Hey Everyone!
Today marked the beginning of Week 7, and I dove straight into Graph Breadth First Search (BFS) problems. BFS is one of the most versatile techniques for solving shortest path problems, and today’s challenges felt like solving intricate puzzles where every connection and transition mattered.
How the Day Played Out
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Minimum Genetic Mutation (Medium Difficulty)
- Task: Determine the minimum number of mutations required to transform a starting gene sequence into a target sequence.
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The Strategy:
- Modeled the problem as a graph where each gene sequence was a node and valid mutations formed edges.
- Used BFS to explore all possible transformations, finding the shortest path to the target sequence.
- Kept track of visited genes in a set to avoid revisiting nodes.
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The Fun Part:
- Traversing the “gene graph” and identifying valid mutations felt like navigating a complex biological network. Watching the shortest mutation path unfold was fascinating.
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Word Ladder (Hard Difficulty)
- Task: Transform one word into another by changing one letter at a time, with intermediate words required to be valid. Find the shortest transformation sequence.
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The Strategy:
- Represented each word as a node in a graph, connecting words that differ by only one letter.
- Preprocessed the word list to group words by generic patterns (e.g., grouping words like
hot,hit, andhutunderh*t), improving BFS efficiency. - Used BFS to find the shortest path from the start word to the target word.
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The Fun Part:
- Watching the word chain grow step by step was like solving a linguistic riddle. It combined logical reasoning with creativity, making it a standout challenge.
What Made Today Unique
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Graph Representation Matters:
- Turning genes and words into graph representations was critical to solving both problems. This reinforced how graphs can model a wide range of scenarios, even those not explicitly described as graphs.
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BFS for Shortest Path Problems:
- BFS proved to be the ideal choice for problems involving equal-weight transitions, ensuring all possibilities were explored in the most efficient way.
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The Power of Preprocessing:
- For Word Ladder, preprocessing the word list into generic patterns significantly improved traversal efficiency, showing how thoughtful preparation can reduce complexity.
Key Takeaways
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Graphs Can Be Hidden:
- Problems like Minimum Genetic Mutation and Word Ladder don’t explicitly mention graphs but can be modeled as one with nodes and edges, unlocking efficient solutions.
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BFS is Layered Exploration:
- BFS works brilliantly for exploring possibilities one level at a time, ensuring optimal solutions in shortest path problems.
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Preprocessing is a Game-Changer:
- Efficiently structuring data before traversal, like grouping words by generic patterns, can dramatically improve algorithm performance.
Reflections
Today’s challenges were both fun and enlightening. Minimum Genetic Mutation felt like solving a biological puzzle, while Word Ladder required a creative blend of logic and language. Both tasks underscored the importance of graph representation and BFS traversal in tackling complex problems efficiently.
What’s Next?
Tomorrow, I’ll shift gears to Divide and Conquer, working on problems like Convert Sorted Array to Binary Search Tree and Sort List. These tasks will test my ability to split problems into manageable parts and seamlessly combine their solutions.
Thank you for following along! Let’s continue exploring, learning, and solving competitive programming puzzles together.
Best regards,
Somuya
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