AVL Tree
Detailed guide and Python implementation for the 'AVL Tree' problem.
1. Concept Overview
The 'AVL Tree' problem is a key challenge in the Trees section.
This implementation focuses on medium-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for AVL Tree.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for AVL Tree carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
Write a function is_avl_balanced(tree_arr) that takes an array representation of a binary tree tree_arr and returns True if the tree is height-balanced (for every node, the height of its left and right subtrees differs by at most 1) and is a valid BST, or False otherwise.
- •0 <= len(tree_arr) <= 1000
Examples
tree_arr = [3, 9, 20, None, None, 15, 7]
True
The tree is a valid BST and the depth difference of left/right subtrees of all nodes is at most 1.
tree_arr = [1, 2, None, 3, None, None, None, 4]
False
The tree is unbalanced because leaf node 4 is at depth 4 while right subtree of node 1 is empty.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.
Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def create_avl_tree_opt(arr: list) -> list:
class AVLTreeNode:
def __init__(self, val=0):
self.val = val
self.left = None
self.right = None
self.height = 1
def get_height(node):
return node.height if node else 0
def get_balance(node):
return get_height(node.left) - get_height(node.right) if node else 0
def rotate_right(y):
x = y.left
T2 = x.right
x.right = y
y.left = T2
y.height = 1 + max(get_height(y.left), get_height(y.right))
x.height = 1 + max(get_height(x.left), get_height(x.right))
return x
def rotate_left(x):
y = x.right
T2 = y.left
y.left = x
x.right = T2
x.height = 1 + max(get_height(x.left), get_height(x.right))
y.height = 1 + max(get_height(y.left), get_height(y.right))
return y
def insert(node, val):
if not node:
return AVLTreeNode(val)
if val < node.val:
node.left = insert(node.left, val)
else:
node.right = insert(node.right, val)
node.height = 1 + max(get_height(node.left), get_height(node.right))
balance = get_balance(node)
# Left Left
if balance > 1 and val < node.left.val:
return rotate_right(node)
# Right Right
if balance < -1 and val > node.right.val:
return rotate_left(node)
# Left Right
if balance > 1 and val > node.left.val:
node.left = rotate_left(node.left)
return rotate_right(node)
# Right Left
if balance < -1 and val < node.right.val:
node.right = rotate_right(node.right)
return rotate_left(node)
return node
if not arr: return []
root = None
for val in arr:
root = insert(root, val)
# Serialize level-order
res = []
queue = [root]
while queue:
curr = queue.pop(0)
if curr:
res.append(curr.val)
queue.append(curr.left)
queue.append(curr.right)
else:
res.append(None)
while res and res[-1] is None:
res.pop()
return resBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def create_avl_tree_brute(arr: list) -> list:
# Standard AVL tree insertion with rotations, returns level order list
class AVLTreeNode:
def __init__(self, val=0):
self.val = val
self.left = None
self.right = None
self.height = 1
def get_height(node):
return node.height if node else 0
def get_balance(node):
return get_height(node.left) - get_height(node.right) if node else 0
def rotate_right(y):
x = y.left
T2 = x.right
x.right = y
y.left = T2
y.height = 1 + max(get_height(y.left), get_height(y.right))
x.height = 1 + max(get_height(x.left), get_height(x.right))
return x
def rotate_left(x):
y = x.right
T2 = y.left
y.left = x
x.right = T2
x.height = 1 + max(get_height(x.left), get_height(x.right))
y.height = 1 + max(get_height(y.left), get_height(y.right))
return y
def insert(node, val):
if not node:
return AVLTreeNode(val)
if val < node.val:
node.left = insert(node.left, val)
else:
node.right = insert(node.right, val)
node.height = 1 + max(get_height(node.left), get_height(node.right))
balance = get_balance(node)
if balance > 1 and val < node.left.val:
return rotate_right(node)
if balance < -1 and val > node.right.val:
return rotate_left(node)
if balance > 1 and val > node.left.val:
node.left = rotate_left(node.left)
return rotate_right(node)
if balance < -1 and val < node.right.val:
node.right = rotate_right(node.right)
return rotate_left(node)
return node
if not arr: return []
root = None
for val in arr:
root = insert(root, val)
return tree_to_list(root)Algorithm Pattern Checklist
When dealing with Trees data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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