#include #include #ifndef RJ //#define RJ // Uncheck for debugging #endif int q, // Number of unsolved Cell positions Grid wise r[81], // Used for sorting and eliminating each unsolved Cell positions Grid wise s[81], // Sudoku Grid 81 Cell positions for clues and solved g[81], // Bitwise Candidates for each unsolved Cell positions Grid wise n[3]; // Number of Naked Singles, Hidden Singles and Guesses Grid wise static int b[512] = { // Bitwise Candidates 0, 1, 2, 12, 3, 13, 23, 123, 4, 14, 24, 124, 34, 134, 234, 1234, 5, 15, 25, 125, 35, 135, 235, 1235, 45, 145, 245, 1245, 345, 1345, 2345, 12345, 6, 16, 26, 126, 36, 136, 236, 1236, 46, 146, 246, 1246, 346, 1346, 2346, 12346, 56, 156, 256, 1256, 356, 1356, 2356, 12356, 456, 1456, 2456, 12456, 3456, 13456, 23456, 123456, 7, 17, 27, 127, 37, 137, 237, 1237, 47, 147, 247, 1247, 347, 1347, 2347, 12347, 57, 157, 257, 1257, 357, 1357, 2357, 12357, 457, 1457, 2457, 12457, 3457, 13457, 23457, 123457, 67, 167, 267, 1267, 367, 1367, 2367, 12367, 467, 1467, 2467, 12467, 3467, 13467, 23467, 123467, 567, 1567, 2567, 12567, 3567, 13567, 23567, 123567, 4567, 14567, 24567, 124567, 34567, 134567, 234567, 1234567, 8, 18, 28, 128, 38, 138, 238, 1238, 48, 148, 248, 1248, 348, 1348, 2348, 12348, 58, 158, 258, 1258, 358, 1358, 2358, 12358, 458, 1458, 2458, 12458, 3458, 13458, 23458, 123458, 68, 168, 268, 1268, 368, 1368, 2368, 12368, 468, 1468, 2468, 12468, 3468, 13468, 23468, 123468, 568, 1568, 2568, 12568, 3568, 13568, 23568, 123568, 4568, 14568, 24568, 124568, 34568, 134568, 234568, 1234568, 78, 178, 278, 1278, 378, 1378, 2378, 12378, 478, 1478, 2478, 12478, 3478, 13478, 23478, 123478, 578, 1578, 2578, 12578, 3578, 13578, 23578, 123578, 4578, 14578, 24578, 124578, 34578, 134578, 234578, 1234578, 378, 1678, 2678, 12678, 3678, 13678, 23678, 123678, 4678, 14678, 24678, 124678, 34678, 134678, 234678, 1234678, 5678, 15678, 25678, 125678, 35678, 135678, 235678, 1235678, 45678, 145678, 245678, 1245678, 345678, 1345678, 2345678, 12345678, 9, 19, 29, 129, 39, 139, 239, 1239, 49, 149, 249, 1249, 349, 1349, 2349, 12349, 59, 159, 259, 1259, 359, 1359, 2359, 12359, 459, 1459, 2459, 12459, 3459, 13459, 23459, 123459, 69, 169, 269, 1269, 369, 1369, 2369, 12369, 469, 1469, 2469, 12469, 3469, 13469, 23469, 123469, 569, 1569, 2569, 12569, 3569, 13569, 23569, 123569, 4569, 14569, 24569, 124569, 34569, 134569, 234569, 1234569, 79, 179, 279, 1279, 379, 1379, 2379, 12379, 479, 1479, 2479, 12479, 3479, 13479, 23479, 123479, 579, 1579, 2579, 12579, 3579, 13579, 23579, 123579, 4579, 14579, 24579, 124579, 34579, 134579, 234579, 1234579, 679, 1679, 2679, 12679, 3679, 13679, 23679, 123679, 4679, 14679, 24679, 124679, 34679, 134679, 234679, 1234679, 5679, 15679, 25679, 125679, 35679, 135679, 235679, 1235679, 45679, 145679, 245679, 1245679, 345679, 1345679, 2345679, 12345679, 89, 189, 289, 1289, 389, 1389, 2389, 12389, 489, 1489, 2489, 12489, 3489, 13489, 23489, 123489, 589, 1589, 2589, 12589, 3589, 13589, 23589, 123589, 4589, 14589, 24589, 124589, 34589, 134589, 