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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Balanced Binary Tree - LeetCode 110</title>
<link rel="stylesheet" href="styles.css">
<script src="https://d3js.org/d3.v7.min.js"></script>
</head>
<body>
<div class="container">
<div class="problem-info">
<h1><span class="problem-number">#0110</span> Balanced Binary Tree</h1>
<p><strong>Problem:</strong> Determine if a binary tree is height-balanced. A height-balanced tree has subtrees that differ in height by at most 1.</p>
<p><strong>Pattern:</strong> DFS - Check height difference at each node, return -1 if unbalanced</p>
<div class="problem-meta">
<span class="meta-tag">🌳 Tree</span>
<span class="meta-tag">⏱️ O(n)</span>
</div>
<div class="file-ref">
📄 Python: <code>python/0110_balanced_binary_tree/0110_balanced_binary_tree.py</code>
</div>
</div>
<div class="explanation-panel">
<h4>🧠 How It Works (Layman's Terms)</h4>
<p>Tree traversal is like <strong>exploring a family tree</strong>:</p>
<ul>
<li><strong>Root:</strong> Start at the top node</li>
<li><strong>Recurse:</strong> Visit left and right children</li>
<li><strong>Base case:</strong> Stop at null/leaf nodes</li>
<li><strong>Combine:</strong> Build answer from subtree results</li>
</ul>
</div>
<div class="visualization-section">
<h3>🎬 Step-by-Step Visualization</h3>
<div class="visualization">
<svg id="mainSvg"></svg>
</div>
<div class="controls">
<button id="stepBtn">Step</button>
<button id="autoBtn">Auto Run</button>
<button id="resetBtn">Reset</button>
<div class="speed-control">
<label for="speed">Speed:</label>
<input type="range" id="speed" min="100" max="2000" value="800">
</div>
</div>
<div class="status" id="status">Click "Step" to check if tree is balanced</div>
<div class="variables">
<div class="var-item">
<span class="var-label">Current Node:</span>
<span id="currentDisplay">-</span>
</div>
<div class="var-item">
<span class="var-label">Heights (L, R):</span>
<span id="heightDisplay">-</span>
</div>
<div class="var-item">
<span class="var-label">Balanced:</span>
<span id="balancedDisplay">-</span>
</div>
</div>
</div>
<div class="code-section">
<h3>💻 Python Solution</h3>
<div class="code-block">
<pre>from typing import Optional
"""
LeetCode Balanced Binary Tree
Problem from LeetCode: https://leetcode.com/problems/balanced-binary-tree/
Description:
Given a binary tree, determine if it is height-balanced.
A height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differs by more than one.
Example 1:
Input: root = [3,9,20,null,null,15,7]
Output: true
Example 2:
Input: root = [1,2,2,3,3,null,null,4,4]
Output: false
Example 3:
Input: root = []
Output: true
"""
class TreeNode:
def __init__(self, val=0, left=None, right=None):
self.val = val
self.left = left
self.right = right
class Solution:
def is_balanced(self, root: Optional[TreeNode]) -> bool:
"""
Determine if the binary tree is height-balanced.
Args:
root: Root of the binary tree
Returns:
bool: True if the tree is height-balanced, False otherwise
"""
# Helper function to calculate height and check balance
def check_height(node):
if not node:
return 0
# Check left subtree
left_height = check_height(node.left)
if left_height == -1:
return -1 # Left subtree is unbalanced
# Check right subtree
right_height = check_height(node.right)
if right_height == -1:
return -1 # Right subtree is unbalanced
# Check if current node is balanced
if abs(left_height - right_height) > 1:
return -1 # Current node is unbalanced
# Return height of current subtree
return max(left_height, right_height) + 1
return check_height(root) != -1
def is_balanced_separate(self, root: Optional[TreeNode]) -> bool:
"""
Alternative implementation with separate height calculation.
Less efficient but more straightforward.
