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Optimal Lab

DSA series #01 · interactive

One problem, three ways

DSA is not about writing code. It is about spotting the pattern and knowing more than one way to solve it. Here is the classic example: find two numbers that add up to 24.

Try each number with every number after it.

4
[0]
↑i
11
[1]
↑j
7
[2]
1
[3]
15
[4]
9
[5]
3
[6]
12
[7]

4 + 11 = 15 ≠ 24

1

checks

Trade-off: No extra memory, easy to get right. Falls over once n grows. time O(n²) · extra memory O(1)

Checks to find the answer in these 8 numbers

  • Check every pair
    23
  • Sort + two pointers
    29
  • One pass + hash map
    6

With 8 numbers, checking every pair is not slow, and sorting first actually costs more. Big-O ignores constants and small inputs. That is why you measure before you optimise.

Now make the input bigger

log scale · 1 check = 1 ns

  • Check every pair O(n²)500B checks · 8.3 min
  • Sort + two pointers O(n log n)20.9M checks · 20.9 ms
  • One pass + hash map O(n)1M checks · 1.0 ms

Same problem, same answer. At a million numbers the pair check takes minutes, the hash map about a millisecond. Knowing the pattern is what lets you pick.

Now solve it

Arrays & Hashing: 19 problems

See all →

In production

Tools and technologies

The pattern is universal; runtimes give you hash maps and sorting without a separate product.

Not tied to one language — use these names when you search docs or design a system.