# Polynomial time optimization problems belong to which complexity class?

Take a look at the FP complexity class.

Technically speaking, it is wrong. However, usually people don’t make a huge difference between the two. Its usually clear from the context whether the problem is a decision or a search problem, hence its clear whether it should be in $$P$$ or $$FP$$.

So, writing that “Finding the shortest $$(s,t)$$ path in the graph $$G$$, is a $$P$$ problem” would actually mean: “Finding the shortest $$(s,t)$$ path in the graph $$G$$, is an $$FP$$ problem” (since the context is clear)