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Must-Read Insights: Key Moments in My Learning Journey

Β· 3 min read
Mahmut Salman
Mahmut Salman
Software Developer

A curated collection of breakthrough moments and essential insights from my algorithm learning journey.

This page highlights the most important revelations and "aha moments" from my learning journey. These are the posts where fundamental concepts finally clicked, where confusion turned into clarity.

🧠 Dynamic Programming Insights​

πŸ’‘ The Hidden dp[i] Pattern - The Aha Moment!​

Post: Wait, Is This Actually DP? A Conversation About Memoization

Why This Matters:

This section reveals one of the most important insights about top-down DP: the dp[i] = ... pattern exists in recursive solutions too - it's just hidden!

Key Insight

When you write:

arr[i] = min;  // In your recursive function

This IS the same as:

dp[i] = min;   // In a loop-based solution

The only difference:

  • Bottom-up: Explicit dp[i] = ... in a loop
  • Top-down: "Hidden" arr[i] = ... in recursion

Same recurrence relation, different execution strategy!

What You'll Learn:

  • Why recursion + memoization = top-down DP
  • How the dp[i] pattern appears in recursive solutions
  • The fundamental equivalence between top-down and bottom-up approaches
  • Why your recursive solution is legitimate DP

Perfect For: Anyone confused about whether their memoized recursive solution "counts" as DP

🎯 Why Parameter Count Matters in DP​

Post: Delete and Earn - DP Dialogue

Why This Matters:

This section reveals a critical insight: the number of parameters in your unoptimized recursive solution directly affects complexity and can make the bottom-up approach much harder to visualize.

Key Insight

Parameter Count = Complexity:

  • More parameters in your recursive function β†’ Higher dimensional DP array
  • More dimensions β†’ Harder to think about bottom-up approach
  • Complex state space β†’ Harder memoization

The Game-Changing Trick: When your recursive solution has too many parameters and feels complex: Transform the problem into a similar DP pattern you already know!

What You'll Learn:

  • How parameter count affects DP complexity
  • Why some recursive solutions are harder to convert to bottom-up
  • The transformation trick: mapping complex problems to familiar patterns
  • How to recognize when transformation is the right approach

Perfect For: When you have a working recursive solution but can't figure out the bottom-up DP, or when your memoization requires complex multi-dimensional arrays

πŸ“š More Essential Reads​

Coming soon: More breakthrough moments and key insights will be added here as I discover them...

How to Use This Page​

  • Bookmark this page - Return here when you need clarity on fundamental concepts
  • Follow the links - Each insight links directly to the relevant section
  • Read in order or jump around - Each insight is self-contained

Last Updated: January 17, 2025