SudokuSolver 2.4 程序實現
本次版本實現了 用C++實現的數獨解題程序 SudokuSolver 2.3 及實例分析 里發現的第三個不完全收縮 grp 算法 thirdGreenWorld。
CQuizDealer 類聲明部分的修改
class CQuizDealer { public: ...
void run(ulong tilsteps = 0); void mode(std::string& ex) { size_t pos = ex.find_first_not_of(" \t"); if (pos != std::string::npos) { ex.erase(0, pos); m_mode = (u8)strtoul(ex.c_str(), 0, 10); } printf("Working mode:%d (1:grp-only; 2:ply-only; other:both grp and ply)\n", (int)m_mode); } ...
private: ... CQuizDealer() : m_state(STA_UNLOADED), ..., m_mode(0) {}; ...
bool completeShrinkByGrp(u8* pGrp); u8 incompleteShrinkByGrp(u8* pGrp); u8 firstGreenWorld(u8* pGrp); u8 incompleteShrinkBy1GW(u8 valSum, u8* pCelSumExs, u8* pGrp); bool sameCandidates(u8 cel1, u8 cel2); u8 anotherGreenWorld(u8* pGrp); u8 incompleteShrinkByAGW(u8 times, u8* pTimesVals, u8* pValsCells, u8* pGrp); u8 thirdGreenWorld(u8* pGrp); u8 incompleteShrinkBy3GW(u8 sum, std::set<u8>& valSet, u8* pGrp); bool unionValsByCombi(u8 sum, u8* pCombi, u8* pGrp, std::set<u8>& unionSet); ...
ulong m_steps; u8 m_mode; // 1:grp-only; 2:ply-only; other:both ... };
去掉了 setOnlyGrpMode 接口，新增了 mode 接口，相應地，原先的 onlygrp 命令換成了 mode [1|2|0] 命令。
增加了 thirdGreenWorld 等接口。
filterCandidates 接口的小修改
u8 CQuizDealer::filterCandidates() { incSteps(); u8 ret = RET_PENDING; if (m_mode != 2) { for (u8 row = 0; row < 9; ++row) if (ret = filterRowGroup(row)) return ret; for (u8 col = 0; col < 9; ++col) if (ret = filterColGroup(col)) return ret; for (u8 blk = 0; blk < 9; ++blk) if (ret = filterBlkGroup(blk)) return ret; } if (m_mode != 1) { for (u8 row = 0; row < 9; ++row) { ret = filterRowCandidatesEx(row); if (IsDone(ret)) return ret; } for (u8 col = 0; col < 9; ++col) { ret = filterColCandidatesEx(col); if (IsDone(ret)) return ret; } } if (ret == RET_SHRUNKEN) { printf("incomplete shrink met, filter again\n"); return filterCandidates(); } return ret; }
修改后，可以只使用 grp 算法求解，也可以只使用 ply 算法求解，缺省是兩者都用。
從舊的 filterOneGroup 接口實現中提煉出 firstGreenWorld
1 u8 CQuizDealer::firstGreenWorld(u8* pGrp) 2 { 3 u8 size = pGrp[0]; 4 u8 celSumExs[100] = {0}; 5 for (u8 idx = 1; idx <= size; ++idx) { 6 u8 valSum = m_seqCell[pGrp[idx]].candidates[0]; 7 u8 base = valSum * 10; 8 celSumExs[base] += 1; 9 u8 pos = base + celSumExs[base]; 10 celSumExs[pos] = pGrp[idx]; 11 } 12 for (u8 idx = 2; idx <= 6; ++idx) { 13 u8 ret = incompleteShrinkBy1GW(idx, celSumExs, pGrp); 14 if (ret != RET_PENDING) 15 return ret; 16 } 17 return RET_PENDING; 18 }
舊 incompleteShrinkByGrp 改為 incompleteShrinkBy1GW
