/*********************                                                        */
/*! \file tableau.cpp
 ** \verbatim
 ** Original author: taking
 ** Major contributors: none
 ** Minor contributors (to current version): mdeters
 ** This file is part of the CVC4 prototype.
 ** Copyright (c) 2009, 2010, 2011  The Analysis of Computer Systems Group (ACSys)
 ** Courant Institute of Mathematical Sciences
 ** New York University
 ** See the file COPYING in the top-level source directory for licensing
 ** information.\endverbatim
 **
 ** \brief [[ Add one-line brief description here ]]
 **
 ** [[ Add lengthier description here ]]
 ** \todo document this file
 **/


#include "theory/arith/tableau.h"

using namespace std;
using namespace CVC4;
using namespace CVC4::theory;
using namespace CVC4::theory::arith;


/*
void Tableau::addRow(ArithVar basicVar,
                     const std::vector<Rational>& coeffs,
                     const std::vector<ArithVar>& variables){

  Assert(coeffs.size() == variables.size());

  //The new basic variable cannot already be a basic variable
  Assert(!d_basicVariables.isMember(basicVar));
  d_basicVariables.add(basicVar);
  ReducedRowVector* row_current = new ReducedRowVector(basicVar,variables, coeffs,d_rowCount, d_columnMatrix);
  d_rowsTable[basicVar] = row_current;

  //A variable in the row may have been made non-basic already.
  //If this is the case we fake pivoting this variable
  vector<ArithVar>::const_iterator varsIter = variables.begin();
  vector<ArithVar>::const_iterator varsEnd = variables.end();

  for( ; varsIter != varsEnd; ++varsIter){
    ArithVar var = *varsIter;

    if(d_basicVariables.isMember(var)){
      EntryID varID = find(basicVar, var);
      TableauEntry& entry = d_entryManager.get(varID);
      const Rational& coeff = entry.getCoefficient();

      loadRowIntoMergeBuffer(var);
      rowPlusRowTimesConstant(coeff, basicVar, var);
      emptyRowFromMergeBuffer(var);
    }
  }
}
*/

/*
ReducedRowVector* Tableau::removeRow(ArithVar basic){
  Assert(isBasic(basic));

  ReducedRowVector* row = d_rowsTable[basic];

  d_basicVariables.remove(basic);
  d_rowsTable[basic] = NULL;

  return row;
}
*/

void Tableau::pivot(ArithVar oldBasic, ArithVar newBasic){
  Assert(isBasic(oldBasic));
  Assert(!isBasic(newBasic));
  Assert(mergeBufferIsEmpty());

  Debug("tableau") << "Tableau::pivot(" <<  oldBasic <<", " << newBasic <<")"  << endl;

  rowPivot(oldBasic, newBasic);
  loadRowIntoMergeBuffer(newBasic);

  ColIterator colIter = colIterator(newBasic);
  while(!colIter.atEnd()){
    EntryID id = colIter.getID();
    TableauEntry& entry = d_entryManager.get(id);

    ++colIter; //needs to be incremented before the variable is removed
    if(entry.getRowVar() == newBasic){ continue; }

    ArithVar basicTo = entry.getRowVar();
    Rational coeff = entry.getCoefficient();

    rowPlusRowTimesConstant(basicTo, coeff, newBasic);
  }
  emptyRowFromMergeBuffer(newBasic);

  //Clear the column for used for this variable

  Assert(mergeBufferIsEmpty());
  Assert(!isBasic(oldBasic));
  Assert(isBasic(newBasic));
  Assert(getColLength(newBasic) == 1);
}

Tableau::~Tableau(){}

void Tableau::setColumnUnused(ArithVar v){
  ColIterator colIter = colIterator(v);
  while(!colIter.atEnd()){
    ++colIter;
  }
}
void Tableau::printTableau() const {
  Debug("tableau") << "Tableau::d_activeRows"  << endl;

  ArithVarSet::const_iterator basicIter = beginBasic(), endIter = endBasic();
  for(; basicIter != endIter; ++basicIter){
    ArithVar basic = *basicIter;
    printRow(basic);
  }
}

void Tableau::printRow(ArithVar basic) const {
  Debug("tableau") << "{" << basic << ":";
  for(RowIterator entryIter = rowIterator(basic); !entryIter.atEnd(); ++entryIter){
    const TableauEntry& entry = *entryIter;
    printEntry(entry);
    Debug("tableau") << ",";
  }
  Debug("tableau") << "}" << endl;
}

void Tableau::printEntry(const TableauEntry& entry) const {
  Debug("tableau") << entry.getColVar() << "*" << entry.getCoefficient();
}

uint32_t Tableau::numNonZeroEntriesByRow() const {
  uint32_t rowSum = 0;
  ArithVarSet::const_iterator i = d_basicVariables.begin(), end = d_basicVariables.end();
  for(; i != end; ++i){
    ArithVar basic = *i;
    rowSum += getRowLength(basic);
  }
  return rowSum;
}

uint32_t Tableau::numNonZeroEntriesByCol() const {
  uint32_t colSum = 0;
  VectorSizeTable::const_iterator i = d_colLengths.begin();
  VectorSizeTable::const_iterator end = d_colLengths.end();
  for(; i != end; ++i){
    colSum += *i;
  }
  return colSum;
}


