees/TreapTest.java @@ -0,0 +1,74 @@ +package com.thealgorithms.datastructures.trees; + +import static org.junit.jupiter.api.Assertions.assertEquals; + +import org.junit.jupiter.api.Test; + +public class TreapTest { + + @Test + public void searchAndFound() { + Treap treap = new Treap(); + treap.insert(5); + treap.insert(9); + treap.insert(6); + treap.insert(2); + treap.insert(3); + treap.insert(8); + treap.insert(1); + assertEquals(5, treap.search(5).value); + } + + @Test + public void searchAndNotFound() { + Treap treap = new Treap(); + treap.insert(5); + treap.insert(9); + treap.insert(6); + treap.insert(2); + treap.insert(3); + treap.insert(8); + treap.insert(1); + assertEquals(null, treap.search(4)); + } + + @Test + public void lowerBound() { + Treap treap = new Treap(); + treap.insert(5); + treap.insert(9); + treap.insert(6); + treap.insert(2); + treap.insert(3); + treap.insert(8); + treap.insert(1); + assertEquals(5, treap.lowerBound(4).value); + } + + @Test + public void upperBound() { + Treap treap = new Treap(); + treap.insert(5); + treap.insert(9); + treap.insert(6); + treap.insert(2); + treap.insert(3); + treap.insert(8); + treap.insert(1); + assertEquals(6, treap.upperBound(5).value); + } + + @Test + public void misc() { + Treap treap = new Treap(); + treap.insert(5); + treap.insert(9); + treap.insert(6); + treap.insert(2); + treap.insert(3); + treap.insert(8); + treap.insert(1); + assertEquals(7, treap.size()); + assertEquals(false, treap.isEmpty()); + } +}