let pr[i] be answer to sub-problem 1..i and there is restaurant built at i. (maximum expected total profit)
How do we calculate pr[i]? Expected profit from location i + max. pr[j], where location of j is at least k apart from location i. pr[i] = p[i] + max(pr[j]), where j is between 1..i-1 and m[i]-m[j] >= k answer to your problem is max(pr[i]) where i=1..n You can do it in O(n), keeping max. pr[i] up to now additionally. On 3/19/07, Ez_Alg <[EMAIL PROTECTED]> wrote: > > BurgerKing's is considering opening a series of restaurants along > RiverSide Freeway. The n possible locations are along a straight line, > and the distances of these locations from the start of RiverSide > Freeway are, in miles and in increasing order,m1;m2; : : : ;mn. The > constraints are as follows: At each location, BurgerKing's may open at > most one restaurant. The expected profit from opening a restaurant at > location i is pi, where pi > 0 and i = 1; 2; : : : ; n. Any two > restaurants should be at least k miles apart, where k is a positive > integer. what is an efficient algorithm to compute the maximum > expected total profit subject to the given constraints. > any help would be appriciated > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/algogeeks -~----------~----~----~----~------~----~------~--~---