EntryID Tableau::findOnRow(ArithVar row, ArithVar col){
  for(RowIterator i = rowIterator(row); !i.atEnd(); ++i){
    EntryID id = i.getID();
    const TableauEntry& entry = *i;
    ArithVar colVar = entry.getColVar();

    if(colVar == col){
      return id;
    }
  }
  return ENTRYID_SENTINEL;
}

EntryID Tableau::findOnCol(ArithVar row, ArithVar col){
  for(ColIterator i = colIterator(col); !i.atEnd(); ++i){
    EntryID id = i.getID();
    const TableauEntry& entry = *i;
    ArithVar rowVar = entry.getRowVar();

    if(rowVar == row){
      return id;
    }
  }
  return ENTRYID_SENTINEL;
}

const TableauEntry& Tableau::findEntry(ArithVar row, ArithVar col){
  bool colIsShorter = getColLength(col) < getRowLength(row);
  EntryID id = colIsShorter ? findOnCol(row,col) : findOnRow(row,col);
  if(id == ENTRYID_SENTINEL){
    return d_failedFind;
  }else{
    return d_entryManager.get(id);
  }
}

void Tableau::removeRow(ArithVar basic){
  RowIterator i = rowIterator(basic);
  while(!i.atEnd()){
    EntryID id = i.getID();
    ++i;
    removeEntry(id);
  }
  d_basicVariables.remove(basic);
}

void Tableau::loadRowIntoMergeBuffer(ArithVar basic){
  Assert(mergeBufferIsEmpty());
  for(RowIterator i = rowIterator(basic); !i.atEnd(); ++i){
    EntryID id = i.getID();
    const TableauEntry& entry = *i;
    ArithVar colVar = entry.getColVar();
    d_mergeBuffer[colVar] = make_pair(id, false);
  }
}

void Tableau::emptyRowFromMergeBuffer(ArithVar basic){
  Assert(isBasic(basic));
  for(RowIterator i = rowIterator(basic); !i.atEnd(); ++i){
    const TableauEntry& entry = *i;
    ArithVar colVar = entry.getColVar();
    Assert(d_mergeBuffer[colVar].first == i.getID());
    d_mergeBuffer[colVar] = make_pair(ENTRYID_SENTINEL, false);
  }

  Assert(mergeBufferIsEmpty());
}


/**
 * Changes basic to newbasic (a variable on the row).
 */
void Tableau::rowPivot(ArithVar basicOld, ArithVar basicNew){
  Assert(mergeBufferIsEmpty());
  Assert(isBasic(basicOld));
  Assert(!isBasic(basicNew));

  EntryID newBasicID = findOnRow(basicOld, basicNew);

  Assert(newBasicID != ENTRYID_SENTINEL);

  TableauEntry& newBasicEntry = d_entryManager.get(newBasicID);
  Rational negInverseA_rs = -(newBasicEntry.getCoefficient().inverse());

  for(RowIterator i = rowIterator(basicOld); !i.atEnd(); ++i){
    EntryID id = i.getID();
    TableauEntry& entry = d_entryManager.get(id);

    entry.getCoefficient() *=  negInverseA_rs;
    entry.setRowVar(basicNew);
  }

  d_rowHeads[basicNew] = d_rowHeads[basicOld];
  d_rowHeads[basicOld] = ENTRYID_SENTINEL;

  d_rowLengths[basicNew] = d_rowLengths[basicOld];
  d_rowLengths[basicOld] = 0;

  d_basicVariables.remove(basicOld);
  d_basicVariables.add(basicNew);
}

void Tableau::addEntry(ArithVar row, ArithVar col, const Rational& coeff){
  Assert(coeff != 0);

  EntryID newId = d_entryManager.newEntry();
  TableauEntry& newEntry =  d_entryManager.get(newId);
  newEntry = TableauEntry( row, col,
                           d_rowHeads[row], d_colHeads[col],
                           ENTRYID_SENTINEL, ENTRYID_SENTINEL,
                           coeff);
  Assert(newEntry.getCoefficient() != 0);

  Debug("tableau") << "addEntry(" << row << "," << col <<"," << coeff << ")" << endl;

