Pattern - Complement Lookup

For two-sum, you're looking for pairs $(x, y)$ where $x + y = target$. So $y = target - x$. For each element $x$:

$1.$ Check if $target - x$ is in the hash map

$2.$ If yes, you found a pair

$3.$ Add $x$ to the hash map

The hash map stores elements you've seen. For each new element, you check if its "complement" was seen before.