Jip J. Dekker
1d9faf38de
git-subtree-dir: software/gecode git-subtree-split: 313e87646da4fc2752a70e83df16d993121a8e40
424 lines
13 KiB
C++
424 lines
13 KiB
C++
/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
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/*
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* Main authors:
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* Christian Schulte <schulte@gecode.org>
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* Mikael Lagerkvist <lagerkvist@gecode.org>
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*
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* Copyright:
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* Christian Schulte, 2001
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* Mikael Lagerkvist, 2005
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*
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* This file is part of Gecode, the generic constraint
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* development environment:
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* http://www.gecode.org
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*
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* Permission is hereby granted, free of charge, to any person obtaining
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* a copy of this software and associated documentation files (the
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* "Software"), to deal in the Software without restriction, including
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* without limitation the rights to use, copy, modify, merge, publish,
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* distribute, sublicense, and/or sell copies of the Software, and to
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* permit persons to whom the Software is furnished to do so, subject to
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* the following conditions:
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*
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* The above copyright notice and this permission notice shall be
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* included in all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
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* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
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* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
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* WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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*
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*/
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#include <gecode/driver.hh>
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#include <gecode/int.hh>
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#include <gecode/minimodel.hh>
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using namespace Gecode;
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/** The maximum number of knights placeable
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*
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* \relates QueensArmies
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*/
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const int kval[] = {
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0, 0, 0, 0, 5,
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9, 15, 21, 29, 37,
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47, 57, 69, 81, 94,
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109
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};
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namespace {
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/** \brief Set of valid positions for the bishops
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* \relates CrowdedChess
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*/
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TupleSet bishops;
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/** \brief Class for solving the bishops sub-problem
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* \relates CrowdedChess
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*/
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class Bishops : public Space {
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public:
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const int n;
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BoolVarArray k;
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bool valid_pos(int i, int j) {
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return (i >= 0 && i < n) && (j >= 0 && j < n);
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}
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Bishops(int size)
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: n(size), k(*this,n*n,0,1) {
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Matrix<BoolVarArray> kb(k, n, n);
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for (int l = n; l--; ) {
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const int il = (n-1) - l;
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BoolVarArgs d1(l+1), d2(l+1), d3(l+1), d4(l+1);
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for (int i = 0; i <= l; ++i) {
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d1[i] = kb(i+il, i);
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d2[i] = kb(i, i+il);
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d3[i] = kb((n-1)-i-il, i);
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d4[i] = kb((n-1)-i, i+il);
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}
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linear(*this, d1, IRT_LQ, 1);
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linear(*this, d2, IRT_LQ, 1);
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linear(*this, d3, IRT_LQ, 1);
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linear(*this, d4, IRT_LQ, 1);
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}
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linear(*this, k, IRT_EQ, 2*n - 2);
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// Forced bishop placement from crowded chess model
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rel(*this, kb(n-1, 0), IRT_EQ, 1);
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rel(*this, kb(n-1, n-1), IRT_EQ, 1);
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branch(*this, k, BOOL_VAR_DEGREE_MAX(), BOOL_VAL_MAX());
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}
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Bishops(Bishops& s) : Space(s), n(s.n) {
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k.update(*this, s.k);
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}
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virtual Space* copy(void) {
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return new Bishops(*this);
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}
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};
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/** \brief Initialize bishops
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* \relates CrowdedChess
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*/
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void init_bishops(int size) {
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Bishops* prob = new Bishops(size);
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DFS<Bishops> e(prob);
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IntArgs ia(size*size);
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delete prob;
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bishops.init(size*size);
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while (Bishops* s = e.next()) {
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for (int i = size*size; i--; )
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ia[i] = s->k[i].val();
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bishops.add(ia);
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delete s;
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}
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bishops.finalize();
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}
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}
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/**
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\brief %Example: Crowded chessboard
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You are given a chessboard together with 8 queens, 8 rooks, 14
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bishops, and 21 knights. The puzzle is to arrange the 51 pieces on
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the chessboard so that no queen shall attack another queen, no rook
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attack another rook, no bishop attack another bishop, and no knight
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attack another knight. No notice is to be taken of the intervention
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of pieces of another type from that under consideration - that is,
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two queens will be considered to attack one another although there
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may be, say, a rook, a bishop, and a knight between them. It is not
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difficult to dispose of each type of piece separately; the
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difficulty comes in when you have to find room for all the
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arrangements on the board simultaneously.
