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In the field of computer science, the method is called generate and test (brute force). In elementary algebra, when solving equations, it is called guess and check. [citation needed] This approach can be seen as one of the two basic approaches to problem-solving, contrasted with an approach using insight and theory.
Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposition in question holds. [1]
For example, biological brains are hardwired to interpret signals such as pain and hunger as negative reinforcements, and interpret pleasure and food intake as positive reinforcements. In some circumstances, animals learn to adopt behaviors that optimize these rewards. This suggests that animals are capable of reinforcement learning. [4] [5]
Some hobbyists have developed computer programs that will solve Sudoku puzzles using a backtracking algorithm, which is a type of brute force search. [3] Backtracking is a depth-first search (in contrast to a breadth-first search), because it will completely explore one branch to a possible solution before moving to another branch.
One way to speed up a brute-force algorithm is to reduce the search space, that is, the set of candidate solutions, by using heuristics specific to the problem class. For example, in the eight queens problem the challenge is to place eight queens on a standard chessboard so that no queen attacks any other.
The brute force algorithm finds a 4-clique in this 7-vertex graph (the complement of the 7-vertex path graph) by systematically checking all C(7,4) = 35 4-vertex subgraphs for completeness. In computer science , the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called ...
Brute force method or proof by exhaustion, a method of mathematical proof Brute-force attack , a cryptanalytic attack Brute-force search , a computer problem-solving technique
Brute force consists of checking all assignments of zeros and ones and counting those that have balanced rows and columns (n / 2 zeros and n / 2 ones). As there are 2 n 2 {\displaystyle 2^{n^{2}}} possible assignments and ( n n / 2 ) n {\displaystyle {\tbinom {n}{n/2}}^{n}} sensible assignments, this strategy is not practical except maybe up to ...