This is a pseudopolynomial time algorithm: polynomial in the magnitude of an important number, not in the number of bits that it takes to write it down. Proble

This is a pseudopolynomial time algorithm: polynomial in the magnitude of an important number, not in the number of bits that it takes to write it down. Problems with those kind of algorithm available don't make P=NP because the problems that don't have known pseudopolynomial solutions, when reduced to problems that do, end up with numbers with logs (rather than magnitudes) polynomial in the size of the original problem. In real life, numbers are often of human scale (rather than the kind you get from reducing a hard SAT instance to knapsack) and a pseudopolynomial algorithm is great.