1 u8 CQuizDealer::incompleteShrinkBy1GW(u8 valSum, u8* pCelSumExs, u8* pGrp) 2 { 3 u8 base = valSum * 10; 4 if (pCelSumExs[base] < valSum) 5 return RET_PENDING; 6 u8 itemSum = 0; 7 Item items[9]; 8 for (u8 pos = 1; pos <= pCelSumExs[base]; ++pos) { 9 u8 idx = 0; 10 for (; idx < itemSum; ++idx) 11 if (sameCandidates(pCelSumExs[base + pos], items[idx].celIdxs[0])) { 12 items[idx].celIdxs[items[idx].sameSum] = pCelSumExs[base + pos]; 13 items[idx].sameSum++; 14 break; 15 } 16 if (idx == itemSum) { 17 items[itemSum].sameSum = 1; 18 items[itemSum].celIdxs[0] = pCelSumExs[base + pos]; 19 ++itemSum; 20 } 21 } 22 for (u8 idx = 0; idx < itemSum; ++idx) { 23 if (items[idx].sameSum > valSum) 24 return RET_WRONG; 25 } 26 bool shrunken = false; 27 for (u8 idx = 0; idx < itemSum; ++idx) { 28 if (items[idx].sameSum < valSum) 29 continue; 30 for (u8 pos = 1; pos <= pGrp[0]; ++pos) { 31 if (inSet(pGrp[pos], (u8*)&(items[idx]))) 32 continue; 33 u8 isVals[10] = {0}; 34 u8 cel1 = items[idx].celIdxs[0]; 35 u8 cel2 = pGrp[pos]; 36 intersection(m_seqCell[cel1].candidates, m_seqCell[cel2].candidates, isVals); 37 if (isVals[0] == 0) 38 continue; 39 shrunken = true; 40 for (u8 valIdx = 1; valIdx <= isVals[0]; ++valIdx) { 41 if (!removeVal(m_seqCell[cel2].candidates, isVals[valIdx])) 42 return RET_WRONG; 43 else 44 printf("1GW: %d shrunken out of [%d,%d]\n", (int)isVals[valIdx], (int)cel2 / 9 + 1, (int)cel2 % 9 + 1); 45 } 46 } 47 } 48 return (shrunken ? RET_SHRUNKEN : RET_PENDING); 49 }
新的 incompleteShrinkByGrp 接口實現
1 u8 CQuizDealer::incompleteShrinkByGrp(u8* pGrp) 2 { 3 u8 ret = firstGreenWorld(pGrp); 4 if (ret != RET_PENDING) 5 return ret; 6 ret = anotherGreenWorld(pGrp); 7 if (ret != RET_PENDING) 8 return ret; 9 return thirdGreenWorld(pGrp); 10 }
新的 filterOneGroup 接口實現
u8 CQuizDealer::filterOneGroup(u8* pGrp) { return (completeShrinkByGrp(pGrp) ? RET_OK : incompleteShrinkByGrp(pGrp)); }
incompleteShrinkByAGW 接口實現的 bug 修改
u8 CQuizDealer::incompleteShrinkByAGW(u8 times, u8* pTimesVals, u8* pValsCells, u8* pGrp) { ... while (true) { u8 celSet[10] = {0}; u8 valSet[10] = {0}; if (matchValsCells(times, combi, pTimesVals, pValsCells, celSet, valSet)) { valSet[0] = times; bool shrunken = false; for (u8 idx = 1; idx <= times; ++idx) { ... if (candiSum < times) { printf("2GW: [%d,%d] candidates %d lower than times %d!\n", (int)(cel / 9 + 1), (int)(cel % 9 + 1), (int)candiSum, (int)times); return RET_WRONG; } shrunken = true; for (u8 pos = 1; pos <= m_seqCell[cel].candidates[0];) { u8 val = m_seqCell[cel].candidates[pos]; if (inSet(val, valSet)) ++pos; else { removeVal(m_seqCell[cel].candidates, val); printf("2GW: %d shrunken out of [%d,%d]\n", (int)val, (int)(cel / 9 + 1), (int)(cel % 9 + 1)); } } } ... } if (!move2NextCombi(times, combi)) break; } return RET_PENDING; }
新增 thirdGreenWorld 接口實現
1 u8 CQuizDealer::thirdGreenWorld(u8* pGrp) 2 { 3 u8 grpSize = pGrp[0]; 4 std::set<u8> valSet; 5 u8 lowSum = 9, highSum = 0; 6 for (u8 idx = 1; idx <= grpSize; ++idx) { 7 u8 valSum = m_seqCell[pGrp[idx]].candidates[0]; 8 if (valSum < lowSum) 9 lowSum = valSum; 10 if (valSum > highSum) 11 highSum = valSum; 12 for (u8 vidx = 1; vidx <= valSum; ++vidx) { 13 u8 val = m_seqCell[pGrp[idx]].candidates[vidx]; 14 valSet.insert(val); 15 } 16 } 17 if (valSet.size() != grpSize) { 18 printf("3GW: shrink went wrong\n"); 19 return RET_WRONG; 20 } 21 if (highSum == valSet.size()) 22 --highSum; 23 for (u8 sum = lowSum; sum <= highSum; ++sum) { 24 u8 ret = incompleteShrinkBy3GW(sum, valSet, pGrp); 25 if (ret != RET_PENDING) 26 return ret; 27 } 28 return RET_PENDING; 29 }
