The Thinking Process: Building vs Validating Logic
The Ultimate Meta-Question
"Do I have to think of all these edge cases at once? Or focus on ONE element and its role?"
This is THE question that separates beginners from problem-solvers!
The Two Modes of Thinking
Mode 1: Building The Logic (Creative Phase)
Focus: ONE element and its local decisions
Mode 2: Validating The Logic (Critical Phase)
Focus: Edge cases and correctness
Critical Insight
You do NOT think about edge cases while building logic! You think about edge cases AFTER you have the logic!
Your confusion: You're trying to do both at the same time! This causes cognitive overload.
The Problem-Solving Flow
Phase 1: UNDERSTAND
- What does the problem want?
- Play with examples
- Understand constraints
Phase 2: DISCOVER PATTERN ← Focus: ONE element
- What can ONE element do?
- What are its options?
- This gives you the CORE LOGIC
Phase 3: FORMALIZE
- Turn the pattern into algorithm
- Write pseudocode
- Define the strategy
Phase 4: VALIDATE ← Focus: Edge cases
- What could go wrong?
- Test edge cases
- Prove correctness
Phase 5: IMPLEMENT
- Write actual code
- Handle edge cases with guards
- Add safety mechanisms
Phase 2: Building Logic (ONE Element Focus)
What You Should Think
"I have number x. What are x's options?"
Looking at x in isolation:
- x could extend something ending at x-1
- x could start something new with x+1, x+2
That's it! Two options.
Which should I prefer?
- Try examples
- Discover: extending is better (incomplete chains are liabilities)
Done! That's the algorithm.
What You Should NOT Think (Yet)
❌ "What if freq[x] = 0?"
❌ "What if need[x] > 0 but no supply?"
❌ "What if we run out of memory?"
❌ "What if the array is empty?"
These are Phase 4 questions!
The Power of Local Thinking
When building logic, you think locally (one element at a time):
Example: Discovering the Algorithm
Input: [1, 2, 3, 3, 4, 5]
Think about element 3 (second one):
"What can this 3 do?"
Option A: Join the [1, 2] chain → make [1, 2, 3]
Option B: Start new [3, 4, 5]
"Which is better?"
If I do B first:
- [3, 4, 5] is fine
- But [1, 2] is stuck! Only length 2!
If I do A first:
- [1, 2, 3] is complete (length 3)
- Then use other 3 for [3, 4, 5]
- Both work!
Conclusion: Prefer A (extending)
Notice: No edge cases! Just exploring what makes sense for ONE element.
Phase 4: Validation (Edge Case Focus)
After you have the logic, NOW you think about edge cases:
Critical Thinking Questions
"What could break this algorithm?"
-
"What if a number is used up?"
- Add guard:
if (freq[x] == 0) continue;
- Add guard:
-
"What if we can't extend or start?"
- Add fail branch:
else { return "fail"; }
- Add fail branch:
-
"What if we have demand but no supply?"
- Analyze: Does guard + fail prevent this?
-
"What if needs remain at the end?"
- Analyze: Are chains still valid?
This is AFTER the algorithm exists!
The Key Distinction
Creating Logic (Phase 2)
| Aspect | Details |
|---|---|
| Question | "What makes sense?" |
| Approach | Think about ONE element's PURPOSE |
| Output | The core algorithm idea |
Example thought:
"Each number either extends or starts.
Extending is better than starting.
That's the strategy!"
Validating Logic (Phase 4)
| Aspect | Details |
|---|---|
| Question | "What could go wrong?" |
| Approach | Think about ALL possible cases |
| Output | Guards, checks, edge case handling |
Example thought:
"What if freq[x] = 0? Add a guard.
What if can't use x? Add fail branch.
What if need[x] but no x? Prove it's OK."
The Mental Separation
Think of it like building a house:
Phase 2: Architecture (ONE element focus)
"Each room needs a door and window.
Kitchen near dining room.
Bedrooms upstairs."
You're thinking about RELATIONSHIPS and PURPOSE.
Not worrying about plumbing leaks yet!
Phase 4: Engineering (ALL cases focus)
"What if water pressure drops?
What if earthquake?
What if electrical short?"
Now you think about EVERYTHING that could fail.
Add safety mechanisms.
You don't design architecture while worrying about earthquakes!
