すべての組み合わせを生成したい場合、制約プログラミングは優れたアプローチです。試してみるために、Gecode (バージョン 3.2.2) を使用してモデルを作成し、問題を解決しました。上記の 2 つの例は非常に簡単に解決できますが、他の例は難しい場合があります。いずれにせよ、生成してテストするよりも優れているはずです。
/*
* Main authors:
* Mikael Zayenz Lagerkvist <lagerkvist@gecode.org>
*
* Copyright:
* Mikael Zayenz Lagerkvist, 2009
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
* WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
*/
#include <gecode/driver.hh>
#include <gecode/int.hh>
#include <gecode/minimodel.hh>
using namespace Gecode;
namespace {
/// List of specifications
extern const int* specs[];
/// Number of specifications
extern const unsigned int n_specs;
}
/**
* \brief Selecting pairs
*
* Given a set of lists of pairs of values, select a pair from each
* list so that no value is selected more than once.
*
*/
class SelectPairs : public Script {
protected:
/// Specification
const int* spec;
/// The values from all selected pairs
IntVarArray s;
public:
/// The actual problem
SelectPairs(const SizeOptions& opt)
: spec(specs[opt.size()]),
s(*this,spec[0] * 2,Int::Limits::min, Int::Limits::max) {
int pos = 1; // Position read from spec
// For all lists
for (int i = 0; i < spec[0]; ++i) {
int npairs = spec[pos++];
// Construct TupleSet for pairs from list i
TupleSet ts;
for (int p = 0; p < npairs; ++p) {
IntArgs tuple(2);
tuple[0] = spec[pos++];
tuple[1] = spec[pos++];
ts.add(tuple);
}
ts.finalize();
// <s[2i],s[2i+1]> must be from list i
IntVarArgs pair(2);
pair[0] = s[2*i]; pair[1] = s[2*i + 1];
extensional(*this, pair, ts);
}
// All values must be pairwise distinct
distinct(*this, s, opt.icl());
// Select values for the variables
branch(*this, s, INT_VAR_SIZE_MIN, INT_VAL_MIN);
}
/// Constructor for cloning \a s
SelectPairs(bool share, SelectPairs& sp)
: Script(share,sp), spec(sp.spec) {
s.update(*this, share, sp.s);
}
/// Perform copying during cloning
virtual Space*
copy(bool share) {
return new SelectPairs(share,*this);
}
/// Print solution
virtual void
print(std::ostream& os) const {
os << "\t";
for (int i = 0; i < spec[0]; ++i) {
os << "(" << s[2*i] << "," << s[2*i+1] << ") ";
if ((i+1) % 10 == 0)
os << std::endl << "\t";
}
if (spec[0] % 10)
os << std::endl;
}
};
/** \brief Main-function
* \relates SelectPairs
*/
int
main(int argc, char* argv[]) {
SizeOptions opt("SelectPairs");
opt.iterations(500);
opt.size(0);
opt.parse(argc,argv);
if (opt.size() >= n_specs) {
std::cerr << "Error: size must be between 0 and "
<< n_specs-1 << std::endl;
return 1;
}
Script::run<SelectPairs,DFS,SizeOptions>(opt);
return 0;
}
namespace {
const int s0[] = {
// Number of lists
3,
// Lists (number of pairs, pair0, pair1, ...)
5, 1,2, 1,3, 1,4, 2,3, 2,4,
3, 1,4, 1,5, 2,5,
5, 1,6, 1,7, 2,5, 2,6, 3,6
};
const int s1[] = {
// Number of lists
3,
// Lists (number of pairs, pair0, pair1, ...)
5, 1,2, 2,3, 3,4, 4,5, 6,7,
5, 1,2, 2,3, 3,4, 4,5, 6,7,
5, 1,2, 2,3, 3,4, 4,5, 6,7
};
const int *specs[] = {s0, s1};
const unsigned n_specs = sizeof(specs)/sizeof(int*);
}