DAY 9 Conquering Binary Tree Challenges

Hello Everyone!

I am Somuya Khandelwal, back with updates from Day 4 of Week 2 of my competitive programming journey. Today’s focus was on Binary Trees, a foundational data structure that appears frequently in technical interviews and real-world applications. Binary trees offer a wide range of challenges, from simple traversals to complex path sum calculations, making them a critical area to master.

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What I Worked On Today

1. Path Sum (Easy Difficulty)

   • Determine if the tree has a root-to-leaf path where the sum of the node values equals a target value.
   • Approach:
     • Used depth-first search (DFS) recursively to check all possible paths.
   • What I Learned:
     • DFS is a natural fit for exploring all root-to-leaf paths in binary trees.
     • Managing state (like the current path sum) across recursive calls is crucial.

2. Sum Root to Leaf Numbers (Medium Difficulty)

   • Calculate the sum of all numbers formed by root-to-leaf paths.
   • Approach:
     • Traversed the tree recursively, keeping track of the number formed at each level.
   • What I Learned:
     • Recursive algorithms are effective for cumulative calculations in binary trees.
     • Carefully managing the backtracking of numbers ensures correctness.

3. Binary Tree Maximum Path Sum (Hard Difficulty)

   • Find the maximum path sum in a binary tree, where the path can start and end at any node.
   • Approach:
     • Used a post-order traversal to compute the maximum gain from each subtree and updated a global maximum.
   • What I Learned:
     • Recursive functions can return useful information (e.g., maximum gain from a subtree) for parent nodes.
     • Managing local and global states is critical for solving complex tree problems.

4. Binary Search Tree Iterator (Medium Difficulty)

   • Design an iterator for a binary search tree (BST) with efficient next() and hasNext() operations.
   • Approach:
     • Used a stack to simulate an in-order traversal of the BST, storing only necessary nodes.
   • What I Learned:
     • Stacks are invaluable for simulating traversals without storing the entire tree structure.
     • Understanding in-order traversal is key to working efficiently with BSTs.

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What I Learned Today

1. Tree Traversal Techniques:

   • Depth-first search (DFS) and post-order traversal are powerful techniques for solving binary tree problems.

2. Recursive State Management:

   • Problems like Binary Tree Maximum Path Sum demonstrated the importance of maintaining and updating state efficiently in recursive calls.

3. Combining Recursion and Iteration:

   • For the BST Iterator, combining stack-based iteration with lazy evaluation provided a memory-efficient solution.

4. Global vs Local States:

   • Managing local calculations and updating global results (e.g., in the Binary Tree Maximum Path Sum) is a crucial skill in tree-based problems.

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Reflections and Challenges

The Binary Tree Maximum Path Sum problem was the most challenging today. Balancing recursive logic with global state updates required multiple iterations to get right, but the learning process was incredibly rewarding. Overall, the problems today solidified my understanding of tree traversal and how to apply recursion effectively.

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Looking Ahead

Tomorrow, I’ll wrap up the week with problems on 1D Dynamic Programming, including Climbing Stairs and House Robber. These challenges will provide insights into state-based decision-making and efficient problem-solving.

Thank you for following along on my journey! Stay tuned for more updates and learnings as I continue to grow in competitive programming.