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Brute force attacks can be made less effective by obfuscating the data to be encoded, something that makes it more difficult for an attacker to recognise when he has cracked the code. One of the measures of the strength of an encryption system is how long it would theoretically take an attacker to mount a successful brute force attack against it.
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]
In computer science, the Knuth–Morris–Pratt algorithm (or KMP algorithm) is a string-searching algorithm that searches for occurrences of a "word" W within a main "text string" S by employing the observation that when a mismatch occurs, the word itself embodies sufficient information to determine where the next match could begin, thus bypassing re-examination of previously matched characters.
To decide if a graph has a Hamiltonian path, one would have to check each possible path in the input graph G. There are n! different sequences of vertices that might be Hamiltonian paths in a given n-vertex graph (and are, in a complete graph), so a brute force search algorithm that tests all possible sequences would be very slow.
The brute force approach entails two steps: For each possible policy, sample returns while following it; Choose the policy with the largest expected discounted return; One problem with this is that the number of policies can be large, or even infinite.
A brute-force approach would be to compute the edit distance to P for all substrings of T, and then choose the substring with the minimum distance. However, this algorithm would have the running time O(n 3 m). A better solution, which was proposed by Sellers, [2] relies on dynamic programming.
An interesting example is the graph isomorphism problem, the graph theory problem of determining whether a graph isomorphism exists between two graphs. Two graphs are isomorphic if one can be transformed into the other simply by renaming vertices. Consider these two problems:
A brute-force search for a knight's tour is impractical on all but the smallest boards. [18] On an 8 × 8 board, for instance, there are 13,267,364,410,532 knight's tours, [14] and a much greater number of sequences of knight moves of the same length. It is well beyond the capacity of modern computers (or networks of computers) to perform ...