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fsss2.cpp
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fsss2.cpp
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/*
*
* Created on: May 13, 2014
* Author: Mladen Dobrichev
*/
//Fast Simple Sudoku Solver 2
#include <stdio.h>
#include <memory.h>
#include "fsss2.h"
//game mode flags
#define MODE_SOLVING 0 //unused, keep solving
#define MODE_STOP_PROCESSING 1 //solved or error
#define MODE_STOP_GUESSING 2 //necessary solutions found
#ifdef COUNT_TRIALS
extern int nTrials;
#endif
//int knownNoLockedCandidatesHits;
//int knownNoLockedCandidatesMisses;
//int knownNoHiddenHits;
//int knownNoHiddenMisses;
template <class X> fsss2<X>::fsss2(X &theCollector) : mode(0), guessDepth(0)
#ifdef USE_LOCKED_CANDIDATES
#ifndef LOCKED_CANDIDATES_ALWAYS
, lockedDone(0)
#endif
#endif
, collector(theCollector)
{}
//only first 81 bits set
constexpr t_128 constraints::mask81 = {0xFFFFFFFFFFFFFFFF, 0x0001FFFF};
//only first 81 + 27 = 108 bits set
//template <class X> const t_128 fsss2<X>::mask108 = {0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFF};
//the first 81 bits for the cells and the 27 bits from position 96+
constexpr t_128 constraints::mask108 = {0xFFFFFFFFFFFFFFFF,0x07FFFFFF0001FFFF};
//the 27 bits from position 96+
//const t_128 constraints::mask27 = {0x0,0x07FFFFFF00000000};
constexpr t_128 constraints::visibleCells[81] = { //1 for all 20 visible cells, 1 for the cell itself, 1 for the three houses
{0x80402010081C0FFF,0x0004020100000100},
{0x00804020101C0FFF,0x0004040100000201},
{0x01008040201C0FFF,0x0004080100000402},
{0x0201008040E071FF,0x0008100100000804},
{0x0402010080E071FF,0x0008200100001008},
{0x0804020100E071FF,0x0008400100002010},
{0x10080402070381FF,0x0010800100004020},
{0x20100804070381FF,0x0011000100008040},
{0x40201008070381FF,0x0012000100010080},
{0x80402010081FFE07,0x0004020200000100},
{0x00804020101FFE07,0x0004040200000201},
{0x01008040201FFE07,0x0004080200000402},
{0x0201008040E3FE38,0x0008100200000804},
{0x0402010080E3FE38,0x0008200200001008},
{0x0804020100E3FE38,0x0008400200002010},
{0x100804020703FFC0,0x0010800200004020},
{0x201008040703FFC0,0x0011000200008040},
{0x402010080703FFC0,0x0012000200010080},
{0x804020100FFC0E07,0x0004020400000100},
{0x0080402017FC0E07,0x0004040400000201},
{0x0100804027FC0E07,0x0004080400000402},
{0x0201008047FC7038,0x0008100400000804},
{0x0402010087FC7038,0x0008200400001008},
{0x0804020107FC7038,0x0008400400002010},
{0x1008040207FF81C0,0x0010800400004020},
{0x2010080407FF81C0,0x0011000400008040},
{0x4020100807FF81C0,0x0012000400010080},
{0x8040E07FF8040201,0x0020020800000100},
{0x0080E07FF8080402,0x0020040800000201},
{0x0100E07FF8100804,0x0020080800000402},
{0x0207038FF8201008,0x0040100800000804},
{0x0407038FF8402010,0x0040200800001008},
{0x0807038FF8804020,0x0040400800002010},
{0x10381C0FF9008040,0x0080800800004020},
{0x20381C0FFA010080,0x0081000800008040},
{0x40381C0FFC020100,0x0082000800010080},
{0x8040FFF038040201,0x0020021000000100},
{0x0080FFF038080402,0x0020041000000201},
{0x0100FFF038100804,0x0020081000000402},
{0x02071FF1C0201008,0x0040101000000804},
{0x04071FF1C0402010,0x0040201000001008},
{0x08071FF1C0804020,0x0040401000002010},
{0x10381FFE01008040,0x0080801000004020},
{0x20381FFE02010080,0x0081001000008040},
{0x40381FFE04020100,0x0082001000010080},
{0x807FE07038040201,0x0020022000000100},
{0x00BFE07038080402,0x0020042000000201},
{0x013FE07038100804,0x0020082000000402},
{0x023FE381C0201008,0x0040102000000804},
{0x043FE381C0402010,0x0040202000001008},
{0x083FE381C0804020,0x0040402000002010},
{0x103FFC0E01008040,0x0080802000004020},
{0x203FFC0E02010080,0x0081002000008040},
{0x403FFC0E04020100,0x0082002000010080},
{0xFFC0201008040201,0x0100024000000703},
{0xFFC0402010080402,0x0100044000000703},
{0xFFC0804020100804,0x0100084000000703},
{0x7FC1008040201008,0x020010400000381C},
{0x7FC2010080402010,0x020020400000381C},
{0x7FC4020100804020,0x020040400000381C},
{0x7FC8040201008040,0x040080400001C0E0},
{0x7FD0080402010080,0x040100400001C0E0},
{0x7FE0100804020100,0x040200400001C0E0},
{0x81C0201008040201,0x01000280000007FF},
{0x81C0402010080402,0x01000480000007FF},
{0x81C0804020100804,0x01000880000007FF},
{0x8E01008040201008,0x02001080000038FF},
{0x8E02010080402010,0x02002080000038FF},
{0x8E04020100804020,0x02004080000038FF},
{0xF008040201008040,0x040080800001C0FF},
{0xF010080402010080,0x040100800001C0FF},
{0xF020100804020100,0x040200800001C0FF},
{0x81C0201008040201,0x010003000001FF03},
{0x81C0402010080402,0x010005000001FF03},
{0x81C0804020100804,0x010009000001FF03},
{0x0E01008040201008,0x020011000001FF1C},
{0x0E02010080402010,0x020021000001FF1C},
{0x0E04020100804020,0x020041000001FF1C},
