用C++实现的数独解题程序 SudokuSolver 2.2 及实例分析
SudokuSolver 2.2 程序实现
根据 用C++实现的数独解题程序 SudokuSolver 2.1 及实例分析 里分析，对 2.1 版做了一些改进和尝试。
CQuizDealer 类声明部分的修改
class CQuizDealer { public: ...
void run(ulong tilsteps = 0); void setOnlyGrpMode() {m_onlyGrp = true;} ...
private: ... CQuizDealer() : m_state(STA_UNLOADED), ..., m_onlyGrp(false) {}; inline void incSteps() {++m_steps;} inline bool IsDone(u8 ret) {return (ret == RET_OK || ret == RET_WRONG);}... u8 filterOneGroup(u8* pGrp); bool completeShrinkByGrp(u8* pGrp, u8* pTimes); u8 incompleteShrinkByGrp(u8 valSum, u8* pCelSumExs, u8* pGrp); bool sameCandidates(u8 cel1, u8 cel2); ...
ulong m_steps; bool m_onlyGrp; ... };
新增的 setOnlyGrpMode 接口用于控制只采用第一类收缩算法求解。
filterCandidates 接口实现修改
u8 CQuizDealer::filterCandidates() { incSteps(); u8 ret = RET_PENDING; 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_onlyGrp) { 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; }
增加了 onlyGrp 控制，即上面所说的是否只采用第一类收缩算法求解。末尾增加的条件递归调用，源自上一篇的实例分析。
filterRowGroup 接口实现修改
u8 CQuizDealer::filterRowGroup(u8 row) { u8 celIdxs[10] = {0}; // first item denotes sum of zeros u8 base = row * 9; for (u8 col = 0; col < 9; ++col) { if (m_seqCell[base + col].val == 0) { celIdxs[0] += 1; celIdxs[celIdxs[0]] = base + col; } } if (celIdxs[0] == 0) return RET_PENDING; u8 ret = filterOneGroup(celIdxs); if (ret == RET_OK) printf("%u) row %d complete shrunken by group\n", m_steps, (int)row + 1); else if (ret == RET_WRONG) printf("%u) row %d shrink by group went WRONG\n", m_steps, (int)row + 1); else if (ret == RET_SHRUNKEN) printf("%u) row %d incomplete shrunken by group\n", m_steps, (int)row + 1); return ret; }
filterColGroup 和 filterBlkGroup 接口修改类似。
filterOneGroup 接口新实现
1 u8 CQuizDealer::filterOneGroup(u8* pGrp) 2 { 3 u8 times[20] = {0}; 4 if (completeShrinkByGrp(pGrp, times)) 5 return RET_OK; 6 7 u8 size = pGrp[0]; 8 u8 celSumExs[100] = {0}; 9 for (u8 idx = 1; idx <= size; ++idx) { 10 u8 valSum = m_seqCell[pGrp[idx]].candidates[0]; 11 u8 base = valSum * 10; 12 celSumExs[base] += 1; 13 u8 pos = base + celSumExs[base]; 14 celSumExs[pos] = pGrp[idx]; 15 } 16 17 for (u8 idx = 2; idx <= 6; ++idx) { 18 u8 ret = incompleteShrinkByGrp(idx, celSumExs, pGrp); 19 if (ret != RET_PENDING) 20 return ret; 21 } 22 return RET_PENDING; 23 }
filterOneGroup 接口的原有实现只支持完全收缩，现在放到了新增 completeShrinkByGrp 接口里：
bool CQuizDealer::completeShrinkByGrp(u8* pGrp, u8* pTimes) { u8 size = pGrp[0]; for (u8 idx = 1; idx <= size; ++idx) { u8 sum = m_seqCell[pGrp[idx]].candidates[0]; for (u8 inn = 1; inn <= sum; ++inn) { u8 val = m_seqCell[pGrp[idx]].candidates[inn]; pTimes[val] += 1; pTimes[val + 9] = pGrp[idx]; } } bool ret = false; for (u8 val = 1; val <= 9; ++val) { if (pTimes[val] == 1) { ret = true; u8 celIdx = pTimes[val + 9]; m_seqCell[celIdx].candidates[0] = 1; m_seqCell[celIdx].candidates[1] = val; } } return ret; }
