solver.cpp

/**********************************************************************
 *
 * A cube 'state' is a vector<int> with 40 entries, the first 20
 * are a permutation of {0,...,19} and describe which cubie is at
 * a certain position (regarding the input ordering). The first
 * twelve are for edges, the last eight for corners.
 *
 * The last 20 entries are for the orientations, each describing
 * how often the cubie at a certain position has been turned
 * counterclockwise away from the correct orientation. Again the
 * first twelve are edges, the last eight are corners. The values
 * are 0 or 1 for edges and 0, 1 or 2 for corners.
 *
 **********************************************************************/

#include <iostream>
#include <string>
#include <vector>
#include <map>
#include <queue>
#include <algorithm>
using namespace std;

//----------------------------------------------------------------------

typedef vector<int> vi;

//----------------------------------------------------------------------

int applicableMoves[] = { 0, 262143, 259263, 74943, 74898 };

// TODO: Encode as strings, e.g. for U use "ABCDABCD"

int affectedCubies[][8] = {
  {  0,  1,  2,  3,  0,  1,  2,  3 },   // U
  {  4,  7,  6,  5,  4,  5,  6,  7 },   // D
  {  0,  9,  4,  8,  0,  3,  5,  4 },   // F
  {  2, 10,  6, 11,  2,  1,  7,  6 },   // B
  {  3, 11,  7,  9,  3,  2,  6,  5 },   // L
  {  1,  8,  5, 10,  1,  0,  4,  7 },   // R
};

vi applyMove ( int move, vi state ) {
  int turns = move % 3 + 1;
  int face = move / 3;
  while( turns-- ){
    vi oldState = state;
    for( int i=0; i<8; i++ ){
      int isCorner = i > 3;
      int target = affectedCubies[face][i] + isCorner*12;
      int killer = affectedCubies[face][(i&3)==3 ? i-3 : i+1] + isCorner*12;;
      int orientationDelta = (i<4) ? (face>1 && face<4) : (face<2) ? 0 : 2 - (i&1);
      state[target] = oldState[killer];
      //state[target+20] = (oldState[killer+20] + orientationDelta) % (2 + isCorner);
      state[target+20] = oldState[killer+20] + orientationDelta;
      if( !turns )
    state[target+20] %= 2 + isCorner;
    }
  }
  return state;
}

int inverse ( int move ) {
  return move + 2 - 2 * (move % 3);
}

//----------------------------------------------------------------------

int phase;

//----------------------------------------------------------------------

vi id ( vi state ) {

  //--- Phase 1: Edge orientations.
  if( phase < 2 )
    return vi( state.begin() + 20, state.begin() + 32 );

  //-- Phase 2: Corner orientations, E slice edges.
  if( phase < 3 ){
    vi result( state.begin() + 31, state.begin() + 40 );
    for( int e=0; e<12; e++ )
      result[0] |= (state[e] / 8) << e;
    return result;
  }

  //--- Phase 3: Edge slices M and S, corner tetrads, overall parity.
  if( phase < 4 ){
    vi result( 3 );
    for( int e=0; e<12; e++ )
      result[0] |= ((state[e] > 7) ? 2 : (state[e] & 1)) << (2*e);
    for( int c=0; c<8; c++ )
      result[1] |= ((state[c+12]-12) & 5) << (3*c);
    for( int i=12; i<20; i++ )
      for( int j=i+1; j<20; j++ )
    result[2] ^= state[i] > state[j];
    return result;
  }

  //--- Phase 4: The rest.
  return state;
}

//----------------------------------------------------------------------

int ddd ( int argc, char** argv ) {

  //--- Define the goal.
  string goal[] = { "UF", "UR", "UB", "UL", "DF", "DR", "DB", "DL", "FR", "FL", "BR", "BL",
            "UFR", "URB", "UBL", "ULF", "DRF", "DFL", "DLB", "DBR" };

  //--- Prepare current (start) and goal state.
  vi currentState( 40 ), goalState( 40 );
  for( int i=0; i<20; i++ ){

    //--- Goal state.
    goalState[i] = i;

    //--- Current (start) state.
    string cubie = argv[i+1];
    while( (currentState[i] = find( goal, goal+20, cubie ) - goal) == 20){
      cubie = cubie.substr( 1 ) + cubie[0];
      currentState[i+20]++;
    }
  }

  //--- Dance the funky Thistlethwaite...
  while( ++phase < 5 ){

    //--- Compute ids for current and goal state, skip phase if equal.
    vi currentId = id( currentState ), goalId = id( goalState );
    if( currentId == goalId )
      continue;

    //--- Initialize the BFS queue.
    queue<vi> q;
    q.push( currentState );
    q.push( goalState );

    //--- Initialize the BFS tables.
    map<vi,vi> predecessor;
    map<vi,int> direction, lastMove;
    direction[ currentId ] = 1;
    direction[ goalId ] = 2;

    //--- Dance the funky bidirectional BFS...
    while( 1 ){

      //--- Get state from queue, compute its ID and get its direction.
      vi oldState = q.front();
      q.pop();
      vi oldId = id( oldState );
      int& oldDir = direction[oldId];

      //--- Apply all applicable moves to it and handle the new state.
      for( int move=0; move<18; move++ ){
    if( applicableMoves[phase] & (1 << move) ){

      //--- Apply the move.
      vi newState = applyMove( move, oldState );
      vi newId = id( newState );
      int& newDir = direction[newId];

      //--- Have we seen this state (id) from the other direction already?
      //--- I.e. have we found a connection?
      if( newDir  &&  newDir != oldDir ){

        //--- Make oldId represent the forwards and newId the backwards search state.
        if( oldDir > 1 ){
          swap( newId, oldId );
          move = inverse( move );
        }

        //--- Reconstruct the connecting algorithm.
        vi algorithm( 1, move );
        while( oldId != currentId ){
          algorithm.insert( algorithm.begin(), lastMove[ oldId ] );
          oldId = predecessor[ oldId ];
        }
        while( newId != goalId ){
          algorithm.push_back( inverse( lastMove[ newId ] ));
          newId = predecessor[ newId ];
        }

        //--- Print and apply the algorithm.
        for( int i=0; i<(int)algorithm.size(); i++ ){
          cout << "UDFBLR"[algorithm[i]/3] << algorithm[i]%3+1;
          currentState = applyMove( algorithm[i], currentState );
        }

        //--- Jump to the next phase.
        goto nextPhasePlease;
      }

      //--- If we've never seen this state (id) before, visit it.
      if( ! newDir ){
        q.push( newState );
        newDir = oldDir;
        lastMove[ newId ] = move;
        predecessor[ newId ] = oldId;
      }
    }
      }
    }
  nextPhasePlease:
    ;
  }
}