How to Practice This Separation
When Building Logic (Phase 2)
DO:
✅ Focus on ONE element's role ✅ Ask: "What can it do?" ✅ Ask: "What makes sense?" ✅ Use small, simple examples ✅ Think about relationships (x relates to x-1 and x+1)
DON'T:
❌ Worry about null pointers ❌ Worry about empty arrays ❌ Worry about all possible inputs ❌ Think about implementation details
When Validating (Phase 4)
DO:
✅ Think adversarially: "How can I break this?" ✅ Test edge cases ✅ Prove correctness ✅ Add guards and checks
DON'T:
❌ Change the core algorithm (unless fundamentally broken) ❌ Add complexity without reason
Concrete Example: Your Journey
What You Did (Accidentally Mixed Phases)
- Saw the algorithm ✓
- Thought: "What if
freq[x]=0butneed[x]>0?" (Phase 4) - Got confused about the core logic (Phase 2)
You jumped to Phase 4 before fully understanding Phase 2!
What You Should Do
-
First understand: "Each element extends or starts" (Phase 2)
- Get this SOLID
- Understand WHY this makes sense
- Don't worry about edge cases yet
-
Then validate: "What if
freq[x]=0?" (Phase 4)- NOW think about what could go wrong
- Add guards
- Prove correctness
The Learning Strategy
For ANY Algorithm Problem
Key Questions:
- 🎯 What does ONE element need to do?
- 🔄 What are its options?
- 🧩 What makes sense locally?
Don't think about null pointers, empty arrays, or corner cases yet!
Actions:
- ✏️ Write the core logic
- 📝 Simple pseudocode
- 🚫 No guards yet
Focus on the pattern, not the problems!
Validation Questions:
- ❓ What could go wrong?
- 🛡️ Add guards
- ✅ Add checks
- 🔬 Prove correctness
Now you can think about all possible scenarios!
Why This Separation Matters
If You Mix Them
Your brain tries to:
- Understand the algorithm
- AND worry about edge cases
- AND prove correctness
- ALL AT ONCE
Result: Cognitive overload! 🤯
You can't see the forest for the trees.
If You Separate Them
Phase 2: Clean, clear thinking
"Ah, each element extends or starts. Simple!"
Phase 4: Systematic validation
"Now let me check if this handles all cases."
Result: Clear understanding! ✨
The Master's Approach
Beginner thinks:
"I need to think about EVERYTHING at once!
The algorithm, edge cases, implementation, proof..."
Master thinks:
"First, what's the core idea? (Phase 2)
Got it? Good.
Now, what could break? (Phase 4)
Handle those.
Done."
The master separates concerns!
Applying This to Your Questions
Your Question Was:
"What if freq[x]=0 but need[x]>0?"
This is a Phase 4 (validation) question!
The Answer Process:
First (Phase 2): Understand the core logic
"Each number extends or starts.
Prefer extending.
That's the strategy."
Don't worry about edge cases yet!
Then (Phase 4): Validate edge cases
"Now, what if freq[x]=0?
Oh, the guard handles it: if (freq[x]==0) continue;
What if need[x]>0 but no x available?
Analyze: chains are already valid length, so OK!"
See the separation?
The Ultimate Answer
Your Question:
"Do I have to think of all these edge cases at once? Or focus on ONE element and its role?"
The Answer:
You focus on ONE element when BUILDING logic (Phase 2).
You think of ALL cases when VALIDATING logic (Phase 4).
NEVER do both at the same time!
Building (Phase 2):
- Mindset: "What makes sense?"
- Focus: ONE element's purpose
Validating (Phase 4):
- Mindset: "What could break?"
- Focus: ALL possible inputs
The Practice Method
For This Problem:
Phase 2 Practice:
- Cover up all the edge case discussions
- Just focus on: "Why extend before start?"
- Get that CRYSTAL clear
Phase 4 Practice:
- Now read the edge cases
- For each one, trace through the code
- Prove it's handled
Do them separately!
The Mantra
"First understand the WHAT (core logic). Then validate the HOW (edge cases). Never mix them while learning!"
Summary Table
| Phase | Focus | Question | Mindset |
|---|---|---|---|
| Creating Logic (Phase 2) | ONE element | "What makes sense?" | Local decisions, simple examples |
| Validating Logic (Phase 4) | ALL cases | "What could break?" | Adversarial thinking, prove correctness |
The Key: DO THEM SEPARATELY!
Your confusion came from trying to do both at once.
Separate them, and everything becomes clear! 🎯