DAY 28 Graphs Reloaded: Cloning and Evaluating Connections

Hello Everyone!

Day 3 of Week 6 was all about pushing deeper into Graph Problems, exploring graph cloning and evaluation-based challenges. Graph problems always feel like solving intricate networks, where every node and edge adds a layer to the story. Today’s tasks tested my ability to manipulate and interpret graphs effectively.

How the Day Played Out

1. Clone Graph (Medium Difficulty)

   • Create a deep copy of an undirected graph.
   • The Strategy:
     • Used a Depth First Search (DFS) approach to traverse the graph and create new nodes while maintaining a mapping of old to new nodes.
     • Ensured every node was cloned exactly once by using a hashmap.
   • The Fun Part:
     • Watching the original graph transform into a perfect copy without losing connections felt like duplicating a masterpiece.

2. Evaluate Division (Medium Difficulty)

   • Given a list of equations and values, calculate the result of queries using these relationships.
   • The Strategy:
     • Modeled the equations as a graph where each variable was a node, and the division result was the weight of the edge.
     • Used DFS to traverse the graph and compute the result for each query.
   • The Fun Part:
     • Treating equations as weighted graphs added a unique twist—it felt like solving puzzles in a mathematical network.

3. Evaluate Di (Task Title Correction Needed)

   • This task required clarification or adjustments, but I used the time to refine solutions for the other two problems.

What Made Today Stand Out

1. Graphs as Relationships:

   • Both problems treated graphs as representations of relationships—whether between nodes in a structure or variables in equations. This perspective made the challenges more intuitive.

2. Mapping and Tracking:

   • Maintaining mappings (e.g., old to new nodes in Clone Graph or visited nodes in Evaluate Division) was crucial for efficiency and accuracy.

3. Graph Construction:

   • Constructing the graph from non-standard inputs (like equations) in Evaluate Division emphasized the importance of preprocessing data effectively.

Key Takeaways

• DFS for Graph Cloning:

  • Depth First Search is a reliable and intuitive choice for cloning graphs, ensuring that all nodes and edges are copied accurately.

• Graphs Are Everywhere:

  • Problems like Evaluate Division show that graphs aren’t just about nodes and edges—they can represent relationships, dependencies, or even mathematical equations.

• Focus on Data Structures:

  • Hashmaps and adjacency lists are indispensable for graph-related tasks. Proper use of these data structures simplifies traversal and manipulation.

Reflections

The Clone Graph problem was a satisfying exercise in maintaining accuracy while traversing and copying complex structures. Evaluate Division stood out for its creativity—transforming equations into a graph and solving queries felt like blending math with computer science.

What’s Next?

Tomorrow, I’ll tackle more Graph Problems, focusing on course scheduling with Course Schedule and Course Schedule II. These will test my understanding of directed acyclic graphs (DAGs) and topological sorting.

Thanks for following along on this journey! Let’s continue exploring and mastering competitive programming together.