Brute forcing

Brute forcing is generally accepted as the term for solving a problem in a roundabout, time-consuming, uncreative, and inconvenient method.

Given the problem "How many outfits can you create with thirteen hats and seven pairs of shoes?", a method involving brute force would be to list all 91 possibilities.

Another method of brute force is the Greedy Algorithm. As an example, given two sets $\{{a}_1,{a}_2,\ldots,{a}_n\}$ and $\{b_1,b_2,\ldots,b_n\}$ how can we maximize the sum of $\sum_{i,j \in n} a_ib_j$? We sort the sets such that they are in increasing or decreasing order; then, the maximal sum is $a_1b_1 + a_2b_2 + a_3b_3 + \ldots a_nb_n$. The "greedy" part is when we maximize the sum each step by taking the largest possible term to add.

See the Rearrangement Inequality for consequences of the example (and a more formal proof).

See also

Invalid username
Login to AoPS