{0x7008040201008040,0x040081000001FFE0},
{0x7010080402010080,0x040101000001FFE0},
{0x7020100804020100,0x040201000001FFE0}
}; //bm128 visibleCells[81]
constexpr t_128 constraints::bitsForHouse[27] = { //1 for the 9 cells in the house
{0x00000000000001FF,0x0000000000000000},
{0x000000000003FE00,0x0000000000000000},
{0x0000000007FC0000,0x0000000000000000},
{0x0000000FF8000000,0x0000000000000000},
{0x00001FF000000000,0x0000000000000000},
{0x003FE00000000000,0x0000000000000000},
{0x7FC0000000000000,0x0000000000000000},
{0x8000000000000000,0x00000000000000FF},
{0x0000000000000000,0x000000000001FF00},
{0x8040201008040201,0x0000000000000100},
{0x0080402010080402,0x0000000000000201},
{0x0100804020100804,0x0000000000000402},
{0x0201008040201008,0x0000000000000804},
{0x0402010080402010,0x0000000000001008},
{0x0804020100804020,0x0000000000002010},
{0x1008040201008040,0x0000000000004020},
{0x2010080402010080,0x0000000000008040},
{0x4020100804020100,0x0000000000010080},
{0x00000000001C0E07,0x0000000000000000},
{0x0000000000E07038,0x0000000000000000},
{0x00000000070381C0,0x0000000000000000},
{0x0000E07038000000,0x0000000000000000},
{0x00070381C0000000,0x0000000000000000},
{0x00381C0E00000000,0x0000000000000000},
{0x81C0000000000000,0x0000000000000703},
{0x0E00000000000000,0x000000000000381C},
{0x7000000000000000,0x000000000001C0E0},
}; //bitsForHouse[27]
//const uint32 constraints::topCellsHouses = 0x00FC007F; //000111111000000000001111111
#ifdef USE_LOCKED_CANDIDATES
constexpr tripletMask constraints::tripletMasks[54] = {
{{0x0000000000000007,0x0000000000000000}, {0x00000000000001F8,0x0000000000000000}, {0x00000000001C0E00,0x0000000000000000}, },
{{0x0000000000000038,0x0000000000000000}, {0x00000000000001C7,0x0000000000000000}, {0x0000000000E07000,0x0000000000000000}, },
{{0x00000000000001C0,0x0000000000000000}, {0x000000000000003F,0x0000000000000000}, {0x0000000007038000,0x0000000000000000}, },
{{0x0000000000000E00,0x0000000000000000}, {0x000000000003F000,0x0000000000000000}, {0x00000000001C0007,0x0000000000000000}, },
{{0x0000000000007000,0x0000000000000000}, {0x0000000000038E00,0x0000000000000000}, {0x0000000000E00038,0x0000000000000000}, },
{{0x0000000000038000,0x0000000000000000}, {0x0000000000007E00,0x0000000000000000}, {0x00000000070001C0,0x0000000000000000}, },
{{0x00000000001C0000,0x0000000000000000}, {0x0000000007E00000,0x0000000000000000}, {0x0000000000000E07,0x0000000000000000}, },
{{0x0000000000E00000,0x0000000000000000}, {0x00000000071C0000,0x0000000000000000}, {0x0000000000007038,0x0000000000000000}, },
{{0x0000000007000000,0x0000000000000000}, {0x0000000000FC0000,0x0000000000000000}, {0x00000000000381C0,0x0000000000000000}, },
{{0x0000000038000000,0x0000000000000000}, {0x0000000FC0000000,0x0000000000000000}, {0x0000E07000000000,0x0000000000000000}, },
{{0x00000001C0000000,0x0000000000000000}, {0x0000000E38000000,0x0000000000000000}, {0x0007038000000000,0x0000000000000000}, },
{{0x0000000E00000000,0x0000000000000000}, {0x00000001F8000000,0x0000000000000000}, {0x00381C0000000000,0x0000000000000000}, },
{{0x0000007000000000,0x0000000000000000}, {0x00001F8000000000,0x0000000000000000}, {0x0000E00038000000,0x0000000000000000}, },
{{0x0000038000000000,0x0000000000000000}, {0x00001C7000000000,0x0000000000000000}, {0x00070001C0000000,0x0000000000000000}, },
{{0x00001C0000000000,0x0000000000000000}, {0x000003F000000000,0x0000000000000000}, {0x0038000E00000000,0x0000000000000000}, },
{{0x0000E00000000000,0x0000000000000000}, {0x003F000000000000,0x0000000000000000}, {0x0000007038000000,0x0000000000000000}, },
{{0x0007000000000000,0x0000000000000000}, {0x0038E00000000000,0x0000000000000000}, {0x00000381C0000000,0x0000000000000000}, },
{{0x0038000000000000,0x0000000000000000}, {0x0007E00000000000,0x0000000000000000}, {0x00001C0E00000000,0x0000000000000000}, },
{{0x01C0000000000000,0x0000000000000000}, {0x7E00000000000000,0x0000000000000000}, {0x8000000000000000,0x0000000000000703}, },
{{0x0E00000000000000,0x0000000000000000}, {0x71C0000000000000,0x0000000000000000}, {0x0000000000000000,0x000000000000381C}, },
{{0x7000000000000000,0x0000000000000000}, {0x0FC0000000000000,0x0000000000000000}, {0x0000000000000000,0x000000000001C0E0}, },
{{0x8000000000000000,0x0000000000000003}, {0x0000000000000000,0x00000000000000FC}, {0x01C0000000000000,0x0000000000000700}, },
{{0x0000000000000000,0x000000000000001C}, {0x8000000000000000,0x00000000000000E3}, {0x0E00000000000000,0x0000000000003800}, },
{{0x0000000000000000,0x00000000000000E0}, {0x8000000000000000,0x000000000000001F}, {0x7000000000000000,0x000000000001C000}, },
{{0x0000000000000000,0x0000000000000700}, {0x0000000000000000,0x000000000001F800}, {0x81C0000000000000,0x0000000000000003}, },
