There are n trading posts along a river numbered 1, 2, 3, ., n. At any of the posts you can rent a canoe to be returned at any other post downstream. (It is impossible to paddle against the river, since it is too fast.) For each possible departure point i and each possible arrival point j (> i), the cost of a rental from i to j is known: it is C[i,j] > 0. However, it can happen that the cost of renting from i to j is higher than the total costs of a series of shorter rentals from i to j. In this case you can return the first canoe at some post k between i and j and continue your journey in a second (and, maybe, third, fourth.) canoe. There is no extra charge for changing canoes in this way. Give a O(n2) time dynamic programming algorithm to determine the minimum cost of a trip from trading post 1 to trading post n. ...

There are n trading posts along a river numbered 1, 2, 3, ., n. At any of the posts you can rent a canoe to be returned at any other post downstream. (It is impossible to paddle against the river, since it is too fast.) For each possible departure point i and each possible arrival point j (> i), the cost of a rental from i to j is known: it is C[i,j] > 0. However, it can happen that the cost of renting from i to j is higher than the total costs of a series of shorter rentals from i to j. In this case you can return the first canoe at some post k between i and j and continue your journey in a second (and, maybe, third, fourth.) canoe. There is no extra charge for changing canoes in this way. Give a O(n2) time dynamic programming algorithm to determine the minimum cost of a trip from trading post 1 to trading post n. ...

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter19: Probabilistic Dynamic Programming

Section19.4: Further Examples Of Probabilistic Dynamic Programming Formulations

Problem 10P

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