124 lines
3.8 KiB
Python
124 lines
3.8 KiB
Python
# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.com
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""
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Ski assignment in Google CP Solver.
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From Jeffrey Lee Hellrung, Jr.:
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PIC 60, Fall 2008 Final Review, December 12, 2008
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http://www.math.ucla.edu/~jhellrun/course_files/Fall%25202008/PIC%252060%2520-%2520Data%2520Structures%2520and%2520Algorithms/final_review.pdf
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'''
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5. Ski Optimization! Your job at Snapple is pleasant but in the winter
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you've decided to become a ski bum. You've hooked up with the Mount
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Baldy Ski Resort. They'll let you ski all winter for free in exchange
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for helping their ski rental shop with an algorithm to assign skis to
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skiers. Ideally, each skier should obtain a pair of skis whose height
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matches his or her own height exactly. Unfortunately, this is generally
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not possible. We define the disparity between a skier and his or her
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skis to be the absolute value of the difference between the height of
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the skier and the pair of skis. Our objective is to find an assignment
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of skis to skiers that minimizes the sum of the disparities.
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...
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Illustrate your algorithm by explicitly filling out the A[i, j] table
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for the following sample data:
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* Ski heights: 1, 2, 5, 7, 13, 21.
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* Skier heights: 3, 4, 7, 11, 18.
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'''
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Compare with the following models:
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* Comet : http://www.hakank.org/comet/ski_assignment.co
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* MiniZinc: http://hakank.org/minizinc/ski_assignment.mzn
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* ECLiPSe : http://www.hakank.org/eclipse/ski_assignment.ecl
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* SICStus: http://hakank.org/sicstus/ski_assignment.pl
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* Gecode: http://hakank.org/gecode/ski_assignment.cpp
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This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
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Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
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"""
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import sys
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from constraint_solver import pywrapcp
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def main():
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# Create the solver.
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solver = pywrapcp.Solver('Ski assignment')
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#
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# data
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#
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num_skis = 6
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num_skiers = 5
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ski_heights = [1, 2, 5, 7, 13, 21]
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skier_heights = [3, 4, 7, 11, 18]
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#
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# variables
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#
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# which ski to choose for each skier
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x = [solver.IntVar(0, num_skis-1, 'x[%i]' % i)
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for i in range(num_skiers)]
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z = solver.IntVar(0, sum(ski_heights), 'z')
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#
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# constraints
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#
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solver.Add(solver.AllDifferent(x))
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z_tmp = [abs(solver.Element(ski_heights, x[i]) - skier_heights[i])
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for i in range(num_skiers)]
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solver.Add(z == sum(z_tmp))
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# objective
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objective = solver.Minimize(z, 1)
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#
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# search and result
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#
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db = solver.Phase(x,
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solver.INT_VAR_DEFAULT,
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solver.INT_VALUE_DEFAULT)
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solver.NewSearch(db, [objective])
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num_solutions = 0
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while solver.NextSolution():
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num_solutions += 1
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print 'total differences:', z.Value()
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for i in range(num_skiers):
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x_val = x[i].Value()
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ski_height = ski_heights[x[i].Value()]
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diff = ski_height - skier_heights[i]
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print 'Skier %i: Ski %i with length %2i (diff: %2i)' %\
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(i, x_val, ski_height, diff )
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print
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solver.EndSearch()
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print
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print "num_solutions:", num_solutions
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print "failures:", solver.Failures()
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print "branches:", solver.Branches()
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print "WallTime:", solver.WallTime()
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if __name__ == '__main__':
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main()
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