新增 incompleteShrinkByGrp 接口实现
1 u8 CQuizDealer::incompleteShrinkByGrp(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 } 44 } 45 return (shrunken ? RET_SHRUNKEN : RET_PENDING); 46 }
里面用到的 Item 结构以及 sameCandidates 接口为：
struct Item { u8 sameSum; u8 celIdxs[9]; Item() {sameSum = 0;} };
bool CQuizDealer::sameCandidates(u8 cel1, u8 cel2)
{
u8 sum = m_seqCell[cel1].candidates[0];
if (sum != m_seqCell[cel2].candidates[0])
return false;
for (u8 idx = 1; idx <= sum; ++idx)
if (m_seqCell[cel1].candidates[idx] != m_seqCell[cel2].candidates[idx])
return false;
return true;
}
filterRowCandidatesEx 接口实现小修改
u8 CQuizDealer::filterRowCandidatesEx(u8 row) { ...
for (u8 idx = 0; idx < 3; ++idx) { ret = filterRowByPolicy1(row, idx, vals, blkTakens); if (IsDone(ret)) return ret; } for (u8 idx = 0; idx < 3; ++idx) { ret = filterRowByPolicy2(row, idx, vals, blkTakens); if (IsDone(ret)) return ret; } return ret; }
filterColCandidatesEx 接口的修改类似。
shrinkRowCandidatesP1 接口实现小修改
u8 CQuizDealer::shrinkRowCandidatesP1(u8* pBlk, u8* pRow, u8 zeroSum, u8 row, u8 colBase) { ... u8 shrunken = 0; for (u8 col = colBase; col < colBase + 3; ++col) { ...
if (ret != RET_PENDING) { printf(" worked by row-ply1.\n"); if (ret == RET_OK) shrunken = 1; // complete else if (ret == RET_SHRUNKEN && shrunken == 0) shrunken = 2; // incomplete } } if (shrunken == 1) { ret = RET_OK; printf("%u) row %d shrunken ply-1 by blk %d\n", m_steps, (u8)row + 1, (u8)colBase / 3 + 1); } else if (shrunken == 2) ret = RET_SHRUNKEN; return ret; }
shrinkRowCandidatesP2 接口以及 shrinkColCandidatesP1 和 shrinkColCandidatesP2 接口的修改类似。
其他小修改
// 1.0 2021/9/20 // 2.0 2021/10/2 // 2.1 2021/10/4 #define STR_VER "Sudoku Solver 2.2 2021/10/10 by readalps\n\n" void showOrderList() { ... printf("onlygrp: only using group shrink\n"); printf("step: step forward\n"); ... } void dealOrder(std::string& strOrder) { ...
else if ("onlygrp" == strOrder) CQuizDealer::instance()->setOnlyGrpMode(); else if ("step" == strOrder)
...
实例分析
继续以 SudokuSolver 1.0：用C++实现的数独解题程序 【二】 里试验过的“最难”数独题为例做分析。在第一次 run 命令的输出中有如下信息：
506) Forward guess [1,4] level 11 at 2 out of 2 [2,1]: 1 4 5 9 shrunken to 5 9 worked by row-ply2. [2,8]: 4 5 9 shrunken to 5 9 worked by row-ply2. 509) Guess [1,3] level 12 at 1 out of 2
第 2 行有两个空位发生了不完全收缩，走的不是第一类收缩算法（by grp），而是第二类收缩算法（by ply）。重新用 runtil 506 命令进到当时的上下文做深入分析：
...
