Binary trees are fundamental data structures in computer science that appear frequently in coding interviews and real-world applications. This guide offers a straightforward explanation of binary trees, their implementation in Python, and common problem-solving patterns.

What is a Binary Tree?

A binary tree is a hierarchical data structure where each node has at most two children, referred to as the left child and right child. Key characteristics include:

  • Every node contains a value and references to its children (if any)
  • There is exactly one root node (the topmost node)
  • Nodes with no children are called leaf nodes
  • The structure naturally represents hierarchical relationships
  • Binary trees enable efficient searching, insertion, and deletion operations

Python Implementation and Basic Operations

Node Structure

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val        # Node value
        self.left = left      # Left child reference
        self.right = right    # Right child reference

Creating a Binary Tree

def create_binary_tree():
    # Create a simple binary tree
    root = TreeNode(1)
    root.left = TreeNode(2)
    root.right = TreeNode(3)
    root.left.left = TreeNode(4)
    root.left.right = TreeNode(5)
    return root

Basic Operations (for Binary Search Trees)

def insert(root, val):
    """Insert a value into a binary search tree"""
    if not root:
        return TreeNode(val)

    if val < root.val:
        root.left = insert(root.left, val)
    else:
        root.right = insert(root.right, val)

    return root

def search(root, val):
    """Search for a value in a binary search tree"""
    if not root or root.val == val:
        return root

    if val < root.val:
        return search(root.left, val)
    else:
        return search(root.right, val)

Binary Tree Traversals

There are four primary ways to traverse a binary tree, each visiting nodes in a different order:

1. Pre-order Traversal (Root → Left → Right)

def preorder_traversal(root):
    result = []

    def dfs(node):
        if not node:
            return

        result.append(node.val)  # Visit root first
        dfs(node.left)           # Then left subtree
        dfs(node.right)          # Finally right subtree

    dfs(root)
    return result

2. In-order Traversal (Left → Root → Right)

def inorder_traversal(root):
    result = []

    def dfs(node):
        if not node:
            return

        dfs(node.left)           # Visit left subtree first
        result.append(node.val)  # Then root
        dfs(node.right)          # Finally right subtree

    dfs(root)
    return result

3. Post-order Traversal (Left → Right → Root)

def postorder_traversal(root):
    result = []

    def dfs(node):
        if not node:
            return

        dfs(node.left)           # Visit left subtree first
        dfs(node.right)          # Then right subtree
        result.append(node.val)  # Finally root

    dfs(root)
    return result

4. Level-order Traversal (Breadth-First)

from collections import deque

def level_order_traversal(root):
    if not root:
        return []

    result = []
    queue = deque([root])

    while queue:
        level_size = len(queue)
        level = []

        for _ in range(level_size):
            node = queue.popleft()
            level.append(node.val)

            if node.left:
                queue.append(node.left)
            if node.right:
                queue.append(node.right)

        result.append(level)

    return result

Common LeetCode Binary Tree Problem Categories

Binary tree problems on LeetCode can generally be classified into these categories:

1. Traversal Problems

  • Implementing various traversal methods
  • Serializing and deserializing binary trees
  • Reconstructing binary trees from traversal results

2. Path Sum Problems

  • Determining if a path with a target sum exists
  • Finding maximum path sum
  • Calculating sum of all paths
  • Finding maximum/minimum depth
  • Validating balanced binary trees
  • Checking if a tree is symmetric
  • Determining if two trees are identical

4. Binary Search Tree (BST) Problems

  • Validating a BST
  • Implementing BST operations (insert, delete)
  • Finding kth smallest element
  • Converting BST to greater sum tree

5. Tree Transformation Problems

  • Flattening binary tree to linked list
  • Converting sorted array to balanced BST
  • Creating mirror/inverted binary tree

Conclusion

Binary trees are versatile data structures that form the foundation for more complex tree variants like AVL trees, Red-Black trees, and B-trees. Understanding the core concepts and traversal patterns presented here will equip you with the knowledge to tackle a wide range of tree-based problems in both interviews and real-world applications.

By mastering these fundamentals, you’ll be better prepared to recognize problem patterns and apply efficient tree-based solutions in your programming journey.