新增 incompleteShrinkBy3GW 接口實現
1 u8 CQuizDealer::incompleteShrinkBy3GW(u8 sum, std::set<u8>& valSet, u8* pGrp) 2 { 3 u8 combi[10] = {0}; 4 combi[0] = pGrp[0]; 5 for (u8 idx = 0; idx < sum; ++idx) 6 combi[idx + 1] = idx; 7 while (true) { 8 std::set<u8> unionSet; 9 if (unionValsByCombi(sum, combi, pGrp, unionSet)) { 10 u8 compSet[10] = {0}; 11 for (std::set<u8>::iterator it = valSet.begin(); it != valSet.end(); ++it) 12 if (unionSet.find(*it) == unionSet.end()) { 13 compSet[0] += 1; 14 compSet[compSet[0]] = *it; 15 } 16 combi[0] = sum; // for soon calling inSet properly 17 u8 cells[10] = {0}; 18 for (u8 pos = 0; pos < pGrp[0]; ++pos) { 19 if (!inSet(pos, combi)) { 20 cells[0] += 1; 21 cells[cells[0]] = pos; 22 } 23 } 24 combi[0] = pGrp[0]; //back again 25 bool shrunken = false; 26 for (u8 idx = 1; idx <= cells[0]; ++idx) { 27 u8 pos = pGrp[cells[idx] + 1]; 28 for (u8 inn = 1; inn <= m_seqCell[pos].candidates[0];) { 29 u8 val = m_seqCell[pos].candidates[inn]; 30 if (inSet(val, compSet)) 31 ++inn; 32 else { 33 shrunken = true; 34 removeVal(m_seqCell[pos].candidates, val); 35 printf("3GW: %d shrunken out of [%d,%d]\n", (int)val, (int)pos / 9 + 1, (int)pos % 9 + 1); 36 } 37 } 38 } 39 if (shrunken) 40 return RET_SHRUNKEN; 41 } 42 if (!move2NextCombi(sum, combi)) 43 break; 44 } 45 return RET_PENDING; 46 }
新增 unionValsByCombi 接口實現
1 bool CQuizDealer::unionValsByCombi(u8 sum, u8* pCombi, u8* pGrp, std::set<u8>& unionSet) 2 { 3 for (u8 idx = 1; idx <= sum; ++idx) { 4 u8 pos = pGrp[pCombi[idx] + 1]; 5 u8 valSum = m_seqCell[pos].candidates[0]; 6 if (valSum > sum) 7 return false; 8 for (u8 vidx = 1; vidx <= valSum; ++vidx) { 9 u8 val = m_seqCell[pos].candidates[vidx]; 10 unionSet.insert(val); 11 } 12 if (unionSet.size() > sum) 13 return false; 14 } 15 return (unionSet.size() == sum); 16 }
其他小修改
// 1.0 2021/9/20 // 2.0 2021/10/2 // 2.1 2021/10/4 // 2.2 2021/10/10 // 2.3 2021/10/17 #define STR_VER "Sudoku Solver 2.4 2021/10/19 by readalps\n\n" void showOrderList() { printf(STR_VER); printf("Order List:\n"); printf("load-quiz <file>: load quiz from file\n"); printf("show: show quiz info\n"); printf("mode [1|2|0]: query or change working mode\n"); printf("step: step forward\n"); printf("run: run till the end or a new solution met\n"); printf("runtil <steps>: run till certain steps run\n"); printf("bye: quit\n"); } void dealOrder(std::string& strOrder) { std::string strEx; if ("bye" == strOrder) setQuit(); else if (matchPrefixEx(strOrder, "load-quiz ", strEx)) CQuizDealer::instance()->loadQuiz(strEx); else if ("show" == strOrder) CQuizDealer::instance()->showQuiz(); else if (matchPrefixEx(strOrder, "mode", strEx)) CQuizDealer::instance()->mode(strEx); else if ("step" == strOrder) CQuizDealer::instance()->step(); else if ("run" == strOrder) CQuizDealer::instance()->run(); else if (matchPrefixEx(strOrder, "runtil ", strEx)) { ulong tilsteps = strtoul(strEx.c_str(), 0, 10); CQuizDealer::instance()->run(tilsteps); } else showOrderList(); }