Args:
root: Root of the binary tree
Returns:
bool: True if the tree is height-balanced, False otherwise
"""
if not root:
return True
# Helper function to calculate height
def height(node):
if not node:
return 0
return max(height(node.left), height(node.right)) + 1
# Check if current node is balanced
if abs(height(root.left) - height(root.right)) > 1:
return False
# Check if both subtrees are balanced
return self.is_balanced_separate(root.left) and self.is_balanced_separate(root.right)
# Helper function to create a binary tree from a list
def create_tree(values, index=0):
if not values or index >= len(values) or values[index] is None:
return None
root = TreeNode(values[index])
root.left = create_tree(values, 2 * index + 1)
root.right = create_tree(values, 2 * index + 2)
return root
if __name__ == '__main__':
# Example usage based on LeetCode sample
solution = Solution()
# Example 1: Balanced tree
# 3
# / \
# 9 20
# / \
# 15 7
tree1 = create_tree([3, 9, 20, None, None, 15, 7])
result1 = solution.is_balanced(tree1)
print(f"Example 1: {result1}") # Expected output: True
# Example 2: Unbalanced tree
# 1
# / \
# 2 2
# / \
# 3 3
# / \
# 4 4
tree2 = create_tree([1, 2, 2, 3, 3, None, None, 4, 4])
result2 = solution.is_balanced(tree2)
print(f"Example 2: {result2}") # Expected output: False
# Example 3: Empty tree
tree3 = None
result3 = solution.is_balanced(tree3)
print(f"Example 3: {result3}") # Expected output: True
# Compare with alternative implementation
print("\nUsing alternative implementation:")
print(f"Example 1: {solution.is_balanced_separate(tree1)}")
print(f"Example 2: {solution.is_balanced_separate(tree2)}")
print(f"Example 3: {solution.is_balanced_separate(tree3)}")
</pre>
</div>
</div>
</div>
<script>
// Balanced tree: [3, 9, 20, null, null, 15, 7]
const tree = {
val: 3,
left: {val: 9, left: null, right: null},
right: {
val: 20,
left: {val: 15, left: null, right: null},
right: {val: 7, left: null, right: null}
}
};
let nodeHeights = {}; // path -> height
let nodeStates = {}; // path -> 'processing' | 'done' | 'unbalanced'
let callStack = [{node: tree, path: 'root', phase: 'visit'}];
let isBalanced = null;
let autoRunning = false;
let autoTimer = null;
const width = 700;
const height = 400;
const svg = d3.select("#mainSvg")
.attr("width", width)
.attr("height", height);
function drawTree(node, x, y, level, path) {
if (!node) return;
const nodeRadius = 28;
const dx = 100 / (level + 1);
const dy = 70;
// Edges
if (node.left) {
svg.append("line")
.attr("x1", x).attr("y1", y + nodeRadius)
.attr("x2", x - dx).attr("y2", y + dy - nodeRadius)
.attr("stroke", "#ddd").attr("stroke-width", 2);
drawTree(node.left, x - dx, y + dy, level + 1, path + 'L');
}
if (node.right) {
svg.append("line")
.attr("x1", x).attr("y1", y + nodeRadius)
.attr("x2", x + dx).attr("y2", y + dy - nodeRadius)
.attr("stroke", "#ddd").attr("stroke-width", 2);
drawTree(node.right, x + dx, y + dy, level + 1, path + 'R');
}
// Node
const state = nodeStates[path];
const nodeHeight = nodeHeights[path];
let fill = "#e3f2fd", stroke = "#1976d2";
if (state === 'processing') {
fill = "#ffeb3b"; stroke = "#f57c00";
} else if (state === 'done') {
fill = "#c8e6c9"; stroke = "#4caf50";
} else if (state === 'unbalanced') {
fill = "#ffcdd2"; stroke = "#e53935";
}
svg.append("circle")
.attr("cx", x).attr("cy", y).attr("r", nodeRadius)
.attr("fill", fill).attr("stroke", stroke).attr("stroke-width", 2);
svg.append("text")
.attr("x", x).attr("y", y + 5)
.attr("text-anchor", "middle")
.attr("font-size", "18px")
.attr("font-weight", "bold")
.text(node.val);
// Height label
if (nodeHeight !== undefined) {
svg.append("rect")
.attr("x", x + nodeRadius + 2).attr("y", y - 10)
.attr("width", 25).attr("height", 20)
.attr("rx", 4)
.attr("fill", "#fff3e0").attr("stroke", "#ff9800");
svg.append("text")
.attr("x", x + nodeRadius + 14).attr("y", y + 5)
.attr("text-anchor", "middle")
.attr("font-size", "12px")
.attr("fill", "#e65100")
.text(`h${nodeHeight}`);
}
}
function draw() {
