Cook’s Theorem The class NP can be defined as the class of problems decidable by a nondeterministic Turing machine in polynomial time. This theorem shows that SAT is NP-complete by encoding the operation of any nondeterministic Turing machine by a boolean formula, in such a way that the machine accepts if and only if that … Read more
It gives all the permutations of the solutions, but I think I’m beating everyone else for code size. item(X) :- member(X,[215, 275, 335, 355, 420, 580]). solution([X|Y], Z) :- item(X), plus(S, X, Z), Z >= 0, solution(Y, S). solution([], 0). Solution with swiprolog: ?- solution(X, 1505). X = [215, 215, 215, 215, 215, 215, 215] … Read more
P stands for polynomial time. NP stands for non-deterministic polynomial time. Definitions: Polynomial time means that the complexity of the algorithm is O(n^k), where n is the size of your data (e. g. number of elements in a list to be sorted), and k is a constant. Complexity is time measured in the number of … Read more
What is NP? NP is the set of all decision problems (questions with a yes-or-no answer) for which the ‘yes’-answers can be verified in polynomial time (O(nk) where n is the problem size, and k is a constant) by a deterministic Turing machine. Polynomial time is sometimes used as the definition of fast or quickly. … Read more
I assume that you are looking for intuitive definitions, since the technical definitions require quite some time to understand. First of all, let’s remember a preliminary needed concept to understand those definitions. Decision problem: A problem with a yes or no answer. Now, let us define those complexity classes. P P is a complexity class … Read more