【非選題】 9. (7 points) Given a set S of n numbers, the k-partition problem is to determine
whether or not S can be partitioned into k subsets of the same sum. For
example, let S ={1,2,9,12,18}. Then for the two-partition problem, we indeed
can partition S into two subsets S1 = {1,2,18} and S2 = {9,12} such that the
sum of all elements in S1 equals to the sum of all elements in S2. In fact, it can
be proved that the two-partition problem is NP-complete. In the situation where
the two-partition problem is already NP-complete, please prove that the
three-partition problem is also NP-complete.
9. During the secondary succession in the forest, with time the number of woody species________.
(A) decreases, being highest at the initial stages of the succession.
(B) increases and then levels off, being highest in the climax vegetation.
(C) does not change - pioneer species at the early stage of the succession are slowly replaced by the same number of climax
species in the late stage.
(D) is unpredictable and depends on the forest system under study.
(E) none of the above.
【非選題】 1.(15%) Two persons are involved in a situation where the public good, G, is privately provided. The
utility function of each individual is denoted as ui(G,x) = ai InG + xi, for all i = 1,2 where x is a
private good. Denote gi as the amount of the public good contributed by the individual i such that
G = g1 +g2. Each individual's budget constraint is shown as xi + gi = my. Assume a1 < a2. How
much will the individual 1 contribute, i.e. g1, in equilibrium?
【非選題】 4. Sundar Pichai, Google's boss, has described the developments in Artificial Intelligence (AI) as "more
profound than fire or electricity". However, it has been found that Al's progress has lagged in many
companies. For exarple, the self-driving lorry firm Starsky Robotics based in San Francisco, closed down
in March 2020. Its founder, Stefan Seltz-Axmacher, stated that the driverless cars show the limits of today's
AI. To effectively develop AI-based driverless cars, what people, organization, and technology issues need
to be addressed? (15%) Considering the driverless cars, what trends do you see pushing or hindering
innovation in AI technologies? (5%)