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+/*
+ * Copyright (c) 2001 Mikhail Kourinny (mkourinny@yahoo.com)
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include "adviseFull.h"
+#include <assert.h>
+#include <stdio.h>
+#include <math.h>
+
+using std::list;
+using std::map;
+using std::set;
+using namespace AdviseFull;
+
+AdviseFull::EquationSet::EquationSet() :
+ _maxPointSet(0)
+{}
+
+AdviseFull::EquationSet::EquationSet(
+ AdviseFast::FactSet const &facts) :
+ _maxPointSet(0)
+{
+ AdviseFast::FactSet::const_iterator i;
+ for(i=facts.begin(); i!=facts.end(); ++i, ++_maxPointSet){
+ Equation e;
+ e.pointSets.insert(_maxPointSet);
+ e.mines = i->second.mines;
+ _equations.push_back(e);
+
+ _pointSets[_maxPointSet] = i->second.pointSet;
+ }
+}
+
+void AdviseFull::EquationSet::normalize()
+{
+ short i=0;
+ set<short> empty;
+ for(i=0; i<_maxPointSet; ++i){
+ if(!_pointSets.count(i)) continue;
+ if(_pointSets[i].empty()){
+ this->substitute(i, empty);
+ continue;
+ }
+ for(short j=i+1;j<_maxPointSet; ++j){
+ if(!_pointSets.count(j)) continue;
+ if(_pointSets[j].empty()){
+ this->substitute(j, empty);
+ continue;
+ }
+
+ CoordSet intersect;
+ set_intersection(
+ _pointSets[i].begin(),
+ _pointSets[i].end(),
+ _pointSets[j].begin(),
+ _pointSets[j].end(),
+ inserter(intersect, intersect.begin()));
+ if(intersect.empty()) continue;
+
+ CoordSet _i, _j;
+ set_difference(
+ _pointSets[i].begin(),
+ _pointSets[i].end(),
+ _pointSets[j].begin(),
+ _pointSets[j].end(),
+ inserter(_i, _i.begin()));
+ set_difference(
+ _pointSets[j].begin(),
+ _pointSets[j].end(),
+ _pointSets[i].begin(),
+ _pointSets[i].end(),
+ inserter(_j, _j.begin()));
+
+ set<short> _ip, _jp;
+ _ip.insert(_maxPointSet);
+ _jp.insert(_maxPointSet);
+ _pointSets[_maxPointSet++] = intersect;
+ _ip.insert(_maxPointSet);
+ _pointSets[_maxPointSet++] = _i;
+ _jp.insert(_maxPointSet);
+ _pointSets[_maxPointSet++] = _j;
+
+ this->substitute(i, _ip);
+ this->substitute(j, _jp);
+ break;
+ }
+ }
+}
+
+void AdviseFull::EquationSet::separate(
+ list<EquationSet> *result) const
+{
+ result->clear(); // :)
+
+ list<Equation> equations = _equations;
+
+ while(!equations.empty()){
+ // Add a new equation set to *results
+ result->push_back(EquationSet());
+ EquationSet &workingSet = result->back();
+ workingSet._maxPointSet = _maxPointSet;
+
+ // Start iteration process
+ // recentlyDeceased is a set of pointSets added on the
+ // last iteration
+ workingSet._equations.push_back(equations.front());
+ set<short> recentlyDeceased = equations.front().pointSets;
+ equations.pop_front();
+
+ // The iteration process
+ while(!recentlyDeceased.empty()){
+
+ // Temporary set<short>
+ set<short> rd;
+
