From 664bcf494f11603a51783e5b1eead7846deac9e2 Mon Sep 17 00:00:00 2001 From: Ian Cowan <38896380+iccowan@users.noreply.github.com> Date: Sun, 31 Oct 2021 01:56:52 -0400 Subject: [PATCH] Check if Binary Tree is Balanced `Closes #2719` (#2732) --- .../Trees/CheckIfBinaryTreeBalanced.java | 274 ++++++++++++++++++ 1 file changed, 274 insertions(+) create mode 100644 DataStructures/Trees/CheckIfBinaryTreeBalanced.java diff --git a/DataStructures/Trees/CheckIfBinaryTreeBalanced.java b/DataStructures/Trees/CheckIfBinaryTreeBalanced.java new file mode 100644 index 00000000..694ceb65 --- /dev/null +++ b/DataStructures/Trees/CheckIfBinaryTreeBalanced.java @@ -0,0 +1,274 @@ +package DataStructures.Trees; + +import java.util.Stack; +import java.util.HashMap; + +/** + * This class will check if a BinaryTree is balanced. + * A balanced binary tree is defined as a binary tree where + * the differenced in height between the left and right + * subtree of each node differs by at most one. + * + * This can be done in both an iterative and recursive + * fashion. Below, `isBalancedRecursive()` is + * implemented in a recursive fashion, and + * `isBalancedIterative()` is implemented in an + * iterative fashion. + * + * @author [Ian Cowan](https://github.com/iccowan) + */ + public class CheckIfBinaryTreeBalanced { + + /** + * This class implements the BinaryTree for these algorithms + */ + class BinaryTree { + /** The root node of the binary tree */ + BTNode root = null; + } + + /** + * This class implements the nodes for the binary tree + */ + class BTNode { + /** The value of the node */ + int value; + + /** The left child of the node */ + BTNode left = null; + + /** The right child of the node */ + BTNode right = null; + + /** Constructor */ + BTNode (int value) { + this.value = value; + } + } + + /** + * Recursive is BT balanced implementation + * + * @param binaryTree The binary tree to check if balanced + */ + public boolean isBalancedRecursive(BinaryTree binaryTree) { + // Create an array of length 1 to keep track of our balance + // Default to true. We use an array so we have an efficient mutable object + boolean[] isBalanced = new boolean[1]; + isBalanced[0] = true; + + // Check for balance and return whether or not we are balanced + isBalancedRecursive(binaryTree.root, 0, isBalanced); + return isBalanced[0]; + } + + /** + * Private helper method to keep track of the depth and balance during + * recursion. We effectively perform a modified post-order traversal where + * we are looking at the heights of both children of each node in the tree + * + * @param node The current node to explore + * @param depth The current depth of the node + * @param isBalanced The array of length 1 keeping track of our balance + */ + private int isBalancedRecursive(BTNode node, int depth, boolean[] isBalanced) { + // If the node is null, we should not explore it and the height is 0 + // If the tree is already not balanced, might as well stop because we + // can't make it balanced now! + if (node == null || ! isBalanced[0]) + return 0; + + // Visit the left and right children, incrementing their depths by 1 + int leftHeight = isBalancedRecursive(node.left, depth + 1, isBalanced); + int rightHeight = isBalancedRecursive(node.right, depth + 1, isBalanced); + + // If the height of either of the left or right subtrees differ by more + // than 1, we cannot be balanced + if (Math.abs(leftHeight - rightHeight) > 1) + isBalanced[0] = false; + + // The height of our tree is the maximum of the heights of the left + // and right subtrees plus one + return Math.max(leftHeight, rightHeight) + 1; + } + + /** + * Iterative is BT balanced implementation + */ + public boolean isBalancedIterative(BinaryTree binaryTree) { + // Default that we are balanced and our algo will prove it wrong + boolean isBalanced = true; + + // Create a stack for our post order traversal + Stack nodeStack = new Stack(); + + // For post order traversal, we'll have to keep track of where we + // visited last + BTNode lastVisited = null; + + // Create a HashMap to keep track of the subtree heights for each node + HashMap subtreeHeights = new HashMap(); + + // We begin at the root of the tree + BTNode node = binaryTree.root; + + // We