117 lines
3.7 KiB
Java
Executable File
117 lines
3.7 KiB
Java
Executable File
/*
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* Copyright 2017 Darian Sastre darian.sastre@minimaxlabs.com
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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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* ************************************************************************
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*
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* Coins grid problem in Google CP Solver.
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*
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* Problem from
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* Tony Hurlimann: "A coin puzzle - SVOR-contest 2007"
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* http://www.svor.ch/competitions/competition2007/AsroContestSolution.pdf
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* "
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* In a quadratic grid (or a larger chessboard) with 31x31 cells, one should
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* place coins in such a way that the following conditions are fulfilled:
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* 1. In each row exactly 14 coins must be placed.
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* 2. In each column exactly 14 coins must be placed.
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* 3. The sum of the quadratic horizontal distance from the main diagonal
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* of all cells containing a coin must be as small as possible.
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* 4. In each cell at most one coin can be placed.
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* The description says to place 14x31 = 434 coins on the chessboard each row
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* containing 14 coins and each column also containing 14 coins.
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* "
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*
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* This is a Java MIP version of
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* http://www.hakank.org/google_or_tools/coins_grid_mip.py
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*
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* which is the MIP version of
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* http://www.hakank.org/google_or_tools/coins_grid.py
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*
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* by Hakan Kjellerstrand (hakank@gmail.com).
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*
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* Java version by Darian Sastre (darian.sastre@minimaxlabs.com)
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*/
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import com.google.ortools.linearsolver.*;
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public class CoinsGridMIP {
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static {
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System.loadLibrary("jniortools");
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}
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private static MPSolver createSolver (String solverType) {
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return new MPSolver("MIPDiet",
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MPSolver.OptimizationProblemType.valueOf(solverType));
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}
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private static void solve(String solverType) {
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MPSolver solver = createSolver(solverType);
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/** invariants */
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int n = 31;
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int c = 14;
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/** variables */
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MPVariable[][] x = new MPVariable[n][n];
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for (int i = 0; i < n; i ++) {
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x[i] = solver.makeBoolVarArray(n);
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}
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/** constraints & objective */
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MPConstraint[] constraints = new MPConstraint[2 * n];
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MPObjective obj = solver.objective();
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for (int i = 0; i < n; i ++) {
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constraints[2*i] = solver.makeConstraint(c, c);
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constraints[2*i + 1] = solver.makeConstraint(c, c);
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for (int j = 0; j < n; j ++) {
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constraints[2*i].setCoefficient(x[i][j], 1);
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constraints[2*i + 1].setCoefficient(x[j][i], 1);
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obj.setCoefficient(x[i][j], (i-j) * (j-i));
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}
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}
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solver.solve();
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for (int i = 0; i < n; i ++) {
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for (int j = 0; j < n; j ++) {
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System.out.print((int) x[i][j].solutionValue() + " ");
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}
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System.out.println();
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}
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}
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public static void main(String[] args) {
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try {
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System.out.println("---- Integer programming example with SCIP (recommended) ----");
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solve("SCIP_MIXED_INTEGER_PROGRAMMING");
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} catch (java.lang.IllegalArgumentException e) {
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System.err.println("Bad solver type: " + e);
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}
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try {
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System.out.println("---- Integer programming example with CBC ----");
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solve("CBC_MIXED_INTEGER_PROGRAMMING");
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} catch (java.lang.IllegalArgumentException e) {
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System.err.println("Bad solver type: " + e);
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}
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try {
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System.out.println("---- Integer programming example with GLPK ----");
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solve("GLPK_MIXED_INTEGER_PROGRAMMING");
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} catch (java.lang.IllegalArgumentException e) {
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System.err.println("Bad solver type: " + e);
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}
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}
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}
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