+ list<Equation>::iterator i = equations.begin();
+ while(i != equations.end()){
+ set<short> intersect;
+ set_intersection(
+ i->pointSets.begin(),
+ i->pointSets.end(),
+ recentlyDeceased.begin(),
+ recentlyDeceased.end(),
+ inserter(intersect, intersect.begin()));
+ if(intersect.empty()){
+ ++i;
+ } else {
+ set_difference(
+ i->pointSets.begin(),
+ i->pointSets.end(),
+ intersect.begin(),
+ intersect.end(),
+ inserter(rd, rd.begin()));
+ workingSet._equations.push_back(*i);
+ i = equations.erase(i);
+ }
+ }
+
+ // Now switch recentlyDeceased
+ set<short>::iterator j;
+ for( j = recentlyDeceased.begin();
+ j != recentlyDeceased.end();
+ ++j)
+ {
+ workingSet._pointSets[*j] =
+ (const_cast<
+ map<short, CoordSet> &>(
+ _pointSets))[*j];
+ }
+
+ recentlyDeceased = rd;
+ }
+ }
+}
+
+map<short, CoordSet> const &AdviseFull::EquationSet::solve(
+ list<Solution> *results) const
+{
+
+#ifdef DEBUG
+ printf("Entering EquationSet::solve\n");
+ prettyprint();
+#endif
+
+ EquationSet eqs = *this;
+
+ // Get the most evident solutions
+ Solution only;
+ list<Equation> &EQS = eqs._equations;
+
+ bool success;
+ do {
+
+ success = false;
+ list<Equation>::iterator i = EQS.begin();
+
+ while(i!=EQS.end()){
+#if defined(DEBUG) && DEBUG >= 2
+ printf("Taking look at the equation...\n");
+#endif
+ // Substitute known values
+ { set<short>::iterator j;
+ set<short> known;
+ for( j = i->pointSets.begin();
+ j != i->pointSets.end();
+ ++j)
+ {
+ if(only.count(*j)){
+ i->mines -= only[*j];
+ known.insert(*j);
+ }
+ }
+
+ // STL bug ??
+ for( j = known.begin();
+ j != known.end();
+ ++j)
+ i->pointSets.erase(*j);
+ }
+ // From now on the equation has no known values
+#if defined(DEBUG) && DEBUG >= 2
+ printf("Substituted known values.\n");
+#endif
+ if(i->mines < 0)
+ // Discrepancy
+ return _pointSets;
+
+
+ if(i->pointSets.empty()){
+#if defined(DEBUG) && DEBUG >= 2
+ printf("Empty equation.\n");
+#endif
+ if(i->mines){
+ // No points, non-zero mine count
+ // No solution
+ return _pointSets;
+ } else {
+ i = EQS.erase(i);
+ continue;
+ }
+ }
+
+ if(i->mines == 0){
+ set<short>::iterator j;
+ for(
+ j=i->pointSets.begin();
+ j!=i->pointSets.end();
+ ++j)
+ only[*j] = 0;
+
+ EQS.erase(i);
+ success = true;
+ break;
+ }
+
+ if(i->pointSets.size() == 1){
+ short j = *i->pointSets.begin();
+
+ if((int)eqs._pointSets[j].size() < i->mines)
+ // Discrepancy !!
+ return _pointSets;
+
+ only[j] = i->mines;
+
+ EQS.erase(i);
+ success = true;
+ break;
+ }
+
+ ++i;
+ }
+
+ } while(success);
+
+ // If no equations left we have a unique solution
+ if(EQS.empty()){
+#ifdef DEBUG
+ printf("Got a single solution!\n");
+#endif
+ results->push_back(only);
+ return _pointSets;
+ }
+
+ // Otherwise the first equation is not empty.