{{0x0000000000000000,0x0000000000003800}, {0x0000000000000000,0x000000000001C700}, {0x0E00000000000000,0x000000000000001C}, },
{{0x0000000000000000,0x000000000001C000}, {0x0000000000000000,0x0000000000003F00}, {0x7000000000000000,0x00000000000000E0}, },
{{0x0000000000040201,0x0000000000000000}, {0x8040201008000000,0x0000000000000100}, {0x0000000000180C06,0x0000000000000000}, },
{{0x0000201008000000,0x0000000000000000}, {0x8040000000040201,0x0000000000000100}, {0x0000C06030000000,0x0000000000000000}, },
{{0x8040000000000000,0x0000000000000100}, {0x0000201008040201,0x0000000000000000}, {0x0180000000000000,0x0000000000000603}, },
{{0x0000000000080402,0x0000000000000000}, {0x0080402010000000,0x0000000000000201}, {0x0000000000140A05,0x0000000000000000}, },
{{0x0000402010000000,0x0000000000000000}, {0x0080000000080402,0x0000000000000201}, {0x0000A05028000000,0x0000000000000000}, },
{{0x0080000000000000,0x0000000000000201}, {0x0000402010080402,0x0000000000000000}, {0x8140000000000000,0x0000000000000502}, },
{{0x0000000000100804,0x0000000000000000}, {0x0100804020000000,0x0000000000000402}, {0x00000000000C0603,0x0000000000000000}, },
{{0x0000804020000000,0x0000000000000000}, {0x0100000000100804,0x0000000000000402}, {0x0000603018000000,0x0000000000000000}, },
{{0x0100000000000000,0x0000000000000402}, {0x0000804020100804,0x0000000000000000}, {0x80C0000000000000,0x0000000000000301}, },
{{0x0000000000201008,0x0000000000000000}, {0x0201008040000000,0x0000000000000804}, {0x0000000000C06030,0x0000000000000000}, },
{{0x0001008040000000,0x0000000000000000}, {0x0200000000201008,0x0000000000000804}, {0x0006030180000000,0x0000000000000000}, },
{{0x0200000000000000,0x0000000000000804}, {0x0001008040201008,0x0000000000000000}, {0x0C00000000000000,0x0000000000003018}, },
{{0x0000000000402010,0x0000000000000000}, {0x0402010080000000,0x0000000000001008}, {0x0000000000A05028,0x0000000000000000}, },
{{0x0002010080000000,0x0000000000000000}, {0x0400000000402010,0x0000000000001008}, {0x0005028140000000,0x0000000000000000}, },
{{0x0400000000000000,0x0000000000001008}, {0x0002010080402010,0x0000000000000000}, {0x0A00000000000000,0x0000000000002814}, },
{{0x0000000000804020,0x0000000000000000}, {0x0804020100000000,0x0000000000002010}, {0x0000000000603018,0x0000000000000000}, },
{{0x0004020100000000,0x0000000000000000}, {0x0800000000804020,0x0000000000002010}, {0x00030180C0000000,0x0000000000000000}, },
{{0x0800000000000000,0x0000000000002010}, {0x0004020100804020,0x0000000000000000}, {0x0600000000000000,0x000000000000180C}, },
{{0x0000000001008040,0x0000000000000000}, {0x1008040200000000,0x0000000000004020}, {0x0000000006030180,0x0000000000000000}, },
{{0x0008040200000000,0x0000000000000000}, {0x1000000001008040,0x0000000000004020}, {0x0030180C00000000,0x0000000000000000}, },
{{0x1000000000000000,0x0000000000004020}, {0x0008040201008040,0x0000000000000000}, {0x6000000000000000,0x00000000000180C0}, },
{{0x0000000002010080,0x0000000000000000}, {0x2010080400000000,0x0000000000008040}, {0x0000000005028140,0x0000000000000000}, },
{{0x0010080400000000,0x0000000000000000}, {0x2000000002010080,0x0000000000008040}, {0x0028140A00000000,0x0000000000000000}, },
{{0x2000000000000000,0x0000000000008040}, {0x0010080402010080,0x0000000000000000}, {0x5000000000000000,0x00000000000140A0}, },
{{0x0000000004020100,0x0000000000000000}, {0x4020100800000000,0x0000000000010080}, {0x00000000030180C0,0x0000000000000000}, },
{{0x0020100800000000,0x0000000000000000}, {0x4000000004020100,0x0000000000010080}, {0x00180C0600000000,0x0000000000000000}, },
{{0x4000000000000000,0x0000000000010080}, {0x0020100804020100,0x0000000000000000}, {0x3000000000000000,0x000000000000C060}, },
}; //tripletMasks
#endif
template <class X> constexpr void fsss2<X>::initEmpty() {
//set all cells and houses as "unsolved"
grid[0] = constraints::mask108;
grid[1] = constraints::mask108;
grid[2] = constraints::mask108;
grid[3] = constraints::mask108;
grid[4] = constraints::mask108;
grid[5] = constraints::mask108;
grid[6] = constraints::mask108;
grid[7] = constraints::mask108;
grid[8] = constraints::mask108;
//no processed digits for hidden singles yet
knownNoHiddenSingles[0] = constraints::mask108;
knownNoHiddenSingles[1] = constraints::mask108;
knownNoHiddenSingles[2] = constraints::mask108;
knownNoHiddenSingles[3] = constraints::mask108;
knownNoHiddenSingles[4] = constraints::mask108;
knownNoHiddenSingles[5] = constraints::mask108;
knownNoHiddenSingles[6] = constraints::mask108;
knownNoHiddenSingles[7] = constraints::mask108;
knownNoHiddenSingles[8] = constraints::mask108;
#ifdef USE_LOCKED_CANDIDATES
