Do sample solutions increase student 'productivity'?
I have three types of exercises in my algorithms classes: homework problems, exam problems, and discussion problems.  I'm not entirely sure which you're asking about.

I release detailed solutions and grading rubrics for all homework and exam problems, in part for the advantages you list, in part to speed up grading, and in part to better calibrate my own expectations for the students.  (If it takes too long for me to write up the solution, the problem is probably too hard for them.)  I take them all down again at the end of each semester.  I don't actually mind if students have access to my old solutions—as long as they write in their own words and cite their sources—because homeworks are only a small part of the course grade.  (Students who are stupid enough to submit my old solutions verbatim, typos and all, are not quite publicly fed to the wolves.)

On the other hand, I deliberately do not release solutions for discussion problems (which we discuss in, you guessed it, discussion sections) because the solutions are not the point.  The point is to practice finding the solution.  I know students are adults, but it takes a lot more discipline to practice hunting when someone just regularly hands you the meat.  Also, some discussion problems reappear later on my exams.

But this is really an individual choice.  I know plenty of algorithms instructors who don't give students solutions, and others who hand out solutions on paper but don't distribute them on the web, and others who distribute them on the web but behind a firewall, and others who beg people like me to please for the love of god stop giving away homework solutions because coming up with good algorithms homework problems is really really HARD.



Update:  Starting in 2017, I now regularly release solutions for my discussion problems, typically a few days after each discussion meeting.  (Just like homework solutions, I take these down at the end of every semester.)  Perhaps as a result, these discussion problems are now effectively fixed from one semester to the next -- in a typical semester I replace 5%-10% of them -- and discussion problems almost never appear on exams.  (I should also clarify that discussion problems do not contribute to the final grade.)

I also include an extra solved problem in each homework, with a complete grading rubric.  Again, these solved problems rarely change (as opposed to the problems the students need to solve, which change every semester).

In both cases, the idea is to provide concrete examples of the structure, precision/formality, and level of detail expected from their own work.    Realistically, once the discussion sections are over, unsolved discussion problems are not as valuable as the solutions; students are busy!  And I have lots of other unsolved exercises in my lecture notes for students who want unsullied practice.

Writing all those lab solutions (just over 100 pages of text) was a lot of work, but now it's done.  The net effect of releasing all these solutions seems to be positive—more clearly for teaching evaluations, but also for student performance.