+ // Find the range for first element
+ short var = *EQS.begin()->pointSets.begin();
+ std::pair<short, short> range;
+ range.first = 0;
+ range.second = eqs._pointSets[var].size();
+
+ // A list of equations containing var
+ list<list<Equation>::iterator> containers;
+ list<Equation>::iterator i;
+ for( i = EQS.begin();
+ i != EQS.end();
+ ++i)
+ {
+ if(i->pointSets.count(var)){
+ i->pointSets.erase(var);
+ containers.push_back(i);
+
+ if(i->mines < range.second)
+ range.second = i->mines;
+
+ // The total size of other point sets
+ // in the equation
+ short totalsize = 0;
+ set<short>::iterator j;
+ for( j = i->pointSets.begin();
+ j != i->pointSets.end();
+ ++j)
+ totalsize += eqs._pointSets[*j].size();
+
+ if(range.first < i->mines - totalsize)
+ range.first = i->mines - totalsize;
+ }
+ }
+ // Found the range
+
+ // Now set properly equation set for first recursion
+ list<list<Equation>::iterator>::iterator super_iter; // ;)
+ short varvalue = range.first;
+ for( super_iter = containers.begin();
+ super_iter != containers.end();
+ ++super_iter)
+ (*super_iter)->mines -= varvalue;
+
+ // Recursive calls here
+ while(varvalue <= range.second){
+ only[var] = varvalue;
+ list<Solution> tempResults;
+ eqs.solve(&tempResults);
+
+ // Mix solutions with only and put them
+ // in *results
+ list<Solution>::iterator j;
+ for( j=tempResults.begin();
+ j!=tempResults.end();
+ ++j)
+ {
+ j->insert(only.begin(), only.end());
+ results->push_back(*j);
+ }
+
+ // Prepare next recursive call
+ ++varvalue;
+ for( super_iter = containers.begin();
+ super_iter != containers.end();
+ ++super_iter)
+ --(*super_iter)->mines;
+ }
+
+ return _pointSets;
+}
+
+void AdviseFull::EquationSet::prettyprint() const
+{
+
+#if defined(DEBUG)
+ printf("Point Sets:\n");
+ map<short, CoordSet>::const_iterator i;
+ for(i=_pointSets.begin(); i!=_pointSets.end(); ++i){
+ printf("%d:", i->first);
+ CoordSet::const_iterator j;
+ for(j=i->second.begin(); j!=i->second.end(); ++j)
+ printf("\t(%d,%d)\n", j->second, j->first);
+ }
+#endif
+
+ printf("Equations:\n");
+ list<Equation>::const_iterator l;
+ for(l=_equations.begin(); l!=_equations.end(); ++l){
+ set<short>::const_iterator j;
+ for(j=l->pointSets.begin(); j!=l->pointSets.end(); ++j)
+ printf("%d ", *j);
+ printf("= %d\n", l->mines);
+ }
+}
+
+void AdviseFull::EquationSet::substitute(
+ short out,
+ set<short> const &in)
+{
+ list<Equation>::iterator i;
+ for( i = _equations.begin();
+ i != _equations.end();
+ ++i)
+ {
+ if(i->pointSets.count(out)){
+ i->pointSets.erase(out);
+ i->pointSets.insert(in.begin(), in.end());
+ }
+ }
+
+ _pointSets.erase(out);
+}
+
+bool AdviseFull::surePoints(
+ map<short, CoordSet> const &m,
+ list<EquationSet::Solution> const &l,
+ CoordSet *surePoints)
+{
+ // A set of candidates to be surePoints
+ list<short> sp;
+ {
+ map<short, CoordSet>::const_iterator i;
+ for(i=m.begin(); i!=m.end(); ++i) sp.push_back(i->first);
+ }
+
+ // Scan solution list
+ list<EquationSet::Solution>::const_iterator i;
+ for(i=l.begin(); i!=l.end(); ++i){
+ list<short>::iterator j = sp.begin();
+ while(j != sp.end()){
+ // Non-empty possibility
+ if((const_cast<EquationSet::Solution &>(*i))[*j]){
+ j = sp.erase(j);
+ if(sp.empty()) // No candidates left
+ return false;
+ } else // Stay alive for now
+ ++j;
+ }
+ }
+
+ // There are SOME sure points;
+ // Fill *surePoints