#ifdef LOCKED_CANDIDATES_USE_CACHE
knownNoLockedCandidates[0] = constraints::mask108;
knownNoLockedCandidates[1] = constraints::mask108;
knownNoLockedCandidates[2] = constraints::mask108;
knownNoLockedCandidates[3] = constraints::mask108;
knownNoLockedCandidates[4] = constraints::mask108;
knownNoLockedCandidates[5] = constraints::mask108;
knownNoLockedCandidates[6] = constraints::mask108;
knownNoLockedCandidates[7] = constraints::mask108;
knownNoLockedCandidates[8] = constraints::mask108;
#endif
#ifndef LOCKED_CANDIDATES_ALWAYS
lockedDone = 0;
#endif
#endif
#ifdef USE_SUBSETS
subsetsDone = 0;
// for(int i = 0; i < 36; i++) knownNoSubsets[i] = constraints::mask108;
#endif //USE_SUBSETS
solved.clear(); //no solved cells yet
trialCandidates.clear(); //unknown cell candidates for T&E
mode = 0; //should solve
guessDepth = 0; //no guessed cells yet
}
template <class X> void fsss2<X>::setCellValue(int pos, int value) {
collector.setCellValue(pos, value);
solved.setBit(pos); //mark cell as "solved"
grid[value - 1].clearBits(constraints::visibleCells[pos]); //mark visible cells as forbidden for the same digit, mark the 3 houses as solved
}
template <class X> void fsss2<X>::eliminateCellValue(int pos, int value) {
grid[value - 1].clearBit(pos);
}
#ifdef USE_LOCKED_CANDIDATES
//template <class X> bool fsss2<X>::doLockedCandidatesForDigit(bm128& tmp) {
// bool found = false;
// for(uint32_t lines = 0x03FFFF & (tmp.toInt32_3()); lines; lines &= (lines - 1)) {
// unsigned int line = 3U * bm128::FindLSBIndex32(lines); //unsolved row or column
// //process the 3 triplets in the line (row or column)
// for(unsigned int t = 0; t < 3; t++) {
// //if(tmp.isDisjoint(constraints::tripletMasks[line + t].self)) continue; //no candidates, possibly resolved box
// bool dl = tmp.isDisjoint(constraints::tripletMasks[line + t].adjacentLine);
// bool db = tmp.isDisjoint(constraints::tripletMasks[line + t].adjacentBox);
// if(dl) {
// //unsolved line with candidates located only within this triplet
// if(!db) {
// tmp.clearBits(constraints::tripletMasks[line + t].adjacentBox);
// found = true;
// //goto next_line;
// return true;
// }
// }
// if(db) {
// //the other two triplets within this box have no candidates
// if(!dl) {
// //other two triplets for this line have candidates, but the box is possibly solved
// if(!tmp.isDisjoint(constraints::tripletMasks[line + t].self)) { //unsolved box
// tmp.clearBits(constraints::tripletMasks[line + t].adjacentLine);
// found = true;
// //goto next_line;
// return true;
// }
// }
// }
// } //triplets in a line
////next_line:
// ;
// } //lines
// return found;
// //return false;
//}
template <class X> bool fsss2<X>::doLockedCandidatesForDigit(bm128& tmp) {
static constexpr int boxNum[18][3] = {
{0,1,2},{0,1,2},{0,1,2},{3,4,5},{3,4,5},{3,4,5},{6,7,8},{6,7,8},{6,7,8},
{0,3,6},{0,3,6},{0,3,6},{1,4,7},{1,4,7},{1,4,7},{2,5,8},{2,5,8},{2,5,8}
};
bool found = false;
uint32_t unsolvedHouses = tmp.toInt32_3();
if(unsolvedHouses == 0) return false;
uint32_t unsolvedBoxes = unsolvedHouses >> 18;
//if(unsolvedBoxes == 0) return false; //never happens
for(uint32_t lines = 0x03FFFF & unsolvedHouses; lines; lines &= (lines - 1)) {
unsigned int line = bm128::FindLSBIndex32(lines); //unsolved row or column
unsigned int lineBase = 3U * line;
//process the 3 triplets in the line (row or column)
for(unsigned int t = 0; t < 3; t++) {
if(0 == (unsolvedBoxes & ((uint32_t) 1) << (boxNum[line][t]))) continue; //resolved box
//if(tmp.isDisjoint(constraints::tripletMasks[lineBase + t].self)) continue; //resolved box
// fprintf(stderr, "?");
// continue; //no candidates, possibly resolved box
// }
bool dl = tmp.isDisjoint(constraints::tripletMasks[lineBase + t].adjacentLine); //all line candidates are within this triplet
bool db = tmp.isDisjoint(constraints::tripletMasks[lineBase + t].adjacentBox); //all box candidates are within this triplet
if(dl) {
//unsolved line with candidates located only within this triplet
if(!db) {
tmp.clearBits(constraints::tripletMasks[lineBase + t].adjacentBox);
found = true;
//goto next_line;
return true;
}
}
if(db) {
//the other two triplets within this box have no candidates
if(!dl) {
//other two triplets for this line have candidates, but the box is possibly solved
//if(!tmp.isDisjoint(constraints::tripletMasks[lineBase + t].self)) { //unsolved box
//if(1 || 0 != (unsolvedBoxes & (((uint32_t) 1) << (boxNum[line][t])))) {
tmp.clearBits(constraints::tripletMasks[lineBase + t].adjacentLine);
found = true;
//goto next_line;
return true;
//}
}
}
} //triplets in a line
//next_line:
;
} //lines
return found;
//return false;
}
#endif
//void fsss2::findBiValueCells(bm128& all) const { //cells with 2 remaining candidates
