Backtracking: Choose, Explore, Undo

Pick or skip gives two choices per step. Some problems have many choices per step: the next number can be any candidate, or the next position can hold any unused element. Then you loop over the choices.

The template

void solve(state, path) {
    if (done) { save a copy of path; return; }
    for (each choice c) {
        if (c is not allowed) continue;
        choose(c);          // change path
        solve(next state);  // explore
        undo(c);            // put path back
    }
}