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It runs in polynomial time on inputs that are in SUBSET-SUM if and only if P = NP: // Algorithm that accepts the NP-complete language SUBSET-SUM. // // this is a polynomial-time algorithm if and only if P = NP. // // "Polynomial-time" means it returns "yes" in polynomial time when // the answer should be "yes", and runs forever when it is "no".
Programming by permutation, sometimes called "programming by accident" or "shotgunning", is an approach to software development wherein a programming problem is solved by iteratively making small changes (permutations) and testing each change to see if it behaves as desired. This approach sometimes seems attractive when the programmer does not ...
algorithm FPTAS is input: ε ∈ (0,1] a list A of n items, specified by their values, , and weights output: S' the FPTAS solution P := max {} // the highest item value K := ε for i from 1 to n do ′ := ⌊ ⌋ end for return the solution, S', using the ′ values in the dynamic program outlined above
In a 1977 review of permutation-generating algorithms, Robert Sedgewick concluded that it was at that time the most effective algorithm for generating permutations by computer. [2] The sequence of permutations of n objects generated by Heap's algorithm is the beginning of the sequence of permutations of n+1 objects.
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number.
A simple algorithm to generate a permutation of n items uniformly at random without retries, known as the Fisher–Yates shuffle, is to start with any permutation (for example, the identity permutation), and then go through the positions 0 through n − 2 (we use a convention where the first element has index 0, and the last element has index n − 1), and for each position i swap the element ...
The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions. The problem can be used to simulate every other problem for which we can verify quickly that a solution is correct.
A one-way permutation is a one-way function that is also a permutation—that is, a one-way function that is bijective. One-way permutations are an important cryptographic primitive , and it is not known if their existence is implied by the existence of one-way functions.