實例分析
“最難”數獨題
繼續以 SudokuSolver 1.0：用C++實現的數獨解題程序 【二】 里試驗過的“最難”數獨題為例做分析。
D:\read\num\Release>sudoku.exe Order please: Sudoku Solver 2.4 2021/10/19 by readalps Order List: load-quiz <file>: load quiz from file show: show quiz info mode [1|2|0]: query or change working mode step: step forward run: run till the end or a new solution met runtil <steps>: run till certain steps run bye: quit Order please: load-quiz s.txt Quiz loaded. Order please: run ... 1014) col 8 complete shrunken by group 1017) Guess [1,6] level 8 at 1 out of 2 1018) row 3 complete shrunken by group 1020) row 3 complete shrunken by group 1GW: 8 shrunken out of [2,7] 1022) row 2 incomplete shrunken by group 1023) Guess [1,8] level 9 at 1 out of 2 1026) row 9 complete shrunken by group 1028) col 6 complete shrunken by group 1031) Guess [2,5] level 10 at 1 out of 2 1034) shrinking 4 from [6,3] went wrong 1035) Forward guess [2,5] level 10 at 2 out of 2 812 753 649 943 682 175 675 491 283 154 237 896 369 845 721 287 169 534 521 974 368 438 526 917 796 318 452 Done [steps:1040, solution sum:1]. Run time: 430 milliseconds; steps: 1040, solution sum: 1. Order please:
第二次 run 命令的輸出信息為：
run
... 1GW: 2 shrunken out of [5,1] 1GW: 9 shrunken out of [5,1] 1GW: 2 shrunken out of [5,2] 1GW: 2 shrunken out of [5,4] 1GW: 9 shrunken out of [5,4] 1GW: 2 shrunken out of [5,8] 1GW: 9 shrunken out of [5,8] 1698) row 5 incomplete shrunken by group 1699) Guess [1,3] level 6 at 1 out of 2 1703) row 1 complete shrunken by group 1705) row 2 complete shrunken by group 1707) row 4 complete shrunken by group 1707) shrinking 9 from blk[5,1] went wrong 1708) Forward guess [1,3] level 6 at 2 out of 2 1709) shrinking 2 from [4,9] went wrong 1710) No more solution (solution sum is 1). 809 000 306 503 600 800 076 090 250 054 007 120 002 045 789 000 100 635 001 000 568 008 500 910 090 000 400 Invalid quiz [steps:1710] - no more solution (solution sum is 1) Run time: 265 milliseconds; steps: 1710, solution sum: 1. Order please:
從輸出的完整信息看，不再有“ply”信息，說明求解過程中只用到了 grp 算法，而沒有用到 ply 算法。
第一次 run 命令走了 1040 步，求得一個解，用時約 430 毫秒；第二次 run 命令用了約 265 毫秒得出結論此 quiz 只有一個解，兩次 run 命令共走了 1710 步。
退出程序並重新進入交互，這次顯式僅用 grp 算法模式求解：
