8927b03942
Some of these imports are not used. The rest of them only import string to use the string.atoi function. But string.atoi(s) on a string input is identical to just int(s). See the docs: "deprecated since 2.0".
165 lines
3.9 KiB
Python
165 lines
3.9 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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Young tableaux in Google CP Solver.
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See
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http://mathworld.wolfram.com/YoungTableau.html
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and
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http://en.wikipedia.org/wiki/Young_tableau
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'''
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The partitions of 4 are
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{4}, {3,1}, {2,2}, {2,1,1}, {1,1,1,1}
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And the corresponding standard Young tableaux are:
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1. 1 2 3 4
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2. 1 2 3 1 2 4 1 3 4
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4 3 2
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3. 1 2 1 3
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3 4 2 4
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4 1 2 1 3 1 4
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3 2 2
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4 4 3
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5. 1
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2
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3
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4
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'''
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Thanks to Laurent Perron for improving this model.
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Compare with the following models:
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* MiniZinc: http://www.hakank.org/minizinc/young_tableaux.mzn
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* Choco : http://www.hakank.org/choco/YoungTableuax.java
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* JaCoP : http://www.hakank.org/JaCoP/YoungTableuax.java
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* Comet : http://www.hakank.org/comet/young_tableaux.co
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* Gecode : http://www.hakank.org/gecode/young_tableaux.cpp
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* ECLiPSe : http://www.hakank.org/eclipse/young_tableaux.ecl
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* Tailor/Essence' : http://www.hakank.org/tailor/young_tableaux.eprime
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* SICStus: http://hakank.org/sicstus/young_tableaux.pl
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* Zinc: http://hakank.org/minizinc/young_tableaux.zinc
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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:
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http://www.hakank.org/google_or_tools/
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"""
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import sys
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from ortools.constraint_solver import pywrapcp
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def main(n=5):
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# Create the solver.
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solver = pywrapcp.Solver("Problem")
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#
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# data
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#
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print "n:", n
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#
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# declare variables
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#
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x = {}
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for i in range(n):
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for j in range(n):
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x[(i, j)] = solver.IntVar(1, n + 1, "x(%i,%i)" % (i, j))
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x_flat = [x[(i, j)] for i in range(n) for j in range(n)]
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# partition structure
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p = [solver.IntVar(0, n + 1, "p%i" % i) for i in range(n)]
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#
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# constraints
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#
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# 1..n is used exactly once
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for i in range(1, n + 1):
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solver.Add(solver.Count(x_flat, i, 1))
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solver.Add(x[(0, 0)] == 1)
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# row wise
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for i in range(n):
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for j in range(1, n):
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solver.Add(x[(i, j)] >= x[(i, j - 1)])
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# column wise
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for j in range(n):
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for i in range(1, n):
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solver.Add(x[(i, j)] >= x[(i - 1, j)])
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# calculate the structure (the partition)
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for i in range(n):
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# MiniZinc/Zinc version:
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# p[i] == sum(j in 1..n) (bool2int(x[i,j] <= n))
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b = [solver.IsLessOrEqualCstVar(x[(i, j)], n) for j in range(n)]
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solver.Add(p[i] == solver.Sum(b))
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solver.Add(solver.Sum(p) == n)
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for i in range(1, n):
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solver.Add(p[i - 1] >= p[i])
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#
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# solution and search
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#
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solution = solver.Assignment()
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solution.Add(x_flat)
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solution.Add(p)
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# db: DecisionBuilder
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db = solver.Phase(x_flat + p,
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solver.CHOOSE_FIRST_UNBOUND,
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solver.ASSIGN_MIN_VALUE)
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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 "p:", [p[i].Value() for i in range(n)]
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print "x:"
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for i in range(n):
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for j in range(n):
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val = x_flat[i * n + j].Value()
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if val <= n:
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print val,
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if p[i].Value() > 0:
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print
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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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n = 5
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if __name__ == "__main__":
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if len(sys.argv) > 1:
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n = int(sys.argv[1])
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main(n)
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