DAY 35 Binary Search: Precision and Logic at Its Best

Hello Everyone!

Today marked the final day of Week 7, and I ended on a high note by tackling Binary Search Problems. Binary search has always been one of my favorite techniques—it's simple yet powerful, and applying it to varied scenarios today reinforced its versatility. These challenges demanded adaptability and a clear understanding of search boundaries.

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How the Day Went

1. Search a 2D Matrix (Medium Difficulty)

   • Task: Given a sorted 2D matrix where each row and column is sorted, determine if a specific target exists.
   • Approach:
     • Instead of treating the matrix as a grid, I imagined it as a 1D array and calculated indices accordingly.
     • Applied binary search over this "virtual" array to locate the target efficiently.
   • Why It Was Fun:
     • The transformation from 2D to 1D was a refreshing mental exercise. It felt like simplifying a seemingly complex problem with a neat little trick.

2. Find Peak Element (Medium Difficulty)

   • Task: Find a peak element in an array, where a peak is defined as a value greater than its neighbors.
   • Approach:
     • Used binary search to focus on regions with a higher neighbor, knowing that moving towards a larger neighbor guarantees a peak.
     • Leveraged the fact that an array always has at least one peak.
   • Why It Was Fun:
     • Watching the search range shrink and zeroing in on the peak felt like solving a puzzle step by step. It was satisfying to see the algorithm find the "summit."

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What Stood Out Today

1. Binary Search in Action:

   • Both problems demonstrated different flavors of binary search—one on a "virtual" array and the other on a peak-finding challenge.

2. Creative Problem Solving:

   • Simplifying the 2D matrix into a 1D representation showed how reimagining the problem space can make solutions more straightforward.

3. Efficiency and Elegance:

   • Binary search's ability to reduce complexity was on full display today. It’s always satisfying to see how a simple algorithm can make problems so much easier to tackle.

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Key Takeaways

• Adapt Binary Search to the Context:

  • Whether it's searching in a virtual array or finding peaks, binary search can be tailored to suit many unique problems.

• Visualize the Problem Differently:

  • For Search a 2D Matrix, thinking of the grid as a single continuous array simplified the implementation and made the problem much clearer.

• Exploit Problem Guarantees:

  • Knowing that a peak must always exist in Find Peak Element allowed for confident binary search without needing extra edge case handling.

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Reflections

Both problems today showcased the beauty of binary search. The Search a 2D Matrix problem was a great example of how transforming the problem space can reduce complexity, while Find Peak Element showed how to apply binary search creatively to solve a different kind of challenge. These tasks were a perfect way to wrap up Week 7.

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Looking Ahead

With Week 7 in the books, I’m ready to dive into Week 8. Next week’s focus will shift to Greedy Algorithms, Advanced Dynamic Programming, and Backtracking Problems. It’s going to be a mix of strategy, optimization, and recursion, and I can’t wait to get started.

Thank you for being part of my journey! Let’s continue exploring, learning, and growing together.

Best,

Somuya