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At the Unseen University, several keen explorer - wizards recently reported back with an astounding discovery: they have located a large forest of sapient pearwood,
At the Unseen University, several keen explorerwizards recently reported
back with an astounding discovery: they have located a large forest of sapient
pearwood, an astonishingly rare material of immense value for constructing
highquality sentient furniture. Since the discovery, the wizards have begun
their own enterprise selling lumber, Pearwood Industries PI Being somewhat
new to the lumber business, and knowing your algorithmic wizardry,
they come to you with a problem.
Given an m times n crosssection of lumber m and n are integers and the
units are in centimeters PI would like to cut the piece of lumber into some
number of smaller pieces for sale. Each section will be a rectangle with integer
dimensions. The value for any k times piece can be looked up in constant time
and the value is not necessarily related to the area of the piece, as some
dimensions are simply in higher demand. For example, a times piece might
be worth $ while a times piece might be worth $
Your wizarding friends have constructed a special saw that is capable of
making a cut horizontally or vertically across any rectangular section of
sapient pearwood at integer centimeter locations. Note that a cut is made
across the entire section of the given piece; no partial cuts are possible.
Describe and analyze an efficient dynamic programming algorithm for
determining how to subdivide a given mtimes n piece to maximize the total value
of the resulting pieces. Use the process and writing style from Handout
For simplicity of exposition, you should describe an algorithm that returns
a number which is the maximum possible revenue. At the very end, in just
a few additional sentences, explain how you would modify your algorithm to
return the actual sequence of cuts that result in the pieces that make up this
optimal revenue.
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