# Brute Force

/brüt fȯrs/

adj. Describes a primitive programming style, one in which the programmer relies on the computer's processing power instead of using his or her own intelligence to simplify the problem, often ignoring problems of scale and applying na"ive methods suited to small problems directly to large ones.

The canonical example of a brute-force algorithm is associated with the 'traveling salesman problem' (TSP), a classical NP-hard problem: Suppose a person is in, say, Boston, and wishes to drive to N other cities. In what order should he or she visit them in order to minimize the distance travelled? The brute-force method is to simply generate all possible routes and compare the distances; while guaranteed to work and simple to implement, this algorithm is clearly very stupid in that it considers even obviously absurd routes (like going from Boston to Houston via San Francisco and New York, in that order). For very small N it works well, but it rapidly becomes absurdly inefficient when N increases (for N = 15, there are already 1,307,674,368,000 possible routes to consider, and for N = 1000 --- well, see bignum).