234589, 1234589, 689, 1689, 2689, 12689, 3689, 13689, 23689, 123689, 4689, 14689, 24689, 124689, 34689, 134689, 234689, 1234689, 5689, 15689, 25689, 125689, 35689, 135689, 235689, 1235689, 45689, 145689, 245689, 1245689, 345689, 1345689, 2345689, 12345689, 789, 1789, 2789, 12789, 3789, 13789, 23789, 123789, 4789, 14789, 24789, 124789, 34789, 134789, 234789, 1234789, 5789, 15789, 25789, 125789, 35789, 135789, 235789, 1235789, 45789, 145789, 245789, 1245789, 345789, 1345789, 2345789, 12345789, 6789, 16789, 26789, 126789, 36789, 136789, 236789, 1236789, 46789, 146789, 246789, 1246789, 346789, 1346789, 2346789, 12346789, 56789, 156789, 256789, 1256789, 356789, 1356789, 2356789, 12356789, 456789, 1456789, 2456789, 12456789, 3456789, 13456789, 23456789,123456789}, B[512] = { // Count bitwise Candidates 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9}, w[81][20] = { // 20 affected Cell positions for 81 Cell positions { 3, 4, 5, 6, 7, 8, 1, 2,10,11,19,20, 9,18,27,36,45,54,63,72}, { 3, 4, 5, 6, 7, 8, 0, 2, 9,11,18,20,10,19,28,37,46,55,64,73}, { 3, 4, 5, 6, 7, 8, 0, 1, 9,10,18,19,11,20,29,38,47,56,65,74}, { 0, 1, 2, 6, 7, 8, 4, 5,13,14,22,23,12,21,30,39,48,57,66,75}, { 0, 1, 2, 6, 7, 8, 3, 5,12,14,21,23,13,22,31,40,49,58,67,76}, { 0, 1, 2, 6, 7, 8, 3, 4,12,13,21,22,14,23,32,41,50,59,68,77}, { 0, 1, 2, 3, 4, 5, 7, 8,16,17,25,26,15,24,33,42,51,60,69,78}, { 0, 1, 2, 3, 4, 5, 6, 8,15,17,24,26,16,25,34,43,52,61,70,79}, { 0, 1, 2, 3, 4, 5, 6, 7,15,16,24,25,17,26,35,44,53,62,71,80}, {12,13,14,15,16,17,10,11, 1, 2,19,20, 0,18,27,36,45,54,63,72}, {12,13,14,15,16,17, 9,11, 0, 2,18,20, 1,19,28,37,46,55,64,73}, {12,13,14,15,16,17, 9,10, 0, 1,18,19, 2,20,29,38,47,56,65,74}, { 9,10,11,15,16,17,13,14, 4, 5,22,23, 3,21,30,39,48,57,66,75}, { 9,10,11,15,16,17,12,14, 3, 5,21,23, 4,22,31,40,49,58,67,76}, { 9,10,11,15,16,17,12,13, 3, 4,21,22, 5,23,32,41,50,59,68,77}, { 9,10,11,12,13,14,16,17, 7, 8,25,26, 6,24,33,42,51,60,69,78}, { 9,10,11,12,13,14,15,17, 6, 8,24,26, 7,25,34,43,52,61,70,79}, { 9,10,11,12,13,14,15,16, 6, 7,24,25, 8,26,35,44,53,62,71,80}, {21,22,23,24,25,26,19,20, 1, 2,10,11, 0, 9,27,36,45,54,63,72}, {21,22,23,24,25,26,18,20, 0, 2, 9,11, 1,10,28,37,46,55,64,73}, {21,22,23,24,25,26,18,19, 0, 1, 9,10, 2,11,29,38,47,56,65,74}, {18,19,20,24,25,26,22,23, 4, 5,13,14, 3,12,30,39,48,57,66,75}, {18,19,20,24,25,26,21,23, 3, 5,12,14, 4,13,31,40,49,58,67,76}, {18,19,20,24,25,26,21,22, 3, 4,12,13, 5,14,32,41,50,59,68,77}, {18,19,20,21,22,23,25,26, 7, 8,16,17, 6,15,33,42,51,60,69,78}, {18,19,20,21,22,23,24,26, 6, 8,15,17, 7,16,34,43,52,61,70,79}, {18,19,20,21,22,23,24,25, 6, 7,15,16, 8,17,35,44,53,62,71,80}, {30,31,32,33,34,35,28,29,37,38,46,47,36,45, 0, 9,18,54,63,72}, {30,31,32,33,34,35,27,29,36,38,45,47,37,46, 1,10,19,55,64,73}, {30,31,32,33,34,35,27,28,36,37,45,46,38,47, 2,11,20,56,65,74}, {27,28,29,33,34,35,31,32,40,41,49,50,39,48, 3,12,21,57,66,75}, {27,28,29,33,34,35,30,32,39,41,48,50,40,49, 4,13,22,58,67,76}, {27,28,29,33,34,35,30,31,39,40,48,49,41,50, 