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send_most_money

examples/notebook/contrib/send_most_money.ipynb

2016-063.9 KB
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Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

send_most_money

<table align="left"> <td> <a href="https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/send_most_money.ipynb">Run in Google Colab</a> </td> <td> <a href="https://github.com/google/or-tools/blob/main/examples/contrib/send_most_money.py">View source on GitHub</a> </td> </table>

First, you must install ortools package in this colab.

python
%pip install ortools

SEND+MOST=MONEY in Google CP Solver.

Alphametic problem were we maximize MONEY.

Problem from the lecture notes: http://www.ict.kth.se/courses/ID2204/notes/L01.pdf

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/

python
from ortools.constraint_solver import pywrapcp


def main(MONEY=0):

  # Create the solver.
  solver = pywrapcp.Solver('Send most money')

  # data

  # declare variables
  s = solver.IntVar(0, 9, 's')
  e = solver.IntVar(0, 9, 'e')
  n = solver.IntVar(0, 9, 'n')
  d = solver.IntVar(0, 9, 'd')
  m = solver.IntVar(0, 9, 'm')
  o = solver.IntVar(0, 9, 'o')
  t = solver.IntVar(0, 9, 't')
  y = solver.IntVar(0, 9, 'y')
  money = solver.IntVar(0, 100000, 'money')

  x = [s, e, n, d, m, o, t, y]

  #
  # constraints
  #
  if MONEY > 0:
    solver.Add(money == MONEY)

  solver.Add(solver.AllDifferent(x))
  solver.Add(money == m * 10000 + o * 1000 + n * 100 + e * 10 + y)
  solver.Add(money > 0)
  solver.Add(1000 * s + 100 * e + 10 * n + d + 1000 * m + 100 * o + 10 * s +
             t == money)
  solver.Add(s > 0)
  solver.Add(m > 0)

  #
  # solution and search
  #
  solution = solver.Assignment()
  solution.Add(x)
  solution.Add(money)

  collector = solver.AllSolutionCollector(solution)
  objective = solver.Maximize(money, 100)
  cargs = [collector]
  if MONEY == 0:
    objective = solver.Maximize(money, 1)
    cargs.extend([objective])

  solver.Solve(
      solver.Phase(x, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MAX_VALUE),
      cargs)

  num_solutions = collector.SolutionCount()
  money_val = 0
  for s in range(num_solutions):
    print('x:', [collector.Value(s, x[i]) for i in range(len(x))])
    money_val = collector.Value(s, money)
    print('money:', money_val)
    print()

  print('num_solutions:', num_solutions)
  print('failures:', solver.Failures())
  print('branches:', solver.Branches())
  print('WallTime:', solver.WallTime())

  if MONEY == 0:
    return money_val


# First get the maximised MONEY, and then show all solutions for
# this value
print('Minimize money...')
money = main(0)
print('\nCheck all solutions for money=%i' % money)
main(money)