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<em>Dudeney, H.E., (1917), Amusements in Mathematics,
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Thomas Nelson and Sons.</em>
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This puzzle can be generalized to chess-boards of size \f$n\f$, where the
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number of pieces to place are:
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- \f$ n \f$ queens
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- \f$ n \f$ rooks
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- \f$ 2n-1 \f$ bishops
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- \f$ k \f$ knights
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where k is a number to maximize.
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The maximum k for some different values of \f$ n \f$ are presented
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below (from Jesper Hansen and Joachim Schimpf, <a
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href="http://www.icparc.ic.ac.uk/eclipse/examples/crowded_chess.ecl.txt">
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ECLiPSe solution</a>
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<TABLE>
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<TR> <TD> n </TD> <TD> k </TD> </TR>
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<TR> <TD> 8 </TD> <TD> 21 </TD> </TR>
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<TR> <TD> 9 </TD> <TD> 29 </TD> </TR>
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<TR> <TD> 10 </TD> <TD> 37 </TD> </TR>
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<TR> <TD> 11 </TD> <TD> 47 </TD> </TR>
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<TR> <TD> 12 </TD> <TD> 57 </TD> </TR>
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<TR> <TD> 13 </TD> <TD> 69 </TD> </TR>
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<TR> <TD> 14 </TD> <TD> 81 </TD> </TR>
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<TR> <TD> 15 </TD> <TD> 94 </TD> </TR>
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<TR> <TD> 16 </TD> <TD> 109 </TD> </TR>
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</TABLE>
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A solution for n = 8 is:
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<TABLE>
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<TR><TD>Q</TD><TD>B</TD><TD>K</TD><TD>.</TD>
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<TD>K</TD><TD>B</TD><TD>K</TD><TD>R</TD></TR>
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<TR><TD>.</TD><TD>K</TD><TD>.</TD><TD>K</TD>
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<TD>Q</TD><TD>K</TD><TD>R</TD><TD>B</TD></TR>
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<TR><TD>B</TD><TD>.</TD><TD>K</TD><TD>R</TD>
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<TD>K</TD><TD>.</TD><TD>K</TD><TD>Q</TD></TR>
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<TR><TD>B</TD><TD>K</TD><TD>R</TD><TD>K</TD>
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<TD>.</TD><TD>Q</TD><TD>.</TD><TD>B</TD></TR>
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<TR><TD>B</TD><TD>R</TD><TD>Q</TD><TD>.</TD>
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<TD>K</TD><TD>.</TD><TD>K</TD><TD>B</TD></TR>
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<TR><TD>R</TD><TD>K</TD><TD>.</TD><TD>K</TD>
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<TD>.</TD><TD>K</TD><TD>Q</TD><TD>B</TD></TR>
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<TR><TD>B</TD><TD>Q</TD><TD>K</TD><TD>.</TD>
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<TD>K</TD><TD>R</TD><TD>K</TD><TD>.</TD></TR>
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<TR><TD>B</TD><TD>K</TD><TD>B</TD><TD>Q</TD>
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<TD>R</TD><TD>K</TD><TD>B</TD><TD>B</TD></TR>
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</TABLE>
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\ingroup Example
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*/
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class CrowdedChess : public Script {
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protected:
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const int n; ///< Board-size
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IntVarArray s; ///< The board
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IntVarArray queens, ///< Row of queen in column x
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rooks; ///< Row of rook in column x
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BoolVarArray knights; ///< True iff the corresponding place has a knight
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/** Symbolic names of pieces. The order determines which piece will
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* be placed first.
