Time a combinatoric algorithm for five elements: it will take six times longer to run it for six, and 42 times longer for seven. Examples include algorithms for many of the acknowledged hard problems—the traveling salesman problem, optimally packing things into a container, partitioning a set of numbers so that each set has the same total, and so on. Often, heuristics are used to reduce the running times of these types of algorithms in particular problem domains.