Order please: bye D:\read\num\Release>sudoku.exe Order please: mode Working mode:0 (1:grp-only; 2:ply-only; other:both grp and ply) Order please: mode 1 Working mode:1 (1:grp-only; 2:ply-only; other:both grp and ply) Order please: load-quiz s.txt Quiz loaded. Order please: run ... 1GW: 8 shrunken out of [2,7] 1022) row 2 incomplete shrunken by group 1023) Guess [1,8] level 9 at 1 out of 2 1026) row 9 complete shrunken by group 1028) col 6 complete shrunken by group 1031) Guess [2,5] level 10 at 1 out of 2 1034) shrinking 4 from [6,3] went wrong 1035) Forward guess [2,5] level 10 at 2 out of 2 812 753 649 943 682 175 675 491 283 154 237 896 369 845 721 287 169 534 521 974 368 438 526 917 796 318 452 Done [steps:1040, solution sum:1]. Run time: 421 milliseconds; steps: 1040, solution sum: 1. Order please: run ... 1GW: 9 shrunken out of [5,8] 1698) row 5 incomplete shrunken by group 1699) Guess [1,3] level 6 at 1 out of 2 1703) row 1 complete shrunken by group 1705) row 2 complete shrunken by group 1707) row 4 complete shrunken by group 1707) shrinking 9 from blk[5,1] went wrong 1708) Forward guess [1,3] level 6 at 2 out of 2 1709) shrinking 2 from [4,9] went wrong 1710) No more solution (solution sum is 1). 809 000 306 503 600 800 076 090 250 054 007 120 002 045 789 000 100 635 001 000 568 008 500 910 090 000 400 Invalid quiz [steps:1710] - no more solution (solution sum is 1) Run time: 265 milliseconds; steps: 1710, solution sum: 1. Order please: bye D:\read\num\Release>
從輸出信息看，除了第一次 run 命令用時比之前略微減少（從 430 減為 421）之外，其他信息完全一致。
再看一下顯式僅用 ply 算法模式求解的輸出信息：
D:\read\num\Release>sudoku.exe Order please: load-quiz s.txt Quiz loaded. Order please: show 800 000 000 003 600 000 070 090 200 050 007 000 000 045 700 000 100 030 001 000 068 008 500 010 090 000 400 Order please: mode 2 Working mode:2 (1:grp-only; 2:ply-only; other:both grp and ply) Order please: run ... 1054) col 6 shrunken ply-1 by vblk 2 [2,8]: 5 7 shrunken to 7 worked by col-ply1. 1056) col 8 shrunken ply-1 by vblk 1 1059) Guess [2,5] level 10 at 1 out of 2 1063) shrinking 8 from [4,7] went wrong 1064) Forward guess [2,5] level 10 at 2 out of 2 812 753 649 943 682 175 675 491 283 154 237 896 369 845 721 287 169 534 521 974 368 438 526 917 796 318 452 Done [steps:1069, solution sum:1]. Run time: 468 milliseconds; steps: 1069, solution sum: 1. Order please: run ... 1335) col 8 shrunken ply-2 by vblk 2 [4,9]: 1 2 4 6 9 shrunken to 1 4 6 9 worked by col-ply2. [5,9]: 1 2 6 9 shrunken to 1 6 9 worked by col-ply2. incomplete shrink met, filter again 1339) Guess [1,3] level 8 at 1 out of 2 ... 2100) row 8 shrunken ply-1 by blk 2 [8,2]: 2 3 4 shrunken to 4 worked by row-ply2. 2102) row 8 shrunken ply-2 by blk 3 [6,1]: 2 7 9 shrunken to 7 worked by row-ply2. [6,3]: 2 4 7 9 shrunken to 4 7 worked by row-ply2. 2104) row 6 shrunken ply-2 by blk 2 2104) shrinking 2 from [8,1] went wrong 2105) No more solution (solution sum is 1). 800 000 306 003 600 800 476 893 251 350 067 100 160 345 700 704 100 635 201 000 568 048 506 910 695 000 400 Invalid quiz [steps:2105] - no more solution (solution sum is 1) Run time: 493 milliseconds; steps: 2105, solution sum: 1. Order please:
可以看出，僅用 ply 算法求解，比起僅用 grp 算法求解，用時和步數都略有增加。第二次 run 命令的輸出里有幾次如下的信息輸出：