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*/
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enum
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{Q, ///< Queen
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R, ///< Rook
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B, ///< Bishop
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K, ///< Knight
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E, ///< Empty square
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PMAX ///< Number of pieces (including empty squares)
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} piece;
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// Is (i,j) a valid position on the board?
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bool valid_pos(int i, int j) {
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return (i >= 0 && i < n) &&
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(j >= 0 && j < n);
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}
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/// Post knight-constraints
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void knight_constraints(void) {
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static const int kmoves[4][2] = {
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{-1,2}, {1,2}, {2,-1}, {2,1}
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};
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Matrix<BoolVarArray> kb(knights, n, n);
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for (int x = n; x--; )
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for (int y = n; y--; )
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for (int i = 4; i--; )
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if (valid_pos(x+kmoves[i][0], y+kmoves[i][1]))
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rel(*this,
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kb(x, y),
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BOT_AND,
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kb(x+kmoves[i][0], y+kmoves[i][1]),
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0);
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}
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public:
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enum {
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PROP_TUPLE_SET, ///< Propagate bishops placement extensionally
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PROP_DECOMPOSE ///< Propagate bishops placement with decomposition
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};
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/// The model of the problem
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CrowdedChess(const SizeOptions& opt)
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: Script(opt),
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n(opt.size()),
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s(*this, n*n, 0, PMAX-1),
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queens(*this, n, 0, n-1),
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rooks(*this, n, 0, n-1),
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knights(*this, n*n, 0, 1) {
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const int nkval = sizeof(kval)/sizeof(int);
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const int nn = n*n, q = n, r = n, b = (2*n)-2,
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k = n <= nkval ? kval[n-1] : kval[nkval-1];
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const int e = nn - (q + r + b + k);
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assert(nn == (e + q + r + b + k));
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Matrix<IntVarArray> m(s, n);
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// ***********************
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// Basic model
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// ***********************
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count(*this, s, E, IRT_EQ, e, opt.ipl());
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count(*this, s, Q, IRT_EQ, q, opt.ipl());
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count(*this, s, R, IRT_EQ, r, opt.ipl());
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count(*this, s, B, IRT_EQ, b, opt.ipl());
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count(*this, s, K, IRT_EQ, k, opt.ipl());
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// Collect rows and columns for handling rooks and queens
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for (int i = 0; i < n; ++i) {
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IntVarArgs aa = m.row(i), bb = m.col(i);
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count(*this, aa, Q, IRT_EQ, 1, opt.ipl());
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count(*this, bb, Q, IRT_EQ, 1, opt.ipl());
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count(*this, aa, R, IRT_EQ, 1, opt.ipl());
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count(*this, bb, R, IRT_EQ, 1, opt.ipl());
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// Connect (queens|rooks)[i] to the row it is in
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element(*this, aa, queens[i], Q, IPL_DOM);
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element(*this, aa, rooks[i], R, IPL_DOM);
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}
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// N-queens constraints
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distinct(*this, queens, IPL_DOM);
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distinct(*this, IntArgs::create(n,0,1), queens, IPL_DOM);
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distinct(*this, IntArgs::create(n,0,-1), queens, IPL_DOM);
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// N-rooks constraints
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distinct(*this, rooks, IPL_DOM);
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// Collect diagonals for handling queens and bishops
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for (int l = n; l--; ) {
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const int il = (n-1) - l;
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IntVarArgs d1(l+1), d2(l+1), d3(l+1), d4(l+1);
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for (int i = 0; i <= l; ++i) {
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d1[i] = m(i+il, i);
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d2[i] = m(i, i+il);
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d3[i] = m((n-1)-i-il, i);
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d4[i] = m((n-1)-i, i+il);
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}
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count(*this, d1, Q, IRT_LQ, 1, opt.ipl());
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count(*this, d2, Q, IRT_LQ, 1, opt.ipl());
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count(*this, d3, Q, IRT_LQ, 1, opt.ipl());
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count(*this, d4, Q, IRT_LQ, 1, opt.ipl());
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if (opt.propagation() == PROP_DECOMPOSE) {
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count(*this, d1, B, IRT_LQ, 1, opt.ipl());
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count(*this, d2, B, IRT_LQ, 1, opt.ipl());
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count(*this, d3, B, IRT_LQ, 1, opt.ipl());
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count(*this, d4, B, IRT_LQ, 1, opt.ipl());
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}
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}
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if (opt.propagation() == PROP_TUPLE_SET) {
