WhoKilledAgatha.java

// Copyright 2011 Hakan Kjellerstrand hakank@gmail.com
// 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.
package com.google.ortools.contrib;

import com.google.ortools.Loader;
import com.google.ortools.constraintsolver.DecisionBuilder;
import com.google.ortools.constraintsolver.IntVar;
import com.google.ortools.constraintsolver.Solver;
import java.io.*;
import java.text.*;
import java.util.*;

public class WhoKilledAgatha {
  /**
   * Implements the Who killed Agatha problem. See
   * http://www.hakank.org/google_or_tools/who_killed_agatha.py
   */
  private static void solve() {
    Solver solver = new Solver("WhoKilledAgatha");

    //
    // data
    //
    final int n = 3;
    final int agatha = 0;
    final int butler = 1;
    final int charles = 2;

    String[] names = {"Agatha", "Butler", "Charles"};

    //
    // variables
    //
    IntVar the_killer = solver.makeIntVar(0, 2, "the_killer");
    IntVar the_victim = solver.makeIntVar(0, 2, "the_victim");

    IntVar[] all = new IntVar[2 * n * n]; // for branching

    IntVar[][] hates = new IntVar[n][n];
    IntVar[] hates_flat = new IntVar[n * n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        hates[i][j] = solver.makeIntVar(0, 1, "hates[" + i + "," + j + "]");
        hates_flat[i * n + j] = hates[i][j];
        all[i * n + j] = hates[i][j];
      }
    }

    IntVar[][] richer = new IntVar[n][n];
    IntVar[] richer_flat = new IntVar[n * n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        richer[i][j] = solver.makeIntVar(0, 1, "richer[" + i + "," + j + "]");
        richer_flat[i * n + j] = richer[i][j];
        all[(n * n) + (i * n + j)] = richer[i][j];
      }
    }

    //
    // constraints
    //

    // Agatha, the butler, and Charles live in Dreadsbury Mansion, and
    // are the only ones to live there.

    // A killer always hates, and is no richer than his victim.
    //     hates[the_killer, the_victim] == 1
    //     hates_flat[the_killer * n + the_victim] == 1
    solver.addConstraint(solver.makeEquality(
        solver
            .makeElement(
                hates_flat, solver.makeSum(solver.makeProd(the_killer, n).var(), the_victim).var())
            .var(),
        1));

    //    richer[the_killer, the_victim] == 0
    solver.addConstraint(solver.makeEquality(
        solver
            .makeElement(
                richer_flat, solver.makeSum(solver.makeProd(the_killer, n).var(), the_victim).var())
            .var(),
        0));

    // define the concept of richer:
    //     no one is richer than him-/herself...
    for (int i = 0; i < n; i++) {
      solver.addConstraint(solver.makeEquality(richer[i][i], 0));
    }

    // (contd...) if i is richer than j then j is not richer than i
    //   if (i != j) =>
    //       ((richer[i,j] = 1) <=> (richer[j,i] = 0))
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if (i != j) {
          IntVar bi = solver.makeIsEqualCstVar(richer[i][j], 1);
          IntVar bj = solver.makeIsEqualCstVar(richer[j][i], 0);
          solver.addConstraint(solver.makeEquality(bi, bj));
        }
      }
    }

    // Charles hates no one that Agatha hates.
    //    forall i in 0..2:
    //       (hates[agatha, i] = 1) => (hates[charles, i] = 0)
    for (int i = 0; i < n; i++) {
      IntVar b1a = solver.makeIsEqualCstVar(hates[agatha][i], 1);
      IntVar b1b = solver.makeIsEqualCstVar(hates[charles][i], 0);
      solver.addConstraint(solver.makeLessOrEqual(solver.makeDifference(b1a, b1b).var(), 0));
    }

    // Agatha hates everybody except the butler.
    solver.addConstraint(solver.makeEquality(hates[agatha][charles], 1));
    solver.addConstraint(solver.makeEquality(hates[agatha][agatha], 1));
    solver.addConstraint(solver.makeEquality(hates[agatha][butler], 0));

    // The butler hates everyone not richer than Aunt Agatha.
    //    forall i in 0..2:
    //       (richer[i, agatha] = 0) => (hates[butler, i] = 1)
    for (int i = 0; i < n; i++) {
      IntVar b2a = solver.makeIsEqualCstVar(richer[i][agatha], 0);
      IntVar b2b = solver.makeIsEqualCstVar(hates[butler][i], 1);
      solver.addConstraint(solver.makeLessOrEqual(solver.makeDifference(b2a, b2b).var(), 0));
    }

    // The butler hates everyone whom Agatha hates.
    //     forall i : 0..2:
    //         (hates[agatha, i] = 1) => (hates[butler, i] = 1)
    for (int i = 0; i < n; i++) {
      IntVar b3a = solver.makeIsEqualCstVar(hates[agatha][i], 1);
      IntVar b3b = solver.makeIsEqualCstVar(hates[butler][i], 1);
      solver.addConstraint(solver.makeLessOrEqual(solver.makeDifference(b3a, b3b).var(), 0));
    }

    // Noone hates everyone.
    //     forall i in 0..2:
    //         (sum j in 0..2: hates[i,j]) <= 2
    for (int i = 0; i < n; i++) {
      IntVar[] tmp = new IntVar[n];
      for (int j = 0; j < n; j++) {
        tmp[j] = hates[i][j];
      }
      solver.addConstraint(solver.makeLessOrEqual(solver.makeSum(tmp).var(), 2));
    }

    // Who killed Agatha?
    solver.addConstraint(solver.makeEquality(the_victim, agatha));

    //
    // search
    //
    DecisionBuilder db =
        solver.makePhase(all, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE);

    solver.newSearch(db);

    //
    // output
    //
    while (solver.nextSolution()) {
      System.out.println("the_killer: " + names[(int) the_killer.value()]);
    }
    solver.endSearch();

    // Statistics
    System.out.println();
    System.out.println("Solutions: " + solver.solutions());
    System.out.println("Failures: " + solver.failures());
    System.out.println("Branches: " + solver.branches());
    System.out.println("Wall time: " + solver.wallTime() + "ms");
  }

  public static void main(String[] args) throws Exception {
    Loader.loadNativeLibraries();
    WhoKilledAgatha.solve();
  }
}