incomplete shrink met, filter again
這正好對應 用C++實現的數獨解題程序 SudokuSolver 2.1 及實例分析 里所言的：這樣的兩次關聯收縮，倘若第一次不完全收縮發生在第五輪的 col-ply 篩查階段，就會導致第二次的完全收縮接續不上，進而多加一次猜測行為。這是一個可改進之處。2.2 版本改進之后一直沒有碰到這種情形，直到這里僅用 ply 算法求解時才碰到。
另一道數獨題
這一道據說也挺有難度：
005 300 000 800 000 020 070 010 500 400 005 300 010 070 006 003 200 080 060 500 009 004 000 030 000 009 700
把這 9 行數字放到一個文本文件（比如 D:\read\num\Release\s.txt）的頭部位置。這次不對輸出做刪節處理，呈現完整的兩次 run 命令輸出：
D:\read\num\Release>sudoku.exe Order please: load-quiz s.txt Quiz loaded. Order please: run 2) row 2 complete shrunken by group 4) row 5 complete shrunken by group 2GW: 2 shrunken out of [4,3] 2GW: 8 shrunken out of [4,3] 2GW: 9 shrunken out of [4,3] 2GW: 5 shrunken out of [6,1] 2GW: 9 shrunken out of [6,1] CelSet: [4,3] [6,1] ValSet: 6 7 6) blk 4 incomplete shrunken by group 7) Guess [6,2] level 1 at 1 out of 2 8) row 5 complete shrunken by group 11) Guess [4,3] level 2 at 1 out of 2 13) col 3 complete shrunken by group 16) Guess [2,3] level 3 at 1 out of 2 18) Guess [3,3] level 4 at 1 out of 2 24) col 8 complete shrunken by group 28) row 3 complete shrunken by group 30) row 1 complete shrunken by group 32) row 1 complete shrunken by group 35) shrinking 1 from [9,1] went wrong 36) Forward guess [3,3] level 4 at 2 out of 2 2GW: 1 shrunken out of [1,8] 2GW: 4 shrunken out of [1,8] 2GW: 6 shrunken out of [1,8] 2GW: 1 shrunken out of [4,8] CelSet: [1,8] [4,8] ValSet: 7 9 37) col 8 incomplete shrunken by group 38) Guess [1,1] level 5 at 1 out of 2 40) shrinking 9 from [2,4] went wrong 41) Forward guess [1,1] level 5 at 2 out of 2 43) Guess [1,2] level 6 at 1 out of 2 46) row 2 complete shrunken by group 48) row 3 complete shrunken by group 50) row 4 complete shrunken by group 52) row 4 complete shrunken by group 54) shrinking 8 from [9,4] went wrong 55) Forward guess [1,2] level 6 at 2 out of 2 57) row 3 complete shrunken by group 59) row 8 complete shrunken by group 1GW: 8 shrunken out of [9,4] 1GW: 2 shrunken out of [9,5] 1GW: 8 shrunken out of [9,5] 1GW: 2 shrunken out of [9,9] 1GW: 8 shrunken out of [9,9] 61) row 9 incomplete shrunken by group 62) Guess [1,8] level 7 at 1 out of 2 64) shrinking 9 from [1,5] went wrong 65) Forward guess [1,8] level 7 at 2 out of 2 67) row 2 complete shrunken by group 69) row 4 complete shrunken by group 71) row 6 complete shrunken by group 73) col 4 complete shrunken by group 1GW: 4 shrunken out of [2,9] 75) blk 3 incomplete shrunken by group 76) Guess [1,5] level 8 at 1 out of 2 78) row 1 complete shrunken by group 81) Guess [1,7] level 9 at 1 out of 2 84) Guess [2,6] level 10 at 1 out of 2 87) row 9 complete shrunken by group 89) col 4 complete shrunken by group 92) Guess [4,2] level 11 at 1 out of 2 92) shrinking 8 from [8,7] went wrong 93) Forward guess [4,2] level 11 at 2 out of 2 93) shrinking 5 from [8,1] went wrong 94) Upward guess [2,6] level 10 at 2 out of 2 