Why is 100 lines of code is sometimes better than two lines of code?

The best example is Find the Fake Coin :- You are given 12 coins. One of them is fake and lighter than the others and you're allowed only 3 times. Find the fake coin.

• You check each coin individually.

• For example: for (i in coins) if (coins[i] != 1) return i;

• Time complexity: worst case: check all 12 coins

• Simple code, but inefficient for larger problems or constrained situations.

This approach is Brute Force approach within 2-line idea.

You're allowed only 3 attempts, so your approach should follow this constraint.

Step 1: Divide into 3 groups of 4 coins each.

Let’s say:

• Group A = coins [0,1,2,3]

• Group B = coins [4,5,6,7]

• Group C = coins [8,9,10,11]

Step 2: Compare A vs B on the balance scale.

• If A == B → fake coin is in Group C

• If A > B → fake coin is in B (lighter group)

• If A < B → fake coin is in A (lighter group)

Step 3: You now have 4 coins.

Repeat the same process by dividing the 4 coins further and comparing.

Within 3 comparisons, you can confidently find the fake coin.

The above approach is better than the brute-force approach because it uses an optimized divide and conquer strategy.