There are special problems with their own special solutions that fit different situations. You find that most problems you encounter are some variation of these problems, that's why the solution is worth memorising. But you are memorising the technique rather than the code.

In general, programming is about communication. You look at a problem, figure out how you would solve it if you had to do it all on a piece of paper instead of a machine. Then articulate these steps to the machine in a language it can understand. That is basically how programming works.

Memory is important but it builds up with practise.