DAY 30 Binary Tree BFS: From Snakes to Mutations

Hello Everyone!

The final day of Week 6 was dedicated to Binary Tree BFS Problems, where Breadth-First Search (BFS) took center stage. BFS is one of the most versatile techniques in problem-solving, especially for grid-based challenges and shortest path calculations. Today’s problems felt like playing strategic games—navigating ladders and mutations while making optimal decisions at every step.

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How the Day Played Out

1. Snakes and Ladders (Medium Difficulty)

   • Task: Find the minimum number of dice rolls required to reach the last square in a game of snakes and ladders.
   • The Strategy:
     • Modeled the board as a graph, with each square as a node connected to other squares based on dice rolls.
     • Used BFS to find the shortest path from the starting square to the last square.
   • The Fun Part:
     • Simulating dice rolls while avoiding the “snakes” and climbing the “ladders” felt like solving a real board game puzzle. Watching the shortest path unfold step-by-step was incredibly satisfying.

2. Minimum Genetic Mutation (Medium Difficulty)

   • Task: Determine the minimum number of mutations needed to transform one gene sequence into another, given a set of valid mutations.
   • The Strategy:
     • Modeled each gene as a node in a graph, with valid mutations forming edges between nodes.
     • Used BFS to find the shortest transformation sequence from the start gene to the target gene.
   • The Fun Part:
     • Navigating genetic sequences as graph nodes felt like solving a maze at the molecular level. It was both intellectually stimulating and creatively engaging.

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What Made Today Special

1. BFS in Action:

   • Both problems showcased BFS as the optimal choice for shortest path calculations in unweighted graph scenarios. BFS’s layer-by-layer approach made it intuitive and effective.

2. Relatable Analogies:

   • Snakes and Ladders mirrored the classic board game, adding a playful element to graph traversal, while Minimum Genetic Mutation introduced a fascinating connection to biology.

3. Simplicity Meets Complexity:

   • While the problems were complex in their themes, their solutions boiled down to simple BFS logic with effective graph modeling, striking a perfect balance.

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Key Takeaways

• BFS for Shortest Path Problems:

  • BFS is an essential algorithm for solving unweighted graph problems efficiently, as demonstrated in both challenges.

• Graph Modeling Simplifies Complex Problems:

  • Transforming game boards and genetic sequences into graph representations made these problems much more manageable and systematic.

• Visualization Enhances Problem-Solving:

  • Thinking of Snakes and Ladders as a board game and Minimum Genetic Mutation as navigating a DNA maze helped design intuitive and effective solutions.

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Reflections

Both problems today were highly engaging and full of insights. Snakes and Ladders stood out for its playful nature and strategic traversal, while Minimum Genetic Mutation offered a unique challenge with its biology-inspired theme. Together, they highlighted the versatility and power of BFS in tackling real-world-inspired puzzles.

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What’s Next?

With Week 6 now complete, I’m excited to plan Week 7, which will focus on Advanced Dynamic Programming, Greedy Algorithms, and Backtracking Problems. The upcoming week promises to bring new challenges and learning opportunities.

Thank you for joining me on this journey! Let’s continue solving, growing, and exploring competitive programming together.

Best regards,

Somuya