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IntVarArgs b(s.size());
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for (int i = s.size(); i--; )
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b[i] = channel(*this, expr(*this, (s[i] == B)));
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extensional(*this, b, bishops, opt.ipl());
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}
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// Handle knigths
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// Connect knigths to board
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for(int i = n*n; i--; )
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knights[i] = expr(*this, (s[i] == K));
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knight_constraints();
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// ***********************
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// Redundant constraints
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// ***********************
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// Queens and rooks not in the same place
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// Faster than going through the channelled board-connection
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for (int i = n; i--; )
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rel(*this, queens[i], IRT_NQ, rooks[i]);
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// Place bishops in two corners (from Schimpf and Hansens solution)
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// Avoids some symmetries of the problem
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rel(*this, m(n-1, 0), IRT_EQ, B);
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rel(*this, m(n-1, n-1), IRT_EQ, B);
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// ***********************
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// Branching
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// ***********************
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// Place each piece in turn
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branch(*this, s, INT_VAR_MIN_MIN(), INT_VAL_MIN());
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}
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/// Constructor for cloning e
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CrowdedChess(CrowdedChess& e)
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: Script(e), n(e.n) {
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s.update(*this, e.s);
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queens.update(*this, e.queens);
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rooks.update(*this, e.rooks);
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knights.update(*this, e.knights);
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}
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/// Copy during cloning
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virtual Space*
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copy(void) {
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return new CrowdedChess(*this);
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}
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/// Print solution
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virtual void
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print(std::ostream& os) const {
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Matrix<IntVarArray> m(s, n);
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char names[PMAX];
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names[E] = '.'; names[Q] = 'Q'; names[R] = 'R';
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names[B] = 'B'; names[K] = 'K';
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const char* sep = n < 8 ? "\t\t" : "\t";
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for (int r = 0; r < n; ++r){
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// Print main board
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os << '\t';
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for (int c = 0; c < n; ++c) {
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if (m(r, c).assigned()) {
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os << names[m(r, c).val()];
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} else {
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os << " ";
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}
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}
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// Print each piece on its own
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for (int p = 0; p < PMAX; ++p) {
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if (p == E) continue;
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os << sep;
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for (int c = 0; c < n; ++c) {
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if (m(r, c).assigned()) {
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if (m(r, c).val() == p)
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os << names[p];
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else
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os << names[E];
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} else {
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os << " ";
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}
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}
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}
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os << std::endl;
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}
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os << std::endl;
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}
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};
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/** \brief Main function
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* \relates CrowdedChess
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*/
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int
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main(int argc, char* argv[]) {
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SizeOptions opt("CrowdedChess");
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opt.propagation(CrowdedChess::PROP_TUPLE_SET);
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opt.propagation(CrowdedChess::PROP_TUPLE_SET,
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"extensional",
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"Use extensional propagation for bishops-placement");
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opt.propagation(CrowdedChess::PROP_DECOMPOSE,
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"decompose",
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"Use decomposed propagation for bishops-placement");
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opt.ipl(IPL_DOM);
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opt.size(8);
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opt.parse(argc,argv);
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if (opt.size() < 5) {
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std::cerr << "Error: size must be at least 5" << std::endl;
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return 1;
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}
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init_bishops(opt.size());
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Script::run<CrowdedChess,DFS,SizeOptions>(opt);
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return 0;
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}
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// STATISTICS: example-any
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