156 lines
4.3 KiB
Python
156 lines
4.3 KiB
Python
# Copyright 2010 Hakan Kjellerstrand hakank@gmail.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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Photo problem in Google CP Solver.
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Problem statement from Mozart/Oz tutorial:
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http://www.mozart-oz.org/home/doc/fdt/node37.html#section.reified.photo
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'''
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Betty, Chris, Donald, Fred, Gary, Mary, and Paul want to align in one
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row for taking a photo. Some of them have preferences next to whom
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they want to stand:
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1. Betty wants to stand next to Gary and Mary.
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2. Chris wants to stand next to Betty and Gary.
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3. Fred wants to stand next to Mary and Donald.
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4. Paul wants to stand next to Fred and Donald.
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Obviously, it is impossible to satisfy all preferences. Can you find
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an alignment that maximizes the number of satisfied preferences?
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'''
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Oz solution:
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6 # alignment(betty:5 chris:6 donald:1 fred:3 gary:7 mary:4 paul:2)
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[5, 6, 1, 3, 7, 4, 2]
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Compare with the following models:
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* MiniZinc: http://www.hakank.org/minizinc/photo_hkj.mzn
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* Comet: http://hakank.org/comet/photo_problem.co
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* SICStus: http://hakank.org/sicstus/photo_problem.pl
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This model was created by Hakan Kjellerstrand (hakank@gmail.com)
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Also see my other Google CP Solver models:
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http://www.hakank.org/google_or_tools/
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"""
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from __future__ import print_function
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import sys
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from ortools.constraint_solver import pywrapcp
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def main(show_all_max=0):
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# Create the solver.
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solver = pywrapcp.Solver("Photo problem")
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#
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# data
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#
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persons = ["Betty", "Chris", "Donald", "Fred", "Gary", "Mary", "Paul"]
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n = len(persons)
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preferences = [
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# 0 1 2 3 4 5 6
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# B C D F G M P
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[0, 0, 0, 0, 1, 1, 0], # Betty 0
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[1, 0, 0, 0, 1, 0, 0], # Chris 1
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[0, 0, 0, 0, 0, 0, 0], # Donald 2
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[0, 0, 1, 0, 0, 1, 0], # Fred 3
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[0, 0, 0, 0, 0, 0, 0], # Gary 4
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[0, 0, 0, 0, 0, 0, 0], # Mary 5
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[0, 0, 1, 1, 0, 0, 0] # Paul 6
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]
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print("""Preferences:
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1. Betty wants to stand next to Gary and Mary.
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2. Chris wants to stand next to Betty and Gary.
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3. Fred wants to stand next to Mary and Donald.
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4. Paul wants to stand next to Fred and Donald.
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""")
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#
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# declare variables
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#
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positions = [solver.IntVar(0, n - 1, "positions[%i]" % i) for i in range(n)]
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# successful preferences
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z = solver.IntVar(0, n * n, "z")
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#
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# constraints
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#
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solver.Add(solver.AllDifferent(positions))
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# calculate all the successful preferences
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b = [
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solver.IsEqualCstVar(abs(positions[i] - positions[j]), 1)
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for i in range(n)
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for j in range(n)
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if preferences[i][j] == 1
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]
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solver.Add(z == solver.Sum(b))
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#
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# Symmetry breaking (from the Oz page):
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# Fred is somewhere left of Betty
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solver.Add(positions[3] < positions[0])
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# objective
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objective = solver.Maximize(z, 1)
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if show_all_max != 0:
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print("Showing all maximum solutions (z == 6).\n")
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solver.Add(z == 6)
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#
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# search and result
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#
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db = solver.Phase(positions, solver.CHOOSE_FIRST_UNBOUND,
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solver.ASSIGN_MAX_VALUE)
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if show_all_max == 0:
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solver.NewSearch(db, [objective])
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else:
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solver.NewSearch(db)
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num_solutions = 0
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while solver.NextSolution():
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print("z:", z.Value())
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p = [positions[i].Value() for i in range(n)]
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print(" ".join(
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[persons[j] for i in range(n) for j in range(n) if p[j] == i]))
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print("Successful preferences:")
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for i in range(n):
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for j in range(n):
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if preferences[i][j] == 1 and abs(p[i] - p[j]) == 1:
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print("\t", persons[i], persons[j])
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print()
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num_solutions += 1
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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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show_all_max = 0 # show all maximal solutions
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if __name__ == "__main__":
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if len(sys.argv) > 1:
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show_all_max = 1
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main(show_all_max)
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