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