loop while: + // - the node stack is empty and the node we explore is null + // AND + // - the tree is still balanced + while (! (nodeStack.isEmpty() && node == null) && isBalanced) { + // If the node is not null, we push it to the stack and continue + // to the left + if (node != null) { + nodeStack.push(node); + node = node.left; + // Once we hit a node that is null, we are as deep as we can go + // to the left + } else { + // Find the last node we put on the stack + node = nodeStack.peek(); + + // If the right child of the node has either been visited or + // is null, we visit this node + if (node.right == null || node.right == lastVisited) { + // We assume the left and right heights are 0 + int leftHeight = 0; + int rightHeight = 0; + + // If the right and left children are not null, we must + // have already explored them and have a height + // for them so let's get that + if (node.left != null) + leftHeight = subtreeHeights.get(node.left); + + if (node.right != null) + rightHeight = subtreeHeights.get(node.right); + + // If the difference in the height of the right subtree + // and left subtree differs by more than 1, we cannot be + // balanced + if (Math.abs(rightHeight - leftHeight) > 1) + isBalanced = false; + + // The height of the subtree containing this node is the + // max of the left and right subtree heighs plus 1 + subtreeHeights.put(node, Math.max(rightHeight, leftHeight) + 1); + + // We've now visited this node, so we pop it from the stack + nodeStack.pop(); + lastVisited = node; + + // Current visiting node is now null + node = null; + // If the right child node of this node has not been visited + // and is not null, we need to get that child node on the stack + } else { + node = node.right; + } + } + } + + // Return whether or not the tree is balanced + return isBalanced; + } + + /** + * Generates the following unbalanced binary tree for testing + * 0 + * / \ + * / \ + * 0 0 + * / / \ + * / / \ + * 0 0 0 + * / \ + * / \ + * 0 0 + * / + * / + * 0 + */ + private BinaryTree buildUnbalancedTree() { + BinaryTree tree = new BinaryTree(); + tree.root = new BTNode(0); + + BTNode root = tree.root; + root.left = new BTNode(0); + root.right = new BTNode(0); + + BTNode left = root.left; + BTNode right = root.right; + + left.left = new BTNode(0); + right.left = new BTNode(0); + right.right = new BTNode(0); + right.left.right = new BTNode(0); + + left = left.left; + left.left = new BTNode(0); + left.left.left = new BTNode(0); + left.left.left.left = new BTNode(0); + + return tree; + } + + /** + * Generates the following balanced binary tree for testing + * 0 + * / \ + * / \ + * 0 0 + * / \ / \ + * / 0 / \ + * 0 0 0 + * / / + * / / + * 0 0 + */ + private BinaryTree buildBalancedTree() { + BinaryTree tree = new BinaryTree(); + tree.root = new BTNode(0); + + BTNode root = tree.root; + root.left = new BTNode(0); + root.right = new BTNode(0); + + BTNode left = root.left; + BTNode right = root.right; + + left.left = new BTNode(0); + left.right = new BTNode(0); + right.left = new BTNode(0); + right.right = new BTNode(0); + + right.right.left = new BTNode(0); + + left.left.left = new BTNode(0); + + return tree; + } + + /** + * Main + */ + public static void main(String[] args) { + // We create a new object to check the binary trees for balance + CheckIfBinaryTreeBalanced balanceCheck = new CheckIfBinaryTreeBalanced(); + + // Build a balanced and unbalanced binary tree + BinaryTree balancedTree = balanceCheck.buildBalancedTree(); + BinaryTree unbalancedTree = balanceCheck.buildUnbalancedTree(); + + // Run basic tests on the algorithms to check for balance + boolean isBalancedRB = balanceCheck.isBalancedRecursive(balancedTree); // true + boolean isBalancedRU = balanceCheck.isBalancedRecursive(unbalancedTree); // false + boolean isBalancedIB = balanceCheck.isBalancedIterative(balancedTree); // true + boolean isBalancedIU = balanceCheck.isBalancedIterative(unbalancedTree); // false + + // Print the results + System.out.println("isBalancedRB: " + isBalancedRB); + System.out.println("isBalancedRU: " + isBalancedRU); + System.out.println("isBalancedIB: " + isBalancedIB); + System.out.println("isBalancedIU: " + isBalancedIU); + } + } \ No newline at end of file