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You are given an array that holds the weights of n people in the class W = (w1, w2, . . . , wn). Your goal is to divide the n people into two teams such that the total weight of the two teams is equal or as close as possible to equal. Describe such an algorithm and give its running time. The total number of people on each team should differ by at most 1. As- sume that M is the maximum weight of a person, i.e., ∀iwi ≤ M. The running time should be a polynomial function of n and M. The output should be the list of people on each team and the difference in weight.
Explain your algorithm (2 points), explain why your algorithm is correct (2 points), and explain the runtime of your algorithm (1 point).
Note: You have to provide a DP solution. Other type of algorithmic solution is not acceptable. To get full points, your solution's runtime needs to be O(n3M) or less (yes there is a more effective solution).
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