95) shrinking 5 from [9,9] went wrong 96) Upward guess [1,7] level 9 at 2 out of 2 96) shrinking 4 from blk[6,9] went wrong 97) Upward guess [1,5] level 8 at 2 out of 2 97) shrinking 7 from [2,9] went wrong 98) Upward guess [2,3] level 3 at 2 out of 2 102) row 3 complete shrunken by group 105) Guess [1,9] level 4 at 1 out of 2 106) row 4 complete shrunken by group 108) col 8 complete shrunken by group 2GW: 6 shrunken out of [8,4] 2GW: 8 shrunken out of [8,4] 2GW: 2 shrunken out of [8,6] 2GW: 6 shrunken out of [8,6] 2GW: 8 shrunken out of [8,6] CelSet: [8,4] [8,6] ValSet: 1 7 110) row 8 incomplete shrunken by group 111) Guess [1,8] level 5 at 1 out of 2 117) shrinking 2 from [4,2] went wrong 118) Forward guess [1,8] level 5 at 2 out of 2 120) shrinking 8 from [9,9] went wrong 121) Upward guess [1,9] level 4 at 2 out of 2 123) Guess [1,7] level 5 at 1 out of 2 124) col 8 complete shrunken by group 2GW: 4 shrunken out of [2,4] 2GW: 1 shrunken out of [8,4] 2GW: 8 shrunken out of [8,4] CelSet: [2,4] [8,4] ValSet: 6 7 126) col 4 incomplete shrunken by group 127) Guess [1,5] level 6 at 1 out of 2 145 327 698 839 654 127 672 918 543 496 185 372 218 473 956 753 296 481 367 542 819 984 761 235 521 839 764 Done [steps:131, solution sum:1]. Run time: 46 milliseconds; steps: 131, solution sum: 1. Order please: run 132) Forward guess [1,5] level 6 at 2 out of 2 1GW: 4 shrunken out of [2,6] 135) row 2 incomplete shrunken by group 136) Guess [2,4] level 7 at 1 out of 2 138) row 3 complete shrunken by group 139) shrinking 8 from blk[8,7] went wrong 140) Forward guess [2,4] level 7 at 2 out of 2 142) row 3 complete shrunken by group 143) shrinking 8 from blk[8,7] went wrong 144) Upward guess [1,7] level 5 at 2 out of 2 146) shrinking 8 from [9,4] went wrong 147) Upward guess [4,3] level 2 at 2 out of 2 149) row 6 complete shrunken by group 151) col 8 complete shrunken by group 154) Guess [4,8] level 3 at 1 out of 2 157) row 6 complete shrunken by group 1GW: 4 shrunken out of [1,7] 1GW: 4 shrunken out of [2,7] 159) col 7 incomplete shrunken by group 160) Guess [3,1] level 4 at 1 out of 2 163) shrinking 8 from [9,5] went wrong 164) Forward guess [3,1] level 4 at 2 out of 2 165) row 2 complete shrunken by group 167) row 7 complete shrunken by group 169) row 9 complete shrunken by group 172) Guess [2,2] level 5 at 1 out of 2 174) Guess [1,2] level 6 at 1 out of 2 176) row 3 complete shrunken by group 178) col 6 complete shrunken by group 180) row 5 complete shrunken by group 183) row 8 complete shrunken by group 184) shrinking 2 from [8,7] went wrong 185) Forward guess [1,2] level 6 at 2 out of 2 187) row 2 complete shrunken by group 189) shrinking 5 from [9,1] went wrong 190) Upward guess [2,2] level 5 at 2 out of 2 193) row 1 complete shrunken by group 194) shrinking 6 from [8,6] went wrong 195) Upward guess [4,8] level 3 at 2 out of 2 196) row 6 