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.

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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.

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Hello Everyone!

The second day of Week 13 created more Binary Tree DFS Challenges, which addressed the node properties of a binary tree and tried to compute specific path sums. Both of these tasks necessitated appropriate manipulation of values during traversal and as such the problems were both fun and rewarding. They had a System of mapping knowledge to which studying was like solving a tree maze, with new ideas playing the role of path each time one turned around.

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How the Day Unfolded

1. Good Nodes in Binary Tree (Medium Level)
   
   Determine how many “good nodes” are in a binary tree. A node is relinquish if the value of node is less than the maximum value of any of the path from the root to that node.

   • The Strategy: – Employed DFS to traverse the tree Looking for the path with the highest sum present in the tree. – Used an increment on the counter variable if they saw a ‘good node’ at the current stage.
   • The Fun Part: It was like seeing a string of treasures when the “good nodes” light up, particularly as the max value is updated dynamically.

2. Path Sum III (Medium Level)
   
   Calculate the number of paths from the root of a binary tree to its leaf nodes which has given sum.

   • The Strategy:
     • Used DFS with a prefix sum approach: Preervered a hash map in order to keep track of the cumulative sums on every node.
     • Whether there was a path with a certain cumulative sum, reached through the hash map.
   • The Fun Part: Updating the paths automatically and counting the coordinates for the valid ones kept the flow elegant, like treasure maps with concealed trails.

Todays highlights

1. Dynamic Value Tracking:
   
   Both problems stressed to keep state information, or dynamic values (such as maximum and cumulative sum) during traversal.

2. Hash Maps in Trees:
   
   Path Sum III showed how the use of hash maps on trees can make certain operations more manageable and straightforward, in the process increasing speed.

3. Real-Time Decisions:
   
   Deciding what actions should be taken at runtime, including the process of identifying “good nodes” or valid paths introduced an interesting element to both.

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Key Takeaways

• DFS with Dynamic Tracking:
  
  Issues such as – count good nodes in binary tree also underscore the usefulness of passing dynamic information such as maximums, during recursive call.

• Prefix Sums Simplify Path Problems:
  
  In the Path Sum III, prefix sums and hash tables easily transformed a possibly quite difficult problem into one easy to solve.

• Real-Time Analysis is Key:
  
  Both problems involved dynamic values, whose analysis and furthermore, update, are done during traversal, highlighting the value of constant decision making.

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Reflections

The Count Good Nodes in Binary Tree was an interesting one in tracking the optimum value of the nodes in the binary tree structure while the Path Sum III was deeper in as made by deep use of prefix sum approach accompanied by path analysis. Combined, these activities demonstrated the effectiveness of DFS in solving binary tree problems with dynamic conditions.

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What’s Next?

One day ahead, I have more Binary Tree DFS Problems, which include Longest ZigZag Path in a Binary Tree and Lowest Common Ancestor of a Binary Tree. These tasks will help me to practice path dynamics, and hierarchical relationship processes effectively.

That is all for today folks, thank you for you’re company and for following my daily rhythms! Let me continue to solve, learn, and progress as one community with you.