🧠 The Thinking Evolution: From Problem to Pattern Recognition | Mental Model

🎯 The Real Question: How do I train my brain to see patterns?

here's the actual thinking process that happens in senior developers' minds:

📖 STEP 1: Read Problem → Extract Core Operations

Raw Problem: Count plates between candles in given ranges

Junior Mind: I need to find plates between candles

Superposition:

1. Wait, let me extract what I'm ACTUALLY doing here...
2. For each query, I need to: find left boundary, find right boundary, count stuff between them
3. This is a BOUNDARY + COUNTING problem, not just a 'find plates' problem

🔍 Mental Framework: Always ask : What am I REALLY doing?

1. Counting? → Think cumulative/prefix
2. Finding boundaries? → Think precomputed positions
3. Repeated work on same data? → Think preprocessing

🔄 STEP 2: Trace Your Manual Solution

The Magic Question: If I were doing this by hand with paper and pencil, what would I do?

For Candles Problem:

1. "I'd scan left to find first candle"
2. "I'd scan right to find last candle"
3. "I'd count stars between them"

Senior Insight: "I'm doing the SAME type of scanning for every query... that's inefficient!"

🎯 Pattern Recognition Trigger:

Whenever you're doing the same type of operation repeatedly → Think preprocessing

🤔 STEP 3: Why Stack Feels Natural

(And Why It's Not Optimal)

why Stack Seemed Right:

• "I need to track opening/closing" → Stack for matching pairs
• "Process left to right" → Stack's natural flow
• "Temporary storage" → Stack's purpose

Why It's Not Optimal:

• Stack solves ONE query at a time
• No reuse of information across queries
• Still O(n) per query worst case

Senior Realization: Stack is good for the LOCAL problem, but I have MULTIPLE queries on the SAME data

💡 STEP 4: The "Multiple Queries" Insight

This is THE key insight that changes everything:

Single Query Problem → Stack/Two-pointer might be fine

Multiple Queries on Same Data → ALWAYS think preprocessing

Mental Shift:

• From: "How do I solve THIS query?"
• To: "What information would make ALL queries trivial?"

The "Aha" Moment: "If I knew the nearest candle to the left and right of every position, any query becomes O(1)!"

🎯 STEP 5: Pattern Recognition Development

The Senior Developer's Mental Database:

1. When I see: Multiple queries on static data I think: Preprocessing + lookup
2. When I see: "Find nearest X to left/right"
3. I think: Precompute nearest arrays
4. When I see: "Count Y between positions i and j" I think: Prefix sums
5. When I see: Range queries I think: Can I precompute this?

How This Database Gets Built:

1. Experience similar problems (you see the pattern 5-10 times)
2. Conscious reflection after solving (What was the real pattern here?)
3. Teaching others (forces you to articulate the pattern)
4. Reading others' solutions (see how they approached it)

🚀 STEP 6: The Meta-Learning Process

What Separates Senior from Junior Thinking:

Junior: Focuses on the specific problem

• "How do I count plates between candles?"

Senior: Focuses on the problem CLASS

• "This is a range query problem with boundaries"
• "I've seen this pattern before in different contexts"

Building Pattern Recognition:

1. Level 1: Solve the problem (any working solution) 
2. Level 2: Optimize the solution (better time/space)
3. Level 3: Recognize the pattern (this is similar to X, Y, Z problems) 
4. Level 4: Abstract the pattern (create mental templates)

🎓 How to Develop This Thinking

1. Post-Problem Reflection (Most Important!)

After solving ANY problem, ask:

• What was I REALLY doing here?
• What information did I need repeatedly?
• How is this similar to other problems I've solved?
• What would make this type of problem trivial?

2. Pattern Journaling

Keep a simple note of patterns you encounter:

• "Boundary finding + counting → Preprocessing"
• "Multiple queries on static data → Precompute"
• "Nested loops with dependency → Can I flatten this?"

