Subset Sum is one of the canonical NP-complete problem. Given a set $$S$$ of positive integers and a target $$B$$, is there a subset of $$S$$ summing to $$B$$? An optimization variant asks for the subset of $$S$$ whose sums is closest to $$B$$.
Subset Sum is NP-hard if the integers in $$S$$ are encoded in binary (i.e., in the usual way), but if they are encoded in unary (that is, $$n$$ is encoded as $$1^n$$, the string consisting of $$n$$ many ones), a dynamic programming algorithm solves Subset Sum in polynomial time.
The trivial $$2^n$$ algorithm (where $$n = |S|$$) for solving Subset Sum can be improved to $$c^n$$ for some $$c < 2$$. Assuming SETH, there is no $$2^{o(n)}$$ algorithm. The best value of $$c$$ (conditional on SETH or similar hardness assumptions) is currently unknown.