Not quite.

Copyright doesn't protect general concepts, methods, or common knowledge. So you could write a program that is remarkably similar to another one and not infringe copyright. Just like you can write a book with the same plot as another without infringing copyright.

Plus given that most programming languages have a finite grammar and a limited number of ways to express general concepts, the individual bits of code that make up most programs are probably not sufficiently original to be copyrightable in themselves.