Two Sum - Hash Map Approach

Use a hash map to store numbers you've seen. For each number $x$, compute the complement $target - x$ and check if it's in the map.

If the complement exists, you found your pair. If not, add the current number to the map and continue.

This takes $O(n)$ time with $O(n)$ space. The brute force approach (checking all pairs) would take $O(n^2)$.