Why Smaller Code Doesn't Always Mean Faster Execution: Lessons from Balls, Doors, and Smart Comparisons

A Classic Starting Point: The 9-Weighted Ball Problem

Let’s start with a classic: you have 9 balls, and one is heavier or lighter. You get only two uses of a balance scale to find the odd one.

The naive solution might be to check each ball individually, linearly. But that takes 8 comparisons in the worst case.

The optimal method? Divide the 9 balls into three groups of three, weigh two groups, and based on the result, you know exactly where the odd one lies. In just 2 comparisons, you've solved a problem that could have taken 8. This is the power of comparative logic and divide-and-conquer.

The deeper lesson here: smaller code (like a simple loop) might look neat, but it's often not the most instruction-efficient approach.

Now , Lets apply the idea to 9 Door problem.

You have 9 doors. Behind each door is a smart lock module that can be queried in a special way.

Out of these, 8 doors have the same lock type, and 1 door has a different lock type (the "odd" door).

You're given access to a lock comparison device.

This device can compare any two doors, and tell you:

✅ "Same lock type"

❌ "Different lock types"

Our Goal - To Use the fewest number of comparisons to find the odd door.

Simple? Yes. Efficient? Not always.

In the worst case, this requires 9 key checks. This is small code but heavy instruction cost.

Trying the Ball Logic: Divide into 3 Groups
Like as we did in the 9 ball problem , and here we would understand that how nature of problem can forces us to refine and make solution optimised to them .

Lets try to apply the same strategy as the ball problem: 🧪📚🤯

• Group doors into three sets of 3

• In each group, check two doors

Sounds clever, right? But it turns out:

• Each group needs 2 comparisons to conclude anything confidently

• Across 3 groups = 6 comparisons worst case

• No significant gain over linear search!

It shows that just applying divide-and-conquer without considering problem nature doesn't always help.

The Real Optimization: 4 Pairs + 1 Leftover
Group doors into 4 pairs:

• (D1, D2), (D3, D4), (D5, D6), (D7, D8)

• Leftover: D9

Logic:

• For each pair, check if both doors fit the key

• If all pairs pass, the leftover door is the mismatched one

• Otherwise, the first failed pair contains the door

Performance:

• Worst case: 4 comparisons

• Best case: 1 comparison

• Average: ~2.5 comparisons

All this by simply maximizing the information gained from each check.
This approach beat both the linear brute-force and the group-of-3 logic. Despite adding a little complexity in the code structure, it reduced the total CPU instructions needed. That means faster execution in practice

⚖️ Nature of the Problem Matters

But suppose if we dont have any comparative matching condition we have to check for each door to find it is the odd door or not .
Without that, no amount of grouping or divide-and-conquer will help.

And in the improved problem of 9 doors where we had the comparative matching condition we were able to form a solution which would only need 4 comparisons at most in the worst case , thus beating the strategy used in 9 ball problem of grouping in 3 pairs of 3 ball each .

So the key insight was :
“The most optimal strategy is problem-specific, not code-specific”

Final Thoughts: Code Size vs. Instruction Cost

This exploration gives us a valuable lesson:

• Smaller code might look elegant

• But fewer lines do NOT mean fewer CPU instructions

• A seemingly longer code can have a smarter structure, leading to fewer operations

Always analyze:

• What comparisons are allowed?

• Can we use grouping to reduce total checks?

• How much information does each step give us?

Because at the end of the day what matters is :

“Performance is not about how short your code looks, but how few instructions your CPU needs to execute”

So next time you write a loop, ask yourself: Can I think smarter instead of just coding shorter?

Till then keep optimising 🫶🏻

#chaicode