// //bm128 all;
// all = solved;
// bm128 duplicates = solved;
// bm128 triplicates = solved;
// for(int d = 0; d < 9; d++) {
// bm128 tmp = grid[d];
// tmp &= all;
// bm128 tmp2 = tmp;
// tmp2 &= duplicates;
// triplicates |= tmp2;
// duplicates |= tmp;
// all |= grid[d];
// }
// all &= constraints::mask81; //clear other bits
// all.clearBits(triplicates);
//}
template <class X> int fsss2<X>::findLeastPopulatedCells(bm128& all) const {
//the following code is written by a member of http://forum.enjoysudoku.com known by pseudonym Blue
//it returns the cells with less number of candidates and works for 0 to 9 candidates (4-bit sum)
bm128 sum0 = grid[0];
bm128 sum1 = grid[1];
bm128 tmp = sum0;
sum0 ^= sum1;
sum1 &= tmp;
bm128 carry = grid[2];
tmp = sum0;
sum0 ^= carry;
carry &= tmp;
sum1 |= carry;
bm128 sum2 = grid[3];
tmp = sum0;
sum0 ^= sum2;
sum2 &= tmp;
tmp = sum1;
sum1 ^= sum2;
sum2 &= tmp;
carry = grid[4];
tmp = sum0;
sum0 ^= carry;
carry &= tmp;
tmp = sum1;
sum1 ^= carry;
carry &= tmp;
sum2 |= carry;
carry = grid[5];
tmp = sum0;
sum0 ^= carry;
carry &= tmp;
tmp = sum1;
sum1 ^= carry;
carry &= tmp;
sum2 |= carry;
carry = grid[6];
tmp = sum0;
sum0 ^= carry;
carry &= tmp;
tmp = sum1;
sum1 ^= carry;
carry &= tmp;
sum2 |= carry;
bm128 sum3 = grid[7];
tmp = sum0;
sum0 ^= sum3;
sum3 &= tmp;
tmp = sum1;
sum1 ^= sum3;
sum3 &= tmp;
tmp = sum2;
sum2 ^= sum3;
sum3 &= tmp;
carry = grid[8];
tmp = sum0;
sum0 ^= carry;
carry &= tmp;
tmp = sum1;
sum1 ^= carry;
carry &= tmp;
tmp = sum2;
sum2 ^= carry;
carry &= tmp;
sum3 |= carry;
all = constraints::mask81;
all.clearBits(solved);
int n = 0;
if (all.isSubsetOf(sum3)) n = 8; else all.clearBits(sum3);
if (all.isSubsetOf(sum2)) n += 4; else all.clearBits(sum2);
if (all.isSubsetOf(sum1)) n += 2; else all.clearBits(sum1);
if (all.isSubsetOf(sum0)) n++; else all.clearBits(sum0);
return n;
}
template <class X> void fsss2<X>::doNakedSingles() { //cells with only one remaining candidate
#if 1
register bm128 g0 = grid[0];
register bm128 g1 = grid[1];
register bm128 g2 = grid[2];
register bm128 g3 = grid[3];
register bm128 g4 = grid[4];
register bm128 g5 = grid[5];
register bm128 g6 = grid[6];
register bm128 g7 = grid[7];
register bm128 g8 = grid[8];
#else
#define g0 (grid[0])
#define g1 (grid[1])
#define g2 (grid[2])
#define g3 (grid[3])
#define g4 (grid[4])
#define g5 (grid[5])
#define g6 (grid[6])
#define g7 (grid[7])
#define g8 (grid[8])
#endif
bm128& slv = solved;
do {
register bm128 all = slv;
{
register bm128 duplicates = slv; //cells with 2 or more candidates
{
register bm128 tmp;
tmp = g0; tmp &= all; duplicates |= tmp; all |= g0;
tmp = g1; tmp &= all; duplicates |= tmp; all |= g1;
tmp = g2; tmp &= all; duplicates |= tmp; all |= g2;
tmp = g3; tmp &= all; duplicates |= tmp; all |= g3;
tmp = g4; tmp &= all; duplicates |= tmp; all |= g4;
tmp = g5; tmp &= all; duplicates |= tmp; all |= g5;
tmp = g6; tmp &= all; duplicates |= tmp; all |= g6;
tmp = g7; tmp &= all; duplicates |= tmp; all |= g7;
tmp = g8; tmp &= all; all |= g8;
if(((bm128)constraints::mask81).isSubsetOf(all)) {
;
}
else {
//there is at least one unsolved cell without any candidate
goto contradiction;
}
duplicates |= tmp;
}
if(((bm128)constraints::mask81).isSubsetOf(duplicates)) {
//sorry, no naked singles
//remove all candidates for the solved cells (even if no eliminations were made here)
//Note: this cleanup is postponed up to there because
// - the above checking is not sensitive to this aspect of the board consistency, and
// - there is a chance contradiction to be detected before the cleanup
g0.clearBits(slv);
g1.clearBits(slv);
g2.clearBits(slv);
g3.clearBits(slv);
g4.clearBits(slv);
g5.clearBits(slv);
g6.clearBits(slv);
g7.clearBits(slv);
g8.clearBits(slv);
grid[0] = g0;
grid[1] = g1;
grid[2] = g2;
grid[3] = g3;
grid[4] = g4;
grid[5] = g5;
grid[6] = g6;
grid[7] = g7;
grid[8] = g8;
return;
}
all = constraints::mask81;
all.clearBits(duplicates);
slv |= all; //mark cells as solved
}
//now find which unique where came from
if(!g0.isDisjoint(all)) {
bm128 theCells = all; theCells &= g0;
for(uint64_t cells = theCells.toInt64(); cells; cells &= (cells - 1)) {
uint32_t cell = (uint32_t) bm128::FindLSBIndex64(cells); //get the rightmost bit index
if(!g0.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g0.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 1);
} //for lower 64 cells
for(uint32_t cells = theCells.toInt32_2(); cells; cells &= (cells - 1)) {
uint32_t cell = 64 + bm128::FindLSBIndex32(cells); //get the rightmost bit index
if(!g0.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g0.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 1);
}
