351 lines
9.3 KiB
C++
351 lines
9.3 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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* Patrick Pekczynski <pekczynski@ps.uni-sb.de>
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*
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* Contributing authors:
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* Christian Schulte <schulte@gecode.org>
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*
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* Copyright:
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* Patrick Pekczynski, 2004
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* Christian Schulte, 2007
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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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#include <algorithm>
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#include <iomanip>
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using namespace Gecode;
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/// Entry in round robin schedule
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class Play {
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public:
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int h; ///< home team
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int a; ///< away team
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int g; ///< game number
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/// Default constructor
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Play(void) : h(0), a(0), g(0) {}
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};
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/// Round robin schedule
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class RRS {
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protected:
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/// Number of teams
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const int teams;
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/// Play information
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Play* plays;
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/// Return number of weeks
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int weeks(void) const {
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return teams-1;
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}
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/// Return number of periods
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int periods(void) const {
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return teams/2;
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}
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/// Game number for game between home team \a h and away team \a a
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int gn(int h, int a) const {
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return teams*(h-1) + a;
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}
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/// Play for period \a p and week \a w
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Play& play(int p, int w) {
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return plays[p*weeks() + w];
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}
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public:
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/**
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* \brief Build a feasible schedule
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*
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* The games of the first week are fixed as:
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* \f$ \langle 1,2 \rangle \cup
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* \{\langle p + 2, t - p + 1\rangle | p \geq 1\}\f$. \n
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* The remaining games are computed by transforming a game
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* \f$ \langle h, a, g \rangle \f$ from the previous week
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* in a new game \f$ \langle h', a'\rangle \f$, where: \n
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* \f$ h' = \left\{
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* \begin{tabular}{l c l}
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* 1 & & if $h = 1$ \\
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* 2 & & if $h = t$ \\
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* $h + 1$ & & otherwise
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* \end{tabular}\right.
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* \f$ and
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* \f$ a' = \left\{
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* \begin{tabular}{l c l}
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* 2 & & if $h = t$ \\
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* a + 1 & & otherwise
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* \end{tabular}\right.
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* \f$
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*
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*
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*/
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RRS(int t) : teams(t), plays(new Play[periods()*weeks()]) {
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// Determine the first game (week 0 period 0)
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play(0,0).h = 1;
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play(0,0).a = 2;
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play(0,0).g = 2;
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// Determine the other games of the first week
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for (int p=1; p<periods(); p++) {
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play(p,0).h = (p + 1) + 1;
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play(p,0).a = teams - (p + 1 - 2);
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play(p,0).g = gn(play(p,0).h,play(p,0).a);
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}
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// Compute the games for the subsequent weeks
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for (int w=1; w<weeks(); w++) {
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for (int p=0; p<periods(); p++) {
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if (play(p,w-1).h == teams)
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play(p,w).h = 2;
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else if (play(p,w-1).h == 1)
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play(p,w).h = 1;
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else
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play(p,w).h = play(p,w-1).h + 1;
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if (play(p,w-1).a == teams)
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play(p,w).a = 2;
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else
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play(p,w).a = play(p,w-1).a + 1;
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// maintain symmetry for (h,a): h < a
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if (play(p,w).h > play(p,w).a)
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std::swap(play(p,w).h,play(p,w).a);
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play(p,w).g = gn(play(p,w).h,play(p,w).a);
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}
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}
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}
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/// Home, away, and game information
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void hag(int w, IntArgs& h, IntArgs& a, IntArgs& g) {
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for (int p=0; p<periods(); p++) {
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h[p] = play(p,w).h;
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a[p] = play(p,w).a;
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g[p] = play(p,w).g;
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}
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}
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/// Delete schedule
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~RRS(void) {
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delete [] plays;
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}
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};
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/**
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* \brief %Example: %Sports league scheduling
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*
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* -# There are \f$ t \f$ teams (\f$ t \f$ even).
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* -# The season lasts \f$ t - 1 \f$ weeks.
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* -# Each game between two different teams occurs exactly once.
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* -# Every team plays one game in each week of the season.
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* -# There are \f$ \displaystyle\frac{t}{2} \f$ periods and each week
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* every period is scheduled for one game.
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* -# No team plays more than twice in the same period over
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* the course of the season.
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*
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* See also problem 26 at http://www.csplib.org/.
