Chain of Thought Prompting

❌ Standard (often wrong on complex problems):
Q: If there are 3 cars, each with 4 wheels, and 2 motorcycles each with 2 wheels, how many wheels total?
A: 16

✅ Chain of Thought:
Q: [same question] Let's think step by step.
A: Cars: 3 × 4 = 12 wheels
   Motorcycles: 2 × 2 = 4 wheels
   Total: 12 + 4 = 16 wheels

"What is the time complexity of merging two sorted arrays of size n and m?
Let's think step by step."

Response:
Step 1: We need to compare elements from both arrays
Step 2: Each comparison advances one pointer by 1
Step 3: Total comparisons ≤ n + m (each element processed once)
Step 4: Therefore time complexity is O(n + m)

Q: I have 5 apples. I give 2 to Alice and 1 to Bob. How many do I have?
A: Start with 5 apples. Give 2 to Alice: 5-2=3. Give 1 to Bob: 3-1=2. Answer: 2.

Q: A train leaves at 9am traveling 60mph. Another leaves at 10am going 80mph.
When does the second catch the first?
A: [let the model continue the pattern]

"Analyze this algorithm:

[code]

Reason through:
1. What does each section do?
2. What data structures are used and why?
3. What is the time complexity? (show derivation)
4. What is the space complexity?
5. Can it be optimized? If so, how?"

"I need to design a caching system for 10M users.

Explore three different architectures:

Option A: Redis cluster with consistent hashing
- Design: ...
- Pros: ...
- Cons: ...

Option B: Memcached with client-side sharding
...

Option C: Application-level caching with Caffeine
...

Given our constraints (high availability, < 5ms latency), recommend the best option and justify."

import openai
from collections import Counter

def self_consistent_answer(question, n=5):
    answers = []
    for _ in range(n):
        response = openai.chat.completions.create(
            model="gpt-4",
            messages=[{"role": "user",
                       "content": question + "\nLet's think step by step."}],
            temperature=0.7  # diversity in reasoning paths
        )
        # Extract final answer from response
        answers.append(extract_answer(response))
    return Counter(answers).most_common(1)[0][0] # majority vote

"Review this Java method for bugs:
[code]

Reason through:
1. What is the function supposed to do?
2. Trace through the logic with input [example]
3. Are there edge cases not handled?
4. Are there concurrency issues?
5. State any bugs found and fixes."