Backtracking

Backtracking is the family that shows up the second a Google prompt asks you to produce every arrangement, every selection, or every valid string. It is high-frequency here and easy to fumble, because the code looks small but the state management is where candidates lose the thread. One skeleton covers the group. Once you can write that skeleton from muscle memory, each problem comes down to two decisions: what a "choice" is, and what state distinguishes one branch from the next.

Every problem here builds a partial answer one decision at a time, recurses to extend it, then undoes the last decision before trying the next one. That undo is everything. It lets a single list act as the working answer for the entire search tree, so you are never copying state around. The art is knowing when a branch is hopeless and cutting it early. A search that prunes well runs in a fraction of the time of one that explores every dead end.