Merge pull request #8556 from maryarm/BAEL-3454

BAEL-3454: Guide to AVL trees in Java

algorithms-miscellaneous-5/src/main/java/com/baeldung/algorithms/balancedbinarytree/AVLTree.java

@@ -0,0 +1,141 @@
+package com.baeldung.algorithms.balancedbinarytree;
+
+public class AVLTree {
+
+    public class Node {
+        int key;
+        int height;
+        Node left;
+        Node right;
+
+        Node(int key) {
+            this.key = key;
+        }
+    }
+
+    private Node root;
+
+    public Node find(int key) {
+        Node current = root;
+        while (current != null) {
+            if (current.key == key) {
+               break;
+            }
+            current = current.key < key ? current.right : current.left;
+        }
+        return current;
+    }
+
+    public void insert(int key) {
+        root = insert(root, key);
+    }
+
+    public void delete(int key) {
+        root = delete(root, key);
+    }
+
+    public Node getRoot() {
+        return root;
+    }
+
+    public int height() {
+        return root == null ? -1 : root.height;
+    }
+
+    private Node insert(Node node, int key) {
+        if (node == null) {
+            return new Node(key);
+        } else if (node.key > key) {
+            node.left = insert(node.left, key);
+        } else if (node.key < key) {
+            node.right = insert(node.right, key);
+        } else {
+            throw new RuntimeException("duplicate Key!");
+        }
+        return rebalance(node);
+    }
+
+    private Node delete(Node node, int key) {
+        if (node == null) {
+            return node;
+        } else if (node.key > key) {
+            node.left = delete(node.left, key);
+        } else if (node.key < key) {
+            node.right = delete(node.right, key);
+        } else {
+            if (node.left == null || node.right == null) {
+                node = (node.left == null) ? node.right : node.left;
+            } else {
+                Node mostLeftChild = mostLeftChild(node.right);
+                node.key = mostLeftChild.key;
+                node.right = delete(node.right, node.key);
+            }
+        }
+        if (node != null) {
+            node = rebalance(node);
+        }
+        return node;
+    }
+
+    private Node mostLeftChild(Node node) {
+        Node current = node;
+        /* loop down to find the leftmost leaf */
+        while (current.left != null) {
+            current = current.left;
+        }
+        return current;
+    }
+
+    private Node rebalance(Node z) {
+        updateHeight(z);
+        int balance = getBalance(z);
+        if (balance > 1) {
+            if (height(z.right.right) > height(z.right.left)) {
+                z = rotateLeft(z);
+            } else {
+                z.right = rotateRight(z.right);
+                z = rotateLeft(z);
+            }
+        } else if (balance < -1) {
+            if (height(z.left.left) > height(z.left.right)) {
+                z = rotateRight(z);
+            } else {
+                z.left = rotateLeft(z.left);
+                z = rotateRight(z);
+            }
+        }
+        return z;
+    }
+
+    private Node rotateRight(Node y) {
+        Node x = y.left;
+        Node z = x.right;
+        x.right = y;
+        y.left = z;
+        updateHeight(y);
+        updateHeight(x);
+        return x;
+    }
+
+    private Node rotateLeft(Node y) {
+        Node x = y.right;
+        Node z = x.left;
+        x.left = y;
+        y.right = z;
+        updateHeight(y);
+        updateHeight(x);
+        return x;
+    }
+
+    private void updateHeight(Node n) {
+        n.height = 1 + Math.max(height(n.left), height(n.right));
+    }
+
+    private int height(Node n) {
+        return n == null ? -1 : n.height;
+    }
+
+    public int getBalance(Node n) {
+        return (n == null) ? 0 : height(n.right) - height(n.left);
+    }
+}

algorithms-miscellaneous-5/src/test/java/com/baeldung/algorithms/balancedbinarytree/AVLTreeUnitTest.java

@@ -0,0 +1,83 @@
+package com.baeldung.algorithms.balancedbinarytree;
+
+import org.junit.Assert;
+import org.junit.Test;
+
+public class AVLTreeUnitTest {
+
+    @Test
+    public void givenEmptyTree_whenHeightCalled_shouldReturnMinus1() {
+        AVLTree tree = new AVLTree();
+        Assert.assertEquals(-1, tree.height());
+    }
+
+    @Test
+    public void givenEmptyTree_whenInsertCalled_heightShouldBeZero() {
+        AVLTree tree = new AVLTree();
+        tree.insert(1);
+        Assert.assertEquals(0, tree.height());
+    }
+
+    @Test
+    public void givenEmptyTree_whenInsertCalled_treeShouldBeAvl() {
+        AVLTree tree = new AVLTree();
+        tree.insert(1);
+        Assert.assertTrue(isAVL(tree));
+    }
+
+    @Test
+    public void givenSampleTree_whenInsertCalled_treeShouldBeAvl() {
+        AVLTree tree = getSampleAVLTree();
+        int newKey = 11;
+        tree.insert(newKey);
+        Assert.assertTrue(isAVL(tree));
+    }
+
+    @Test
+    public void givenSampleTree_whenFindExistingKeyCalled_shouldReturnMatchedNode() {
+        AVLTree tree = getSampleAVLTree();
+        int existingKey = 2;
+        AVLTree.Node result = tree.find(existingKey);
+        Assert.assertEquals(result.key, existingKey);
+    }
+
+    @Test
+    public void givenSampleTree_whenFindNotExistingKeyCalled_shouldReturnNull() {
+        AVLTree tree = getSampleAVLTree();
+        int notExistingKey = 11;
+        AVLTree.Node result = tree.find(notExistingKey);
+        Assert.assertNull(result);
+    }
+
+    @Test
+    public void givenEmptyTree_whenDeleteCalled_treeShouldBeAvl() {
+        AVLTree tree = new AVLTree();
+        tree.delete(1);
+        Assert.assertTrue(isAVL(tree));
+    }
+
+    @Test
+    public void givenSampleTree_whenDeleteCalled_treeShouldBeAvl() {
+        AVLTree tree = getSampleAVLTree();
+        tree.delete(1);
+        Assert.assertTrue(isAVL(tree, tree.getRoot()));
+    }
+
+    private boolean isAVL(AVLTree tree) {
+       return isAVL(tree, tree.getRoot());
+    }
+
+    private boolean isAVL(AVLTree tree, AVLTree.Node node) {
+        if ( node == null )
+            return true;
+        int balance = tree.getBalance(node);
+        return (balance <= 1 && balance >= -1) && isAVL(tree, node.left) && isAVL(tree, node.right);
+    }
+
+    private AVLTree getSampleAVLTree() {
+        AVLTree avlTree = new AVLTree();
+        for (int i = 0; i < 10; i++)
+            avlTree.insert(i);
+        return avlTree;
+    }
+}