  ++d_entriesInUse;

  if(d_rowHeads[row] != ENTRYID_SENTINEL)
    d_entryManager.get(d_rowHeads[row]).setPrevRowID(newId);

  if(d_colHeads[col] != ENTRYID_SENTINEL)
    d_entryManager.get(d_colHeads[col]).setPrevColID(newId);

  d_rowHeads[row] = newId;
  d_colHeads[col] = newId;
  ++d_rowLengths[row];
  ++d_colLengths[col];
}

void Tableau::removeEntry(EntryID id){
  Assert(d_entriesInUse > 0);
  --d_entriesInUse;

  TableauEntry& entry = d_entryManager.get(id);

  ArithVar row = entry.getRowVar();
  ArithVar col = entry.getColVar();

  Assert(d_rowLengths[row] > 0);
  Assert(d_colLengths[col] > 0);


  --d_rowLengths[row];
  --d_colLengths[col];

  EntryID prevRow = entry.getPrevRowID();
  EntryID prevCol = entry.getPrevColID();

  EntryID nextRow = entry.getNextRowID();
  EntryID nextCol = entry.getNextColID();

  if(d_rowHeads[row] == id){
    d_rowHeads[row] = nextRow;
  }
  if(d_colHeads[col] == id){
    d_colHeads[col] = nextCol;
  }

  entry.markBlank();

  if(prevRow != ENTRYID_SENTINEL){
    d_entryManager.get(prevRow).setNextRowID(nextRow);
  }
  if(nextRow != ENTRYID_SENTINEL){
    d_entryManager.get(nextRow).setPrevRowID(prevRow);
  }

  if(prevCol != ENTRYID_SENTINEL){
    d_entryManager.get(prevCol).setNextColID(nextCol);
  }
  if(nextCol != ENTRYID_SENTINEL){
    d_entryManager.get(nextCol).setPrevColID(prevCol);
  }

  d_entryManager.freeEntry(id);
}

void Tableau::rowPlusRowTimesConstant(ArithVar basicTo, const Rational& c, ArithVar basicFrom){

  Debug("tableau") << "rowPlusRowTimesConstant("
                   << basicTo << "," << c << "," << basicFrom << ")"
                   << endl;

  Assert(debugNoZeroCoefficients(basicTo));
  Assert(debugNoZeroCoefficients(basicFrom));

  Assert(c != 0);
  Assert(isBasic(basicTo));
  Assert(isBasic(basicFrom));
  Assert( d_usedList.empty() );


  RowIterator i = rowIterator(basicTo);
  while(!i.atEnd()){
    EntryID id = i.getID();
    TableauEntry& entry = d_entryManager.get(id);
    ArithVar colVar = entry.getColVar();

    ++i;
    if(bufferPairIsNotEmpty(d_mergeBuffer[colVar])){
      d_mergeBuffer[colVar].second = true;
      d_usedList.push_back(colVar);

      EntryID inOtherRow = d_mergeBuffer[colVar].first;
      const TableauEntry& other = d_entryManager.get(inOtherRow);
      entry.getCoefficient() += c * other.getCoefficient();

      if(entry.getCoefficient().sgn() == 0){
        removeEntry(id);
      }
    }
  }

  for(RowIterator i = rowIterator(basicFrom); !i.atEnd(); ++i){
    const TableauEntry& entry = *i;
    ArithVar colVar = entry.getColVar();

    if(!(d_mergeBuffer[colVar]).second){
      Rational newCoeff =  c * entry.getCoefficient();
      addEntry(basicTo, colVar, newCoeff);
    }
  }

  clearUsedList();

  if(Debug.isOn("tableau")) { printTableau(); }
}

void Tableau::clearUsedList(){
  ArithVarArray::iterator i, end;
  for(i = d_usedList.begin(), end = d_usedList.end(); i != end; ++i){
    ArithVar pos = *i;
    d_mergeBuffer[pos].second = false;
  }
  d_usedList.clear();
}

void Tableau::addRow(ArithVar basic,
                     const std::vector<Rational>& coefficients,
                     const std::vector<ArithVar>& variables)
{
  Assert(coefficients.size() == variables.size() );
  Assert(!isBasic(basic));

  d_basicVariables.add(basic);

  if(Debug.isOn("tableau")){ printTableau(); }

  addEntry(basic, basic, Rational(-1));

  vector<Rational>::const_iterator coeffIter = coefficients.begin();
  vector<ArithVar>::const_iterator varsIter = variables.begin();
  vector<ArithVar>::const_iterator varsEnd = variables.end();

  for(; varsIter != varsEnd; ++coeffIter, ++varsIter){
    const Rational& coeff = *coeffIter;
    ArithVar var_i = *varsIter;
    addEntry(basic, var_i, coeff);
  }

  varsIter = variables.begin();
  coeffIter = coefficients.begin();
  for(; varsIter != varsEnd; ++coeffIter, ++varsIter){
    ArithVar var = *varsIter;

    if(isBasic(var)){
      Rational coeff = *coeffIter;

      loadRowIntoMergeBuffer(var);
      rowPlusRowTimesConstant(basic, coeff,  var);
      emptyRowFromMergeBuffer(var);
    }
  }

  if(Debug.isOn("tableau")) { printTableau(); }

  Assert(debugNoZeroCoefficients(basic));