if(all.isSubsetOf(theCells)) continue;
all.clearBits(theCells);
}
if(!g1.isDisjoint(all)) {
bm128 theCells = all; theCells &= g1;
for(uint64_t cells = theCells.toInt64(); cells; cells &= (cells - 1)) {
uint32_t cell = (uint32_t) bm128::FindLSBIndex64(cells); //get the rightmost bit index
if(!g1.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g1.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 2);
} //for lower 64 cells
for(uint32_t cells = theCells.toInt32_2(); cells; cells &= (cells - 1)) {
uint32_t cell = 64 + bm128::FindLSBIndex32(cells); //get the rightmost bit index
if(!g1.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g1.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 2);
}
if(all.isSubsetOf(theCells)) continue;
all.clearBits(theCells);
}
if(!g2.isDisjoint(all)) {
bm128 theCells = all; theCells &= g2;
for(uint64_t cells = theCells.toInt64(); cells; cells &= (cells - 1)) {
uint32_t cell = (uint32_t) bm128::FindLSBIndex64(cells); //get the rightmost bit index
if(!g2.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g2.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 3);
} //for lower 64 cells
for(uint32_t cells = theCells.toInt32_2(); cells; cells &= (cells - 1)) {
uint32_t cell = 64 + bm128::FindLSBIndex32(cells); //get the rightmost bit index
if(!g2.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g2.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 3);
}
if(all.isSubsetOf(theCells)) continue;
all.clearBits(theCells);
}
if(!g3.isDisjoint(all)) {
bm128 theCells = all; theCells &= g3;
for(uint64_t cells = theCells.toInt64(); cells; cells &= (cells - 1)) {
uint32_t cell = (uint32_t) bm128::FindLSBIndex64(cells); //get the rightmost bit index
if(!g3.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g3.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 4);
} //for lower 64 cells
for(uint32_t cells = theCells.toInt32_2(); cells; cells &= (cells - 1)) {
uint32_t cell = 64 + bm128::FindLSBIndex32(cells); //get the rightmost bit index
if(!g3.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g3.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 4);
}
if(all.isSubsetOf(theCells)) continue;
all.clearBits(theCells);
}
if(!g4.isDisjoint(all)) {
bm128 theCells = all; theCells &= g4;
for(uint64_t cells = theCells.toInt64(); cells; cells &= (cells - 1)) {
uint32_t cell = (uint32_t) bm128::FindLSBIndex64(cells); //get the rightmost bit index
if(!g4.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g4.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 5);
} //for lower 64 cells
for(uint32_t cells = theCells.toInt32_2(); cells; cells &= (cells - 1)) {
uint32_t cell = 64 + bm128::FindLSBIndex32(cells); //get the rightmost bit index
if(!g4.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g4.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 5);
}
if(all.isSubsetOf(theCells)) continue;
all.clearBits(theCells);
}
if(!g5.isDisjoint(all)) {
bm128 theCells = all; theCells &= g5;
for(uint64_t cells = theCells.toInt64(); cells; cells &= (cells - 1)) {
uint32_t cell = (uint32_t) bm128::FindLSBIndex64(cells); //get the rightmost bit index
if(!g5.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g5.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 6);
} //for lower 64 cells
for(uint32_t cells = theCells.toInt32_2(); cells; cells &= (cells - 1)) {
uint32_t cell = 64 + bm128::FindLSBIndex32(cells); //get the rightmost bit index
if(!g5.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g5.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 6);
}
if(all.isSubsetOf(theCells)) continue;
all.clearBits(theCells);
}
if(!g6.isDisjoint(all)) {
bm128 theCells = all; theCells &= g6;
for(uint64_t cells = theCells.toInt64(); cells; cells &= (cells - 1)) {
uint32_t cell = (uint32_t) bm128::FindLSBIndex64(cells); //get the rightmost bit index
if(!g6.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g6.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 7);
} //for lower 64 cells
for(uint32_t cells = theCells.toInt32_2(); cells; cells &= (cells - 1)) {
uint32_t cell = 64 + bm128::FindLSBIndex32(cells); //get the rightmost bit index
if(!g6.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g6.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 7);
}
if(all.isSubsetOf(theCells)) continue;
all.clearBits(theCells);
}
if(!g7.isDisjoint(all)) {
bm128 theCells = all; theCells &= g7;
for(uint64_t cells = theCells.toInt64(); cells; cells &= (cells - 1)) {
uint32_t cell = (uint32_t) bm128::FindLSBIndex64(cells); //get the rightmost bit index
if(!g7.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g7.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 8);
