Yuckdonald's is considering opening a series of restaurants along Quaint Valley Highway (QVH).The n possible locations are along a straight line, and the distances of these locations from the start of QVH are, in miles and in increasing order,m1;m2; : : : ;mn. The constraints are as follows: 1)At each location,Yuckdonald's may open at most one restaurant.The expected profi t from opening a restaurant at location i is pi, where pi > 0 and i = 1; 2; : : : ; n. 2)Any two restaurants should be at least k miles apart, where k is a positive integer. Give an effi cient algorithm to compute the maximum expected total pro fit subject to the given constraints.
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