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In this problem, we want to determine a set of states with the smallest total population that achieves an electoral college win. specifically, for each state i, for i = 1, 2, . . , n, let pi be its population and vi its electoral votes. all electoral votes of a state go a single candidate, and so the (overall) winning candidate is the one who receives at least v = b( p i vi)/2c + 1 electoral votes. our goal is to find the set of states s for which p i∈s pi is as small as possible subject to the constraint that p i∈s vi ≥ v . design a dynamic programming algorithm for this problem; prove its correctness; and analyze its time complexity.