complete shrunken by group 199) Guess [3,8] level 4 at 1 out of 2 2GW: 1 shrunken out of [1,7] 2GW: 8 shrunken out of [1,7] 2GW: 1 shrunken out of [2,7] CelSet: [1,7] [2,7] ValSet: 6 9 201) col 7 incomplete shrunken by group 202) Guess [1,9] level 5 at 1 out of 2 203) shrinking 1 from [4,4] went wrong 204) Forward guess [1,9] level 5 at 2 out of 2 206) shrinking 1 from [4,4] went wrong 207) Upward guess [3,8] level 4 at 2 out of 2 208) col 3 complete shrunken by group 210) col 7 complete shrunken by group 212) col 6 complete shrunken by group 214) blk 1 complete shrunken by group 1GW: 1 shrunken out of [7,7] 1GW: 4 shrunken out of [7,7] 1GW: 1 shrunken out of [8,9] 1GW: 1 shrunken out of [9,9] 1GW: 4 shrunken out of [9,9] 216) blk 9 incomplete shrunken by group 217) Guess [1,9] level 5 at 1 out of 2 218) col 2 complete shrunken by group 221) shrinking 9 from [5,3] went wrong 222) Forward guess [1,9] level 5 at 2 out of 2 223) col 7 complete shrunken by group 225) col 7 complete shrunken by group 230) shrinking 8 from [4,4] went wrong 231) Upward guess [6,2] level 1 at 2 out of 2 232) row 6 complete shrunken by group 234) row 5 complete shrunken by group 236) row 6 complete shrunken by group 239) row 8 complete shrunken by group 241) row 9 complete shrunken by group 243) col 3 complete shrunken by group 245) blk 9 complete shrunken by group 248) Guess [1,2] level 2 at 1 out of 2 251) shrinking 7 from [1,9] went wrong 252) Forward guess [1,2] level 2 at 2 out of 2 254) row 3 complete shrunken by group 257) Guess [2,3] level 3 at 1 out of 2 1GW: 2 shrunken out of [9,1] 1GW: 8 shrunken out of [9,4] 1GW: 2 shrunken out of [9,5] 1GW: 8 shrunken out of [9,5] 1GW: 2 shrunken out of [9,9] 1GW: 8 shrunken out of [9,9] 258) row 9 incomplete shrunken by group 259) Guess [1,1] level 4 at 1 out of 2 260) shrinking 6 from [2,4] went wrong 261) Forward guess [1,1] level 4 at 2 out of 2 3GW: 2 shrunken out of [7,5] 3GW: 8 shrunken out of [7,5] 263) col 5 incomplete shrunken by group 264) Guess [2,7] level 5 at 1 out of 2 266) shrinking 2 from [7,7] went wrong 267) Forward guess [2,7] level 5 at 2 out of 2 268) row 1 complete shrunken by group 271) row 1 complete shrunken by group 273) row 5 complete shrunken by group 3GW: shrink went wrong 275) row 7 shrink by group went WRONG 276) Upward guess [2,3] level 3 at 2 out of 2 280) row 5 complete shrunken by group 282) col 7 complete shrunken by group 283) shrinking 6 from [2,4] went wrong 284) No more solution (solution sum is 1). 145 300 900 839 050 127 672 018 543 426 005 371 518 473 296 793 261 485 067 500 819 954 000 632 081 609 750 Invalid quiz [steps:284] - no more solution (solution sum is 1) Run time: 63 milliseconds; steps: 284, solution sum: 1. Order please: bye D:\read\num\Release>
可以看到，這個 quiz 的求解過程，出現的最深猜測級別為 11 級：
92) Guess [4,2] level 11 at 1 out of 2
僅比前面那個 quiz 少一級。但從用時和步數看，這個 quiz 要容易不少。