} //for lower 64 cells
for(uint32_t cells = theCells.toInt32_2(); cells; cells &= (cells - 1)) {
uint32_t cell = 64 + bm128::FindLSBIndex32(cells); //get the rightmost bit index
if(!g7.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g7.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 8);
}
if(all.isSubsetOf(theCells)) continue;
all.clearBits(theCells);
}
{
bm128 theCells = all; theCells &= g8;
for(uint64_t cells = theCells.toInt64(); cells; cells &= (cells - 1)) {
uint32_t cell = (uint32_t) bm128::FindLSBIndex64(cells); //get the rightmost bit index
if(!g8.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g8.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 9);
} //for lower 64 cells
for(uint32_t cells = theCells.toInt32_2(); cells; cells &= (cells - 1)) {
uint32_t cell = 64 + bm128::FindLSBIndex32(cells); //get the rightmost bit index
if(!g8.isBitSet(cell)) goto contradiction; //two naked singles for the same digit in the same house
g8.clearBits(constraints::visibleCells[cell]);
collector.setCellValue(cell, 9);
}
}
} while(!((bm128)constraints::mask81).isSubsetOf(slv));
//finally all 81 cells are solved
//a slower alternative for contradiction checking within the loops
// slv = g0;
// slv |= g1;
// slv |= g2;
// slv |= g3;
// slv |= g4;
// slv |= g5;
// slv |= g6;
// slv |= g7;
// slv |= g8;
// if(!slv.isZero())
// goto contradiction;
if(collector.solutionFound()) {
//collector doesn't ask for more solutions, we are done
mode = MODE_STOP_PROCESSING | MODE_STOP_GUESSING;
return;
}
//continue with next possible solution
contradiction:
mode = MODE_STOP_PROCESSING;
return;
}
template <class X> void fsss2<X>::doEliminations() {
bool guessAuto = true;
nakedAgain:
doNakedSingles();
if(mode) goto backtrack;
//hidden singles
//if(0)
{
int found;
do {
found = 0;
for(int d = 0; d < 9; d++) { //for each digit
if(knownNoHiddenSingles[d] == grid[d]) {
//knownNoHiddenHits++;
continue;
}
//knownNoHiddenMisses++;
againSameHidden:
//for each unsolved house
for(uint32_t houses = grid[d].toInt32_3(); houses; houses &= (houses - 1)) {
uint32_t house = bm128::FindLSBIndex32(houses);
bm128 tmp = grid[d];
tmp &= constraints::bitsForHouse[house]; //mask other candidates and leave only these from the current house
//if(tmp.isZero()) goto contradiction;
//find whether the house has a single candidate and obtain its position
//exploit the fact that when (x & (x-1)) == 0 then x has 0 or 1 bits set
if(tmp.hasMin2Bits())
continue; //too many candidates
//find the bit
int cell;
{
uint64_t low64 = tmp.toInt64();
uint32_t high17 = tmp.toInt32_2();
if(low64) {
if(high17)
continue; //candidates in both low and high part of the house
//get the position of the single candidate in the low part of the house
cell = (int) bm128::FindLSBIndex64(low64);
goto single_found;
}
if(high17) {
//get the position of the single candidate in the high part of the house
cell = 64 + bm128::FindLSBIndex32(high17);
goto single_found;
}
}
//no any candidate for this digit in this unsolved house
goto contradiction;
single_found:
collector.setCellValue(cell, d + 1);
solved.setBit(cell); //mark cell as "solved"
grid[d].clearBits(constraints::visibleCells[cell]); //mark visible cells as forbidden for the same digit, mark the 3 houses as solved
//at this point the solved cell still isn't cleared from all 9 masks, but doNakedSingles does it
doNakedSingles(); //checking for a single candidate in a cell, possible eliminations in other digits
if(mode) goto backtrack;
found = d; //if the latest found is in the 1-st digit d == 0, then repeating search for hidden singles is redundant
goto againSameHidden;
} //for houses
knownNoHiddenSingles[d] = grid[d];
} //for d
} while(found);
} //end of hidden singles
//locked candidates
#ifdef USE_LOCKED_CANDIDATES
#ifndef LOCKED_CANDIDATES_ALWAYS
if(lockedDone == 0)
#endif
{
bool found = false;
//if a digit in a row is within a single triplet, then remove digit from the other two box triplets and vice versa
for (int d = 0; d < 9; d++) {
#ifdef LOCKED_CANDIDATES_USE_CACHE
if(knownNoLockedCandidates[d] == grid[d]) {
//knownNoLockedCandidatesHits++;
continue;
}
//knownNoLockedCandidatesMisses++;
if(doLockedCandidatesForDigit(grid[d])) {
found = true;
}
else {
knownNoLockedCandidates[d] = grid[d];
}
#else
found |= doLockedCandidatesForDigit(grid[d]);
#endif
}
#ifndef LOCKED_CANDIDATES_ALWAYS
lockedDone = 1;
#endif
if(found) {
#ifdef USE_SUBSETS
//subsetsDone = 0;
#endif //USE_SUBSETS
goto nakedAgain;
}
//lockedDone = 1;
} //end of locked candidates
#endif //USE_LOCKED_CANDIDATES
#ifdef USE_SUBSETS
//subsets
//if(subsetsDone == 0) {
if(1 || subsetsDone < 5) {
bool eliminationFound = false;