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*
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* \ingroup Example
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*/
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class SportsLeague : public Script {
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protected:
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const int teams; ///< number of teams
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IntVarArray home; ///< home teams
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IntVarArray away; ///< away teams
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IntVarArray game; ///< game numbers
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/// Return number of weeks
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int weeks(void) const {
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return teams-1;
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}
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/// Return number of periods
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int periods(void) const {
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return teams/2;
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}
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/// Home team in period \a p and week \a w
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IntVar& h(int p, int w) {
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return home[p*teams + w];
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}
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/// Home team in period \a p and week \a w
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const IntVar& h(int p, int w) const {
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return home[p*teams + w];
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}
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/// Away team in period \a p and week \a w
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IntVar& a(int p, int w) {
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return away[p*teams + w];
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}
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/// Away team in period \a p and week \a w
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const IntVar& a(int p, int w) const {
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return away[p*teams + w];
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}
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/// Return game number for game in period \a p and week \a w
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IntVar& g(int p, int w) {
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return game[p*weeks() + w];
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}
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/// Return game number for game in period \a p and week \a w
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const IntVar& g(int p, int w) const {
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return game[p*weeks() + w];
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}
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public:
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/// Setup model
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SportsLeague(const SizeOptions& opt) :
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Script(opt),
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teams(opt.size()),
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home(*this, periods() * teams, 1, weeks()),
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away(*this, periods() * teams, 2, weeks()+1),
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game(*this, weeks()*periods(), 2, teams*weeks())
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{
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// Initialize round robin schedule
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RRS r(teams);
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// Domain for gamenumber of period
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for (int w=0; w<weeks(); w++) {
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IntArgs rh(periods()), ra(periods()), rg(periods());
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IntVarArgs n(*this,periods(),0,periods()-1);
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distinct(*this, n, opt.ipl());
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r.hag(w,rh,ra,rg);
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for (int p=0; p<periods(); p++) {
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element(*this, rh, n[p], h(p,w));
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element(*this, ra, n[p], a(p,w));
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element(*this, rg, n[p], g(p,w));
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}
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}
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/// (h,a) and (a,h) are the same game, focus on home (that is, h<a)
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for (int p=0; p<periods(); p++)
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for (int w=0; w<teams; w++)
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rel(*this, h(p,w), IRT_LE, a(p,w));
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// Home teams in first week are ordered
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{
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IntVarArgs h0(periods());
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for (int p=0; p<periods(); p++)
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h0[p] = h(p,0);
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rel(*this, h0, IRT_LE);
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}
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// Fix first pair
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rel(*this, h(0,0), IRT_EQ, 1);
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rel(*this, a(0,0), IRT_EQ, 2);
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/// Column constraint: each team occurs exactly once
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for (int w=0; w<teams; w++) {
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IntVarArgs c(teams);
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for (int p=0; p<periods(); p++) {
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c[2*p] = h(p,w); c[2*p+1] = a(p,w);
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}
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distinct(*this, c, opt.ipl());
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}
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/// Row constraint: no team appears more than twice
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for (int p=0; p<periods(); p++) {
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IntVarArgs r(2*teams);
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for (int t=0; t<teams; t++) {
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r[2*t] = h(p,t);
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r[2*t+1] = a(p,t);
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}
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IntArgs values(teams);
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for (int i=1; i<=teams; i++)
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values[i-1] = i;
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count(*this, r, IntSet(2,2), values, opt.ipl());
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}
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// Redundant constraint
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for (int p=0; p<periods(); p++)
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for (int w=0; w<weeks(); w ++)
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rel(*this, teams * h(p,w) + a(p,w) - g(p,w) == teams);
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distinct(*this, game, opt.ipl());
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branch(*this, game, INT_VAR_NONE(), INT_VAL_SPLIT_MIN());
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}
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/// Constructor for cloning \a s
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SportsLeague(SportsLeague& s)
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: Script(s), teams(s.teams) {
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home.update(*this, s.home);
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away.update(*this, s.away);
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game.update(*this, s.game);
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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 SportsLeague(*this);
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}
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/// Print solution
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virtual void print(std::ostream& os) const {
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// print period index
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os << "\t ";
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for (int p=0; p<periods(); p++) {
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os << "P[";
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os.width(2);
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os << p << "] ";
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}
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os << std::endl;
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// print entries
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for (int w=0; w<weeks(); w++) {
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os << "\tW[";
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os.width(2);
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os << w+1 << "]: ";
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for (int p=0; p<periods(); p++) {
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os.width(2);
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os << h(p,w).val() << '-';
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os.width(2);
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os << a(p,w).val() << " ";
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}
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os << std::endl;
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}
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}
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};
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/** \brief Main-function
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* \relates SportsLeague
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*/
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int
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main(int argc, char* argv[]) {
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SizeOptions opt("Sports League Scheduling");
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opt.ipl(IPL_DOM);
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opt.size(18);
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opt.parse(argc,argv);
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if (opt.size() < 5) {
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std::cerr<< "No Solution for less than 5 teams!" << std::endl;
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return 1;
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}
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if (opt.size() % 2 != 0) {
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std::cerr << "Number of teams has to be even!" << std::endl;
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return 1;
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}
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Script::run<SportsLeague, DFS,SizeOptions>(opt);
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return 0;
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}
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// STATISTICS: example-any
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