+ list<short>::iterator isp;
+ map<short, CoordSet> &mm = const_cast<map<short, CoordSet> &>(m);
+ for(isp = sp.begin(); isp != sp.end(); ++isp)
+ surePoints->insert(mm[*isp].begin(), mm[*isp].end());
+
+ return true;
+}
+
+float AdviseFull::variantNumberFraction(
+ map<short, CoordSet> const &m,
+ EquationSet::Solution const &dividend,
+ EquationSet::Solution const &divisor,
+ float fraction)
+{
+ short count_difference = 0;
+ float quotient = 1;
+
+ EquationSet::Solution::const_iterator i;
+ for(i=divisor.begin(); i!=divisor.end(); ++i){
+ int j = i->first;
+ assert(m.count(j));
+ int size = (const_cast<map<short, CoordSet> &>(m))[j].size();
+ int dvd = (const_cast<EquationSet::Solution &>(dividend))[j];
+ int dvr = (const_cast<EquationSet::Solution &>(divisor))[j];
+
+ count_difference += dvd - dvr;
+
+ if(dvd < dvr){
+ dvr = size - dvr;
+ dvd = size - dvd;
+ }
+ while(dvr < dvd) {
+ float num = size-dvr++;
+ quotient *= num/dvr;
+ }
+ }
+
+ // Sorry, expensive call, but I'm lazy :((
+ if(count_difference){
+ assert(fraction != 0.);
+#if defined(DEBUG)
+ float correction = pow( fraction/(1-fraction), count_difference );
+ cout << "Got into correction, " <<
+ count_difference << ' ' << correction << endl;
+#endif
+ quotient *= pow( (1-fraction)/fraction , -count_difference );
+ }
+
+#if defined(DEBUG) && DEBUG >= 2
+ printf("variantNumberFraction: %.02f.\n", quotient);
+#endif
+
+ return quotient;
+}
+
+void AdviseFull::getProbabilities(
+ map<short, CoordSet> const &m,
+ list<EquationSet::Solution> const &l,
+ ProbabilityMap *probabilities,
+ float fraction)
+{
+ assert(!l.empty());
+ EquationSet::Solution const &front = l.front();
+
+ float probabilitiesSum = 0;
+ map<short, float> probs;
+ { map<short, CoordSet>::const_iterator i;
+ for(i=m.begin(); i!=m.end(); ++i)
+ probs[i->first] = 0;
+ }
+
+ list<EquationSet::Solution>::const_iterator i;
+ for(i=l.begin(); i!=l.end(); ++i){
+ float frac = variantNumberFraction(m, *i, front, fraction);
+ EquationSet::Solution::const_iterator j;
+ for(j=i->begin(); j!=i->end(); ++j)
+ probs[j->first] += j->second*frac;
+ probabilitiesSum += frac;
+ }
+
+ probabilities->clear();
+
+ map<short, float>::iterator j;
+ for(j=probs.begin(); j!= probs.end(); ++j){
+ CoordSet const &ps = const_cast<map<short, CoordSet> &>(m)[j->first];
+ j->second /= ps.size() * probabilitiesSum;
+ CoordSet::const_iterator k;
+ for(k=ps.begin(); k!=ps.end(); ++k)
+ probabilities->insert(
+ std::pair<float, Coord>(j->second, *k));
+ }
+
+ // That's it :)
+}
+
+void AdviseFull::adviseFull(
+ AdviseFast::FactSet *facts,
+ CoordSet *surePoints,
+ ProbabilityMap *probabilities)
+{
+ EquationSet eqs(*facts);
+
+#if defined(DEBUG) && DEBUG >= 2
+ eqs.prettyprint();
+#endif
+
+ eqs.normalize();
+#if defined(DEBUG) && DEBUG >= 2
+ eqs.prettyprint();
+#endif
+
+ list<EquationSet> eqss;
+ eqs.separate(&eqss);
+#ifdef DEBUG
+ {list<EquationSet>::iterator i;
+ for(i=eqss.begin(); i!=eqss.end(); ++i)
+ i->prettyprint();
+ }
+#endif
+
+
+ // OK, uneffective, but simple :(
+ surePoints->clear();
+ probabilities->clear();
+
+ // Get a fraction;
+ float fraction;
+ { BaseField const *f = facts->getField();
+ fraction = ((float)f->nbMines()) / (f->width() * f->height());
+ }
+
+ /* From now on the first equation set on the list includes
+ * the equation corresponding to "total" fact. This is the
+ * first equation on the set.