  Assert(debugMatchingCountsForRow(basic));
  Assert(getColLength(basic) == 1);
}

bool Tableau::debugNoZeroCoefficients(ArithVar basic){
  for(RowIterator i=rowIterator(basic); !i.atEnd(); ++i){
    const TableauEntry& entry = *i;
    if(entry.getCoefficient() == 0){
      return false;
    }
  }
  return true;
}
bool Tableau::debugMatchingCountsForRow(ArithVar basic){
  for(RowIterator i=rowIterator(basic); !i.atEnd(); ++i){
    const TableauEntry& entry = *i;
    ArithVar colVar = entry.getColVar();
    uint32_t count = debugCountColLength(colVar);
    Debug("tableau") << "debugMatchingCountsForRow "
                     << basic << ":" << colVar << " " << count
                     <<" "<< d_colLengths[colVar] << endl;
    if( count != d_colLengths[colVar] ){
      return false;
    }
  }
  return true;
}


uint32_t Tableau::debugCountColLength(ArithVar var){
  Debug("tableau") << var << " ";
  uint32_t count = 0;
  for(ColIterator i=colIterator(var); !i.atEnd(); ++i){
    const TableauEntry& entry = *i;
    Debug("tableau") << "(" << entry.getRowVar() << ", " << i.getID() << ") ";
    ++count;
  }
  Debug("tableau") << endl;
  return count;
}

uint32_t Tableau::debugCountRowLength(ArithVar var){
  uint32_t count = 0;
  for(RowIterator i=rowIterator(var); !i.atEnd(); ++i){
    ++count;
  }
  return count;
}

/*
void ReducedRowVector::enqueueNonBasicVariablesAndCoefficients(std::vector< ArithVar >& variables,std::vector< Rational >& coefficients) const{
  for(const_iterator i=begin(), endEntries=end(); i != endEntries; ++i){
    ArithVar var = (*i).getArithVar();
    const Rational& q = (*i).getCoefficient();
    if(var != basic()){
      variables.push_back(var);
      coefficients.push_back(q);
    }
  }
  }*/

Node Tableau::rowAsEquality(ArithVar basic, const ArithVarToNodeMap& map){
  using namespace CVC4::kind;

  Assert(getRowLength(basic) >= 2);

  vector<Node> nonBasicPairs;
  for(RowIterator i = rowIterator(basic); !i.atEnd(); ++i){
    const TableauEntry& entry = *i;
    ArithVar colVar = entry.getColVar();
    if(colVar == basic) continue;
    Node var = (map.find(colVar))->second;
    Node coeff = mkRationalNode(entry.getCoefficient());

    Node mult = NodeBuilder<2>(MULT) << coeff << var;
    nonBasicPairs.push_back(mult);
  }

  Node sum = Node::null();
  if(nonBasicPairs.size() == 1 ){
    sum = nonBasicPairs.front();
  }else{
    Assert(nonBasicPairs.size() >= 2);
    NodeBuilder<> sumBuilder(PLUS);
    sumBuilder.append(nonBasicPairs);
    sum = sumBuilder;
  }
  Node basicVar = (map.find(basic))->second;
  return NodeBuilder<2>(EQUAL) << basicVar << sum;
}

double Tableau::densityMeasure() const{
  Assert(numNonZeroEntriesByRow() == numNonZeroEntries());
  Assert(numNonZeroEntriesByCol() == numNonZeroEntries());

  uint32_t n = getNumRows();
  if(n == 0){
    return 1.0;
  }else {
    uint32_t s = numNonZeroEntries();
    uint32_t m = d_colHeads.size();
    uint32_t divisor = (n *(m - n + 1));

    Assert(n >= 1);
    Assert(m >= n);
    Assert(divisor > 0);
    Assert(divisor >= s);

    return (double(s)) / divisor;
  }
}

void TableauEntryManager::freeEntry(EntryID id){
  Assert(get(id).blank());
  Assert(d_size > 0);

  d_freedEntries.push(id);
  --d_size;
}

EntryID TableauEntryManager::newEntry(){
  EntryID newId;
  if(d_freedEntries.empty()){
    newId = d_entries.size();
    d_entries.push_back(TableauEntry());
  }else{
    newId = d_freedEntries.front();
    d_freedEntries.pop();
  }
  ++d_size;
  return newId;
}