3. Problem Classification Practice

Before coding, spend 2 minutes classifying:

• Is this a counting problem?
• Is this a boundary problem?
• Is this a repeated computation problem?
• What's the underlying pattern here?

4. Exposure to Problem Families

You don't need to solve 1000 problems. You need to solve problems from different FAMILIES:

• Range Query Family (prefix sums, segment trees)
• Boundary Finding Family (nearest element problems)
• Path Problems Family (DP, backtracking)
• Matching Problems Family (stack, two-pointer)

🎯 The Ultimate Meta-Skill

The question that transforms your thinking:

"If I had to solve 1000 queries like this, what would I precompute?"

This single question will push you toward the most efficient solutions because it forces you to think about:

• What information is reusable?
• What computations am I repeating?
• How can I pay the cost once and reuse forever?

💼 Senior Developer Wisdom

The real skill isn't knowing every algorithm. It's developing the intuition to:

1. Extract the core operation from problem noise
2. Recognize when you're repeating work
3. Think in terms of information reuse
4. Map new problems to familiar patterns

Remember: Every senior developer went through the same evolution. The difference is conscious reflection on the thinking process, not just the coding process.

The pattern recognition comes from solving the SAME underlying pattern in 5-10 different disguises. Then one day, you see a new problem and think: "Oh, this is just the boundary + counting pattern again!"

🎯 Recognition Patterns by Problem Type

🔍 "Multiple Queries" Signal:

2055. Plates Between Candles ⭐
1310. XOR Queries of a Subarray
1906. Minimum Absolute Difference Queries
303. Range Sum Query - Immutable

📊 "Boundary + Content" Signal:

42. Trapping Rain Water ⭐
84. Largest Rectangle in Histogram
907. Sum of Subarray Minimums
2104. Sum of Subarray Ranges

🔄 "Repeated Computation" Signal:

560. Subarray Sum Equals K ⭐
238. Product of Array Except Self
974. Subarray Sums Divisible by K
1248. Count Number of Nice Subarrays

🎯 "Nearest Element" Signal:

496. Next Greater Element I ⭐
739. Daily Temperatures
901. Online Stock Span
1793. Maximum Score of a Good Subarray

🎯 The Key Insight for Your Growth

Notice how your candles problem fits perfectly into the Boundary + Multiple Queries pattern! This is exactly the type of pattern recognition that comes with experience.

🧠 Mental Model for Each Category

When you see these phrases in a problem:

1. "Multiple queries" → Think preprocessing
2. "Between X and Y" → Think boundary arrays
3. "Sum of range [i,j]" → Think prefix sums
4. "Nearest greater/smaller" → Think stack + preprocessing
5. "Count subarrays with..." → Think prefix + hash map

🚀 Accelerated Learning Strategy

Don't solve them all at once! Instead:

1. Master one pattern completely (e.g., basic prefix sums)
2. Solve 3-4 problems from that pattern
3. Reflect on the commonalities
4. Move to next pattern

The magic happens when you solve problem #50 and immediately think: "Oh, this is just the boundary preprocessing pattern from problem #12!"

💡 Senior Developer Secret

Most experienced developers have only solved 200-300 LeetCode problems, but they've deeply understood the patterns within them. It's not about quantity it's about conscious pattern extraction.

The problems I've marked with ⭐ are the ones that, once mastered, will give you the intuition to recognise the pattern in dozens of other problems without solving them all.

Focus on understanding why each solution works, not just how to implement it. That's what builds the pattern recognition muscle!

This are the derived wisdom shared!

Rewire Your Problem-Solving Loop

Junior Approach:

Problem → Code → Solve (Linear, reactive)

Senior Approach:

Problem → Deconstruct → Pattern Match → Optimize → Solve (Iterative, reflective)

Exercise:

For your next problem, spend 10 minutes just thinking before coding:

1. What’s the brute-force solution’s bottleneck?
2. What computations are repeated?
3. What known pattern fits this bottleneck?