//int subsetIndex = 0; //01,02,03,04,05,06,07,08,12,13,14,15,16,17,18,23,24,25,26,27,28,34,35,36,37,38,45,46,47,48,56,57,58,67,68,78
for(int d1 = 0, subsetIndex = 0; d1 < 8; d1++) {
for(int d2 = d1 + 1; d2 < 9; d2++, subsetIndex++) {
//for(int d2 = d1 + 1; d2 < 9; d2++) {
bm128 any = grid[d1];
any |= grid[d2];
if(any == knownNoSubsets[subsetIndex])
continue;
bool pairFound = false;
bm128 ss;
ss.clear();
bm128 both = grid[d1];
both &= grid[d2];
//for each unsolved for both digits house
for(uint32_t houses = both.toInt32_3(); houses; houses &= (houses - 1)) {
bm128 tmp = any;
tmp &= constraints::bitsForHouse[bm128::FindLSBIndex32(houses)]; //mask other candidates and leave only these from the current house
if(2 == tmp.popcount_128()) {
//only 2 digits in 2 cells in the same house
ss |= tmp;
//ss = tmp;
pairFound = true;
//trialCandidates |= ss;
//break;
}
}
//eliminate the candidates from other digits
if(pairFound) {
for(int d = 0; d < 9; d++) {
if((d != d1) && (d != d2)) {
if(!grid[d].isDisjoint(ss)) {
grid[d].clearBits(ss);
eliminationFound = true;
//goto nakedAgain;
}
}
}
}
else {
knownNoSubsets[subsetIndex] = any;
}
}
}
//subsetsDone = 1;
//subsetsDone++;
if(eliminationFound) {
#ifdef USE_LOCKED_CANDIDATES
lockedDone = 0;
#endif
goto nakedAgain;
}
//subsetsDone = 1;
}
#endif //USE_SUBSETS
//Prepare a guess
nextGuess:
{
//At this point the existence of unsolved house(s) w/o candidates crashes the algorithm!!!
//Find an unsolved cell with less possibilities
int optDigit;
int optCell;
int minCellValues = 2;
guessAuto = collector.beforeGuess(guessDepth, optCell, optDigit);
//find first of the best-to-guess candidates
if(guessAuto) {
bm128 all;
//try reusing previously found candidates
all = trialCandidates;
all.clearBits(solved);
if(all.isZero()) {
//find new candidates
minCellValues = findLeastPopulatedCells(all);
if(minCellValues == 2) {
trialCandidates = all; //reuse them on next guess only if they are bi-values
}
// else if(minCellValues > 3) {
// //find house with less candidates from a particular digit, exit on first bi-position house/digit
// int minValueLocations = 100;
// for (int d = 0; d < 9; d++) {
// for (int h = 0; h < 27; h++) {
// if (!grid[d].isBitSet(81 + h))
// continue;
// bm128 tmp = grid[d];
// tmp &= constraints::bitsForHouse[h];
// tmp &= constraints::mask81;
// int n = tmp.popcount_128();
// if (n < minValueLocations) {
// optDigit = d;
// optCell = tmp.getFirstBit1Index96();
// if(n == 2) { //not so bad, a bi-position is found
// //break;
// goto bestCellFound;
// }
// minValueLocations = n;
// }
// }
// }
// if(minValueLocations < minCellValues) { //prefer n-location
// goto bestCellFound;
// }
// }
}
#ifdef GUESS_STRATEGY_2
//strategy 1: least value, then least cell index //234.922 seconds. Trials = 737 680 539
//if((guessDepth & 1) == 0) //flip-flop
//if(solved.popcount_128() > 18)
//if(solved.popcount_128() < 10) //low-clue pencilmark-only puzzles
if(minCellValues == 2 && solved.popcount_128() > 22)
//if(minCellValues == 2)
//if(0)
#endif
{
for(optDigit = 0; optDigit < 7; optDigit++) { //prefer the least value
if(!all.isDisjoint(grid[optDigit])) {
all &= grid[optDigit];
optCell = all.getFirstBit1Index96(); //prefer the lefttmost position (unless reversely initialized)
goto bestCellFound;
}
}
optDigit = 7; //digit 8 must have optCell, worst case not covered above is a bi-value {8,9} cell
all &= grid[7];
optCell = all.getFirstBit1Index96();
}
#ifdef GUESS_STRATEGY_2
else
//strategy 2a (experimental): most direct eliminations for the GUESSED value
{
bm128 uncheckedCells(all);
int maxEliminations = 0;
for(uint64_t cells = uncheckedCells.toInt64(); cells; cells &= (cells - 1)) {
uint32_t cell = (uint32_t) bm128::FindLSBIndex64(cells); //get the rightmost bit index
for(int d = 0; d < 9; d++) {
if(!grid[d].isBitSet(cell)) continue;
bm128 eliminations(grid[d]);
eliminations &= constraints::visibleCells[cell];
eliminations &= constraints::mask81;
int numEliminations = eliminations.popcount_128();
if(maxEliminations < numEliminations) {
optDigit = d;
optCell = cell;
if(numEliminations >= 20) goto bestCellFound;
maxEliminations = numEliminations;
}
}
} //for lower 64 cells
for(uint32_t cells = uncheckedCells.toInt32_2(); cells; cells &= (cells - 1)) {
uint32_t cell = 64 + bm128::FindLSBIndex32(cells); //get the rightmost bit index
for(int d = 0; d < 9; d++) {
if(!grid[d].isBitSet(cell)) continue;
bm128 eliminations(grid[d]);
eliminations &= constraints::visibleCells[cell];
eliminations &= constraints::mask81;
int numEliminations = eliminations.popcount_128();
if(maxEliminations < numEliminations) {
optDigit = d;
optCell = cell;
if(numEliminations >= 20) goto bestCellFound;