svg.selectAll("*").remove();
svg.append("text")
.attr("x", width / 2).attr("y", 25)
.attr("text-anchor", "middle")
.attr("font-weight", "bold")
.text("Check if Binary Tree is Height-Balanced");
drawTree(tree, width / 2, 70, 0, 'root');
// Result
if (isBalanced !== null) {
svg.append("rect")
.attr("x", width / 2 - 80).attr("y", height - 60)
.attr("width", 160).attr("height", 45)
.attr("rx", 10)
.attr("fill", isBalanced ? "#c8e6c9" : "#ffcdd2")
.attr("stroke", isBalanced ? "#4caf50" : "#e53935");
svg.append("text")
.attr("x", width / 2).attr("y", height - 30)
.attr("text-anchor", "middle")
.attr("font-size", "18px")
.attr("font-weight", "bold")
.text(isBalanced ? "✓ Balanced" : "✗ Not Balanced");
}
}
function step() {
if (callStack.length === 0 || isBalanced === false) {
if (isBalanced === null) isBalanced = true;
document.getElementById("balancedDisplay").textContent =
isBalanced ? "Yes ✓" : "No ✗";
document.getElementById("status").textContent =
isBalanced ? "Tree is balanced!" : "Tree is NOT balanced!";
draw();
return false;
}
const {node, path, phase, leftH, rightH} = callStack.pop();
if (!node) {
// Null node has height 0
nodeHeights[path] = 0;
return callStack.length > 0;
}
if (phase === 'visit') {
nodeStates[path] = 'processing';
document.getElementById("currentDisplay").textContent = `Node ${node.val}`;
// Need to process children first
callStack.push({node, path, phase: 'checkRight'});
if (node.left) {
callStack.push({node: node.left, path: path + 'L', phase: 'visit'});
} else {
nodeHeights[path + 'L'] = 0;
}
document.getElementById("status").textContent =
`Visiting node ${node.val}, checking left subtree...`;
} else if (phase === 'checkRight') {
callStack.push({node, path, phase: 'calculate', leftH: nodeHeights[path + 'L']});
if (node.right) {
callStack.push({node: node.right, path: path + 'R', phase: 'visit'});
} else {
nodeHeights[path + 'R'] = 0;
}
document.getElementById("status").textContent =
`Node ${node.val}: left height = ${nodeHeights[path + 'L']}, checking right...`;
} else if (phase === 'calculate') {
const lh = nodeHeights[path + 'L'] || 0;
const rh = nodeHeights[path + 'R'] || 0;
const diff = Math.abs(lh - rh);
document.getElementById("heightDisplay").textContent = `(${lh}, ${rh}), diff=${diff}`;
if (diff > 1) {
nodeStates[path] = 'unbalanced';
isBalanced = false;
document.getElementById("status").textContent =
`Node ${node.val}: heights ${lh} and ${rh} differ by ${diff} > 1 - UNBALANCED!`;
} else {
nodeHeights[path] = 1 + Math.max(lh, rh);
nodeStates[path] = 'done';
document.getElementById("status").textContent =
`Node ${node.val}: balanced! Height = 1 + max(${lh}, ${rh}) = ${nodeHeights[path]}`;
}
}
draw();
return callStack.length > 0 && isBalanced !== false;
}
function reset() {
nodeHeights = {};
nodeStates = {};
callStack = [{node: tree, path: 'root', phase: 'visit'}];
isBalanced = null;
autoRunning = false;
if (autoTimer) clearInterval(autoTimer);
document.getElementById("currentDisplay").textContent = "-";
document.getElementById("heightDisplay").textContent = "-";
document.getElementById("balancedDisplay").textContent = "-";
document.getElementById("status").textContent =
'Click "Step" to check if tree is balanced';
document.getElementById("autoBtn").textContent = "Auto Run";
draw();
}
function autoRun() {
if (autoRunning) {
autoRunning = false;
clearInterval(autoTimer);
document.getElementById("autoBtn").textContent = "Auto Run";
} else {
autoRunning = true;
document.getElementById("autoBtn").textContent = "Pause";
const speed = 2100 - document.getElementById("speed").value;
autoTimer = setInterval(() => {
if (!step()) {
autoRunning = false;
clearInterval(autoTimer);
document.getElementById("autoBtn").textContent = "Auto Run";
}
}, speed);
}
}
document.getElementById("stepBtn").addEventListener("click", step);
document.getElementById("autoBtn").addEventListener("click", autoRun);
document.getElementById("resetBtn").addEventListener("click", reset);
draw();
</script>
</body>
</html>