DAY 62 Binary Tree DFS: Tracking and Summing

Hello Everyone!

Day 2 of Week 13 brought more Binary Tree DFS Challenges, focusing on tracking node properties and calculating specific path sums. These tasks required dynamic tracking of values during traversal, making the problems both engaging and rewarding. It felt like navigating a tree maze where every step revealed a new insight.

How the Day Played Out

1. Count Good Nodes in Binary Tree (Medium Difficulty)

   • Count the number of "good nodes" in a binary tree. A node is good if the value of the node is greater than or equal to the maximum value along the path from the root to the node.
   • The Strategy:
     • Used DFS to traverse the tree while maintaining the maximum value encountered along the path.
     • Incremented the count if the current node's value met the "good node" condition.
   • The Fun Part:
     • Dynamically updating the maximum value and seeing the "good nodes" light up during traversal felt like revealing a path of treasures.

2. Path Sum III (Medium Difficulty)

   • Count the number of paths that sum up to a given value in a binary tree.
   • The Strategy:
     • Used DFS with a prefix sum approach:
     • Maintained a hash map to store the cumulative sums at each node.
     • Checked if there was a path with a cumulative sum equal to the target by querying the hash map.
   • The Fun Part:
     • Watching the paths form dynamically and counting the valid ones felt like solving a treasure map with hidden routes.

What Made Today Special

1. Dynamic Value Tracking:

   • Both problems emphasized the importance of maintaining dynamic values (like maximums and cumulative sums) during traversal.

2. Hash Maps in Trees:

   • Path Sum III demonstrated how hash maps can simplify complex tree operations, enhancing efficiency.

3. Real-Time Decisions:

   • Traversing while making decisions dynamically, such as identifying "good nodes" or valid paths, added an exciting challenge to both tasks.

Key Takeaways

• DFS with Dynamic Tracking:

  • Problems like Count Good Nodes in Binary Tree highlight the value of passing dynamic information (like maximums) during recursive calls.

• Prefix Sums Simplify Path Problems:

  • In Path Sum III, using prefix sums and hash maps turned a potentially complex problem into an elegant solution.

• Real-Time Analysis is Key:

  • Both problems required analyzing and updating values dynamically during traversal, reinforcing the importance of real-time decision-making.

Reflections

The Count Good Nodes in Binary Tree problem was a rewarding exercise in dynamic value tracking, while Path Sum III added depth with its prefix sum approach and path analysis. Together, these tasks showcased the versatility and efficiency of DFS in solving binary tree problems with dynamic constraints.

What’s Next?

Tomorrow, I’ll tackle more Binary Tree DFS Problems, focusing on Longest ZigZag Path in a Binary Tree and Lowest Common Ancestor of a Binary Tree. These tasks will test my ability to handle path dynamics and hierarchical relationships efficiently.

Thank you for following along! Let’s keep solving, learning, and growing together.