Loop Invariants Part 1 — The One Concept That Makes Algorithms Click

Topics covered: loops, accumulators, hash maps, lookup patterns, data structure → invariant mapping Most people solve algorithms by trial and error. Write code, run tests, tweak, repeat. Eventually it passes. They move on. But they can't tell you why it passed. And when the next problem looks slightly different — same pattern, different wrapping — they're back to guessing. The fix isn't more LeetCode. It's one concept that makes every loop make sense: the invariant. Once you see it, you can't unsee it. It's in every algorithm you've already written. You were just never told to look. So here's the invariant — not as a formal proof, but as a tool. One you can use immediately, and understand completely by the end of this post. TL;DR — An invariant is what must stay true at every step of your loop. Pick a data structure → it defines what invariant you can write → verify it holds before, during, and after the loop → the update becomes obvious. When code fails: find the step where the invari