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```
package com.thealgorithms.datastructures.trees;
import java.util.HashMap;
import java.util.Stack;
/**
* 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<BTNode> nodeStack = new Stack<BTNode>();
// 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<BTNode, Integer> subtreeHeights = new HashMap<BTNode, Integer>();
// 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);
}
}
```