Once you get it down into problems like "sort this list" the code practically writes itself and the correct algorithms are simple to determine. Figuring out how to take a complex problem and break it down into problems that you then can throw your algorithm knowledge at is a whole art that takes years of study. A firm grasp of algorithms is essential but not sufficient and it can only help inform your decisions, not provide firm answers.
Picking the right problems is the heart of programming. Figuring out which algorithm to throw at a sub-problem is the heart of contract work.
That is true. To create a application, one needs a Use Case. A Use Case will provide the most abstract solution to what the app will be doing. Then you can take the top down design approach, by dividing the Use Case into a several abstract sub problems. That is known as code architecture and belongs to System Engineering. The System Engineer needs a domain-expert help to identify what problems that needs to be solved.
Then..
Programming is carrying out those abstract sub-problems (interfaces) to become a concrete solution using a specific programming language. To complete such a task, one needs a person that knows his/hers algorithms design techniques, sorting, searching, string processing, graph problems, combinatorial problems, geometric problems and numerical problems. And lastly, the analysis of the respective algorithms.
Once you know what to solve, its just a matter of being able to carry out the task.
I think you might have confused the programmers job with the job of actually creating the entire software - which in general terms is non-sense. To sum up:
The software engineer (the project lead) takes care of identifying the sub-problems, after creating the Use Case with the domain expert (often the customer).
The programmer solves those sub-problems bottoms up, by focusing on creating the atomic parts as efficient as possible.
The programmer solves those sub-problems bottoms up, by focusing on creating the atomic parts as efficient as possible."
This is how yucky enterprise monstrosities get built. The "software engineer"/programmer division is nonsensical and sounds like something one would find in Wipro or Accenture, not so much at (say) Google or Facebook.
"I think you might have confused the programmers job with the job of actually creating the entire software - which in general terms is nonsense."
:-D .
The term you are looking for (since you seem to be fond of labels to sratify coders), for people who just implement whatever their "lead" tells them to is "code monkey".
Yes, a code monkey is a term I'm familiar with. But you need good communication skills too.