DAY 31 Exploring Graph BFS: From Mutations to Word Ladders

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 two intricate puzzles where every connection mattered.

How the Day Played Out

1. Minimum Genetic Mutation (Medium Difficulty)

   • Determine the minimum number of mutations required to transform a starting gene sequence into a target sequence.
   • The Strategy:
     • Treated each gene as a node and valid mutations as edges in a graph.
     • Used BFS to explore all possible transformations and find the shortest path to the target sequence.
     • Maintained a set of visited genes to prevent revisiting nodes.
   • The Fun Part:
     • Navigating the “gene graph” and identifying valid mutations felt like traversing a biological network.

2. Word Ladder (Hard Difficulty)

   • Transform one word into another by changing one letter at a time, with each intermediate word required to be valid. Find the shortest transformation sequence.
   • The Strategy:
     • Represented each word as a node, connecting words that differ by a single letter.
     • Used BFS to find the shortest path from the start word to the end word.
     • Preprocessed the word list to group words by generic patterns, significantly improving efficiency.
   • The Fun Part:
     • Watching the transformation chain grow step by step was like solving a cryptographic riddle—it was both challenging and exciting.

What Made Today Unique

1. Graph Representation Matters:

   • Transforming genes and words into graph representations was key to solving both problems. It highlighted how flexible graphs are for modeling real-world scenarios.

2. Shortest Path with BFS:

   • BFS shines in problems where every step has equal weight, making it the perfect choice for finding the shortest transformation sequence.

3. Efficient Preprocessing:

   • For Word Ladder, grouping words by generic patterns (e.g., h*t for hot) made the traversal efficient, showcasing the importance of preprocessing.

Key Takeaways

• Graphs Aren’t Always Obvious:

  • Problems like Minimum Genetic Mutation and Word Ladder don’t explicitly mention graphs but can be modeled as one with nodes and edges.

• BFS for Layered Exploration:

  • BFS is ideal for problems where you need to explore all possibilities at one level before moving deeper.

• Preprocessing Saves Time:

  • Grouping and indexing data before traversal, as in Word Ladder, can significantly reduce computation during BFS.

Reflections

Both problems today were challenging but rewarding. Minimum Genetic Mutation felt like a biological puzzle, while Word Ladder was a mix of logic and wordplay. The emphasis on efficient graph representation and traversal deepened my appreciation for BFS as a versatile algorithm.

What’s Next?

Tomorrow, I’ll shift focus to Divide and Conquer, tackling Convert Sorted Array to Binary Search Tree and Sort List. These tasks will test my ability to split problems into manageable parts and combine solutions seamlessly.

Thanks for following along! Let’s keep learning and solving together.