DAY 28 Graphs Reloaded: Cloning and Evaluating Connections

Hello Everyone!

Day 3 of Week 6 was all about pushing further into Graph Problems, focusing on graph cloning and evaluation-based challenges. Graphs always feel like intricate networks, where every node and edge tells a part of the story. Today’s tasks tested my ability to construct, manipulate, and interpret graphs effectively, making it an exciting day of problem-solving.

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How the Day Played Out

1. Clone Graph (Medium Difficulty)

   • Task: Create a deep copy of an undirected graph.
   • The Strategy:
     • Implemented a Depth First Search (DFS) approach to traverse the graph, creating new nodes while maintaining a mapping between old and new nodes.
     • Used a hashmap to ensure each node was cloned exactly once, avoiding redundancy.
   • The Fun Part:
     • Watching the original graph transform into a perfect replica was incredibly satisfying—it felt like duplicating a masterpiece without missing any details.

2. Evaluate Division (Medium Difficulty)

   • Task: Given a list of equations and values, compute the result of queries based on the relationships.
   • The Strategy:
     • Modeled the equations as a weighted graph, where nodes represented variables and edges represented division values.
     • Used DFS to traverse the graph and calculate results for each query by accumulating edge weights.
   • The Fun Part:
     • Transforming equations into a graph and treating them as weighted connections was a unique twist. It felt like solving a mathematical puzzle within a network.

3. Evaluate Di (Clarification Task)

   • This task needed clarification or adjustments, so I focused on refining my solutions for the other problems. This helped ensure accuracy and efficiency in my approaches.

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What Made Today Stand Out

1. Graphs as Relationships:

   • Both problems highlighted how graphs can represent relationships—whether between nodes in a structure or variables in equations. This abstraction made the challenges more relatable and intuitive.

2. Mapping and State Management:

   • Efficient mappings, such as the old-to-new node hashmap in Clone Graph and visited nodes in Evaluate Division, were critical for managing state and ensuring accuracy.

3. Graph Construction from Data:

   • Constructing a graph from unconventional inputs, like equations in Evaluate Division, emphasized the importance of preprocessing and structuring data effectively before solving.

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Key Takeaways

• DFS is Ideal for Graph Cloning:

  • Depth First Search provides a systematic way to traverse and copy graphs, ensuring that all nodes and edges are accurately duplicated.

• Graphs Go Beyond Nodes and Edges:

  • Problems like Evaluate Division illustrate that graphs can represent relationships, equations, or dependencies, broadening their application scope.

• Data Structures Simplify Complexities:

  • Using hashmaps and adjacency lists made managing graphs intuitive and allowed for efficient traversal and query resolution.

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Reflections

The Clone Graph problem was a rewarding exercise in precision and accuracy, as every node and edge needed to be perfectly replicated. Evaluate Division stood out for its creativity—it was a great blend of math and computer science, requiring me to construct and traverse a graph in a non-traditional context. Both problems reinforced the versatility and importance of graphs in competitive programming.

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What’s Next?

Tomorrow, I’ll focus on more Graph Problems, including Course Schedule and Course Schedule II. These tasks will challenge my understanding of directed acyclic graphs (DAGs) and topological sorting.

Thank you for following my journey! Let’s keep solving, learning, and growing together as we explore the fascinating world of competitive programming.

Best regards,

Somuya