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Advanced algorithioms
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Travelling salesman problem (and obvious algorithm) - Input : A finite set of "cities" {1, . . . , n} and a set of positive integer "distances" d(i, j) between i and j for each pair i < j. [d(i,j)=d( ... j,i)] Output : A permutation i1, . . . , in of cities 1, . . . , n such that the sum ∑(1≤j≤n−1) d(ij , ij+1) + d(i1, in) is as small as possible. This sum is the length of a tour starting in the city i1, visiting all the cities in a certain order and returning back to i1. Obvious algorithm is try every permutation of cities (n!) Boolean satisfiability problem (and obvious algorithm) - Input : A Boolean formula F with variables x1, . . . , xn. Output : Yes if F is satisfiable, else No obvious "brute force" algorithm examines in arbitrary order all possible evaluations of variables. If one evaluation the value of F is true, then F is satisfiable and the output is Yes, else the output in No [Show More]
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