+ *
+ * Give it a special treatment ;) */
+ if(!eqss.empty()) do {
+ EquationSet prime = eqss.front();
+ EquationSet::Equation total = prime._equations.front();
+ prime._equations.pop_front();
+
+ list<EquationSet> prime_sep;
+ prime.separate(&prime_sep);
+
+ // Find a pool
+ list<EquationSet::Equation>::iterator i = prime._equations.begin();
+ while(!prime._equations.empty()){
+ set<short>::iterator j;
+ for( j = i->pointSets.begin();
+ j != i->pointSets.end();
+ ++j)
+ prime._pointSets.erase(*j);
+ i = prime._equations.erase(i);
+ }
+
+ assert(prime._pointSets.size() <= 1);
+ if(prime._pointSets.size() == 0) break;
+
+ short pool = prime._pointSets.begin()->first;
+ CoordSet const &p = prime._pointSets[pool];
+#ifdef DEBUG
+ cout << "Prime equation set:" << endl <<
+ " separated into " << prime_sep.size() << endl <<
+ " pool size is " << p.size() << endl;
+#endif
+ // Euristic
+ // if( prime_sep.size () > 6 && p.size() >= prime_sep.size() * 10){
+ if(p.size() < (prime_sep.size()+1) * 10)
+ // No special treatment!!
+ break;
+
+
+ // Actually, just substitute prime (!!!)
+ eqss.pop_front();
+ eqss.insert(eqss.begin(),
+ prime_sep.begin(),
+ prime_sep.end());
+
+ prime._equations.clear();
+ EquationSet::Equation o;
+ o.pointSets.insert(pool);
+ // #### is the convertion right ? (NH)
+ o.mines = (ushort)(fraction * p.size());
+ // A precaution
+ if(o.mines == 0) o.mines = 1; // ;)
+
+ prime._equations.push_front(o);
+ eqss.push_front(prime);
+
+
+#ifdef DEBUG
+ cout << "Specially treated:" << endl;
+ {
+ list<EquationSet>::iterator i;
+ for(i=eqss.begin(); i!=eqss.end(); ++i)
+ i->prettyprint();
+ }
+#endif
+ } while (false);
+
+ list<EquationSet>::const_iterator i;
+ for(i=eqss.begin(); i!=eqss.end(); ++i){
+ CoordSet sp; ProbabilityMap pb;
+
+ list<EquationSet::Solution> solutions;
+ map<short, CoordSet> const &m = i->solve(&solutions);
+#ifdef DEBUG
+ printf("Got solutions.\n");
+#if defined(DEBUG) && DEBUG >= 2
+ { list<EquationSet::Solution>::iterator i;
+ for( i = solutions.begin();
+ i != solutions.end();
+ ++i)
+ {
+ EquationSet::Solution::iterator j;
+ for(j=i->begin(); j!=i->end(); ++j)
+ printf("%d:\t%d\n",
+ j->first, j->second);
+ printf("\n");
+ }
+ }
+#endif
+#endif
+
+ //bool sure =
+ AdviseFull::surePoints(m, solutions, &sp);
+ surePoints->insert(sp.begin(), sp.end());
+
+ getProbabilities(m, solutions, &pb, fraction);
+ probabilities->insert(pb.begin(), pb.end());
+ }
+
+ // That's it
+ return;
+}
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