examples/notebook/contrib/set_covering_skiena.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Set covering in Google CP Solver.
Example from Steven Skiena, The Stony Brook Algorithm Repository http://www.cs.sunysb.edu/~algorith/files/set-cover.shtml ''' Input Description: A set of subsets S_1, ..., S_m of the universal set U = {1,...,n}.
Problem: What is the smallest subset of subsets T subset S such that \cup_{t_i in T} t_i = U? ''' Data is from the pictures INPUT/OUTPUT.
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/
from ortools.constraint_solver import pywrapcp
def main():
# Create the solver.
solver = pywrapcp.Solver('Set covering Skiena')
#
# data
#
num_sets = 7
num_elements = 12
belongs = [
# 1 2 3 4 5 6 7 8 9 0 1 2 elements
[1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], # Set 1
[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], # 2
[0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], # 3
[0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0], # 4
[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], # 5
[1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0], # 6
[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1] # 7
]
#
# variables
#
x = [solver.IntVar(0, 1, 'x[%i]' % i) for i in range(num_sets)]
# number of choosen sets
z = solver.IntVar(0, num_sets * 2, 'z')
# total number of elements in the choosen sets
tot_elements = solver.IntVar(0, num_sets * num_elements)
#
# constraints
#
solver.Add(z == solver.Sum(x))
# all sets must be used
for j in range(num_elements):
s = solver.Sum([belongs[i][j] * x[i] for i in range(num_sets)])
solver.Add(s >= 1)
# number of used elements
solver.Add(tot_elements == solver.Sum([
x[i] * belongs[i][j] for i in range(num_sets) for j in range(num_elements)
]))
# objective
objective = solver.Minimize(z, 1)
#
# search and result
#
db = solver.Phase(x, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)
solver.NewSearch(db, [objective])
num_solutions = 0
while solver.NextSolution():
num_solutions += 1
print('z:', z.Value())
print('tot_elements:', tot_elements.Value())
print('x:', [x[i].Value() for i in range(num_sets)])
solver.EndSearch()
print()
print('num_solutions:', num_solutions)
print('failures:', solver.Failures())
print('branches:', solver.Branches())
print('WallTime:', solver.WallTime(), 'ms')
main()