Consider the following design problem. A farmer is building a wire fence on his land. He has planted N wooden posts into the ground but has not put wire between them yet. The positions of these wooden posts are final; they cannot be moved. Wire placed between posts follows a straight line, and the farmer must place wire between the posts such that it forms an enclosure. The farmer is smart and will not allow the wires to cross. See the figure below, where the posts are the circles, and the lines are the wire (ignore the post numbering). However, the farmer would like the fence to enclose as much land as possible. He is willing to let some of his posts go unused (that is, not be part of the wire fence), so long as it maximizes the amount of land that the fence encloses. What algorithm would you use to solve this problem? Give a brief description of how it would work and the asymptotic run time as a function of N.
Consider the following design problem. A farmer is building a wire fence on his land. He has planted N wooden posts into the ground but has not put wire between them yet. The positions of these wooden posts are final; they cannot be moved. Wire placed between posts follows a straight line, and the farmer must place wire between the posts such that it forms an enclosure.
The farmer is smart and will not allow the wires to cross. See the figure below, where the posts are the circles, and the lines are the wire (ignore the post numbering). However, the farmer would like the fence to enclose as much land as possible. He is willing to let some of his posts go unused (that is, not be part of the wire fence), so long as it maximizes the amount of land that the fence encloses.
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