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 naive
methods suited to small problems directly to large ones. The term
can also be used in reference to programming style: brute-force
programs are written in a heavyhanded, tedious way, full of
repetition and devoid of any elegance or useful abstraction (see
also {brute force and ignorance}).

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 the
cities be visited 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}). Sometimes,
unfortunately, there is no better general solution than brute
force. See also {NP-}.

A more simple-minded example of brute-force programming is finding
the smallest number in a large list by first using an existing
program to sort the list in ascending order, and then picking the
first number off the front.