506) Forward guess [1,4] level 11 at 2 out of 2 820 703 601 003 600 807 070 090 203 050 007 104 000 045 706 007 100 935 001 009 568 008 500 319 090 000 472 Steps:506 Candidates: [1,3]: 4 5 9 [1,5]: 5 [1,8]: 4 5 9 [2,1]: 1 4 5 9 [2,2]: 1 4 [2,5]: 1 2 5 [2,6]: 1 2 4 [2,8]: 4 5 9 [3,1]: 1 4 5 6 [3,3]: 4 5 6 [3,4]: 4 8 [3,6]: 1 4 8 [3,8]: 4 5 [4,1]: 2 3 6 9 [4,3]: 2 6 9 [4,4]: 2 3 8 9 [4,5]: 2 3 6 8 [4,8]: 2 8 [5,1]: 1 2 3 9 [5,2]: 1 3 8 [5,3]: 2 9 [5,4]: 2 3 8 9 [5,8]: 2 8 [6,1]: 2 4 6 [6,2]: 4 6 8 [6,5]: 2 6 8 [6,6]: 2 6 8 [7,1]: 2 3 4 7 [7,2]: 3 4 [7,4]: 2 3 4 [7,5]: 2 3 7 [8,1]: 2 4 6 7 [8,2]: 4 6 [8,5]: 2 6 7 [8,6]: 2 4 6 [9,1]: 3 5 6 [9,3]: 5 6 [9,4]: 3 8 [9,5]: 1 3 6 8 [9,6]: 1 6 8 The foremost cell with 1 candidate(s) at [1,5] At guess level 11 [1,4] 2 Run time: 326 milliseconds; steps: 506, solution sum: 0. Order please:
由 The foremost cell with 1 candidate(s) at [1,5] 可知当时 [1,5] 位置可以直接填值。先走完这一步：
Order please: step 820 753 601 003 600 807 070 090 203 050 007 104 000 045 706 007 100 935 001 009 568 008 500 319 090 000 472 Steps:507 Candidates: [1,3]: 4 9 [1,8]: 4 9 [2,1]: 1 4 5 9 [2,2]: 1 4 [2,5]: 1 2 [2,6]: 1 2 4 [2,8]: 4 5 9 [3,1]: 1 4 5 6 [3,3]: 4 5 6 [3,4]: 4 8 [3,6]: 1 4 8 [3,8]: 4 5 [4,1]: 2 3 6 9 [4,3]: 2 6 9 [4,4]: 2 3 8 9 [4,5]: 2 3 6 8 [4,8]: 2 8 [5,1]: 1 2 3 9 [5,2]: 1 3 8 [5,3]: 2 9 [5,4]: 2 3 8 9 [5,8]: 2 8 [6,1]: 2 4 6 [6,2]: 4 6 8 [6,5]: 2 6 8 [6,6]: 2 6 8 [7,1]: 2 3 4 7 [7,2]: 3 4 [7,4]: 2 3 4 [7,5]: 2 3 7 [8,1]: 2 4 6 7 [8,2]: 4 6 [8,5]: 2 6 7 [8,6]: 2 4 6 [9,1]: 3 5 6 [9,3]: 5 6 [9,4]: 3 8 [9,5]: 1 3 6 8 [9,6]: 1 6 8 The foremost cell with 2 candidate(s) at [1,3] At guess level 11 [1,4] 2 Order please:
走完 507 步时，第 2 行的空位候选值分布情况为：
[2,1]: 1 4 5 9 [2,2]: 1 4 [2,5]: 1 2 [2,6]: 1 2 4 [2,8]: 4 5 9
这里，5 和 9 只能填入两个空位，即 [2,1] 和 [2,8] 中，因此，这两个空位只能是一个填 5 另一个填 9。于是，这两个空位里的除 5 和 9 之外的其他候选值都可以排除掉。这和上一篇的实例分析部分发现的 grp 算法可改进之处还不一样，这是新发现的一处可以改进 grp 算法的地方。