5,14,23,59,68,77}, {27,28,29,30,31,32,34,35,43,44,52,53,42,51, 6,15,24,60,69,78}, {27,28,29,30,31,32,33,35,42,44,51,53,43,52, 7,16,25,61,70,79}, {27,28,29,30,31,32,33,34,42,43,51,52,44,53, 8,17,26,62,71,80}, {39,40,41,42,43,44,37,38,28,29,46,47,27,45, 0, 9,18,54,63,72}, {39,40,41,42,43,44,36,38,27,29,45,47,28,46, 1,10,19,55,64,73}, {39,40,41,42,43,44,36,37,27,28,45,46,29,47, 2,11,20,56,65,74}, {36,37,38,42,43,44,40,41,31,32,49,50,30,48, 3,12,21,57,66,75}, {36,37,38,42,43,44,39,41,30,32,48,50,31,49, 4,13,22,58,67,76}, {36,37,38,42,43,44,39,40,30,31,48,49,32,50, 5,14,23,59,68,77}, {36,37,38,39,40,41,43,44,34,35,52,53,33,51, 6,15,24,60,69,78}, {36,37,38,39,40,41,42,44,33,35,51,53,34,52, 7,16,25,61,70,79}, {36,37,38,39,40,41,42,43,33,34,51,52,35,53, 8,17,26,62,71,80}, {48,49,50,51,52,53,46,47,28,29,37,38,27,36, 0, 9,18,54,63,72}, {48,49,50,51,52,53,45,47,27,29,36,38,28,37, 1,10,19,55,64,73}, {48,49,50,51,52,53,45,46,27,28,36,37,29,38, 2,11,20,56,65,74}, {45,46,47,51,52,53,49,50,31,32,40,41,30,39, 3,12,21,57,66,75}, {45,46,47,51,52,53,48,50,30,32,39,41,31,40, 4,13,22,58,67,76}, {45,46,47,51,52,53,48,49,30,31,39,40,32,41, 5,14,23,59,68,77}, {45,46,47,48,49,50,52,53,34,35,43,44,33,42, 6,15,24,60,69,78}, {45,46,47,48,49,50,51,53,33,35,42,44,34,43, 7,16,25,61,70,79}, {45,46,47,48,49,50,51,52,33,34,42,43,35,44, 8,17,26,62,71,80}, {57,58,59,60,61,62,55,56,64,65,73,74,63,72, 0, 9,18,27,36,45}, {57,58,59,60,61,62,54,56,63,65,72,74,64,73, 1,10,19,28,37,46}, {57,58,59,60,61,62,54,55,63,64,72,73,65,74, 2,11,20,29,38,47}, {54,55,56,60,61,62,58,59,67,68,76,77,66,75, 3,12,21,30,39,48}, {54,55,56,60,61,62,57,59,66,68,75,77,67,76, 4,13,22,31,40,49}, {54,55,56,60,61,62,57,58,66,67,75,76,68,77, 5,14,23,32,41,50}, {54,55,56,57,58,59,61,62,70,71,79,80,69,78, 6,15,24,33,42,51}, {54,55,56,57,58,59,60,62,69,71,78,80,70,79, 7,16,25,34,43,52}, {54,55,56,57,58,59,60,61,69,70,78,79,71,80, 8,17,26,35,44,53}, {66,67,68,69,70,71,64,65,55,56,73,74,54,72, 0, 9,18,27,36,45}, {66,67,68,69,70,71,63,65,54,56,72,74,55,73, 1,10,19,28,37,46}, {66,67,68,69,70,71,63,64,54,55,72,73,56,74, 2,11,20,29,38,47}, {63,64,65,69,70,71,67,68,58,59,76,77,57,75, 3,12,21,30,39,48}, {63,64,65,69,70,71,66,68,57,59,75,77,58,76, 4,13,22,31,40,49}, {63,64,65,69,70,71,66,67,57,58,75,76,59,77, 5,14,23,32,41,50}, {63,64,65,66,67,68,70,71,61,62,79,80,60,78, 6,15,24,33,42,51}, {63,64,65,66,67,68,69,71,60,62,78,80,61,79, 7,16,25,34,43,52}, {63,64,65,66,67,68,69,70,60,61,78,79,62,80, 8,17,26,35,44,53}, {75,76,77,78,79,80,73,74,55,56,64,65,54,63, 0, 9,18,27,36,45}, {75,76,77,78,79,80,72,74,54,56,63,65,55,64, 1,10,19,28,37,46}, {75,76,77,78,79,80,72,73,54,55,63,64,56,65, 2,11,20,29,38,47}, {72,73,74,78,79,80,76,77,58,59,67,68,57,66, 3,12,21,30,39,48}, {72,73,74,78,79,80,75,77,57,59,66,68,58,67, 4,13,22,31,40,49}, {72,73,74,78,79,80,75,76,57,58,66,67,59,68, 5,14,23,32,41,50}, {72,73,74,75,76,77,79,80,61,62,70,71,60,69, 6,15,24,33,42,51}, {72,73,74,75,76,77,78,80,60,62,69,71,61,70, 7,16,25,34,43,52}, {72,73,74,75,76,77,78,79,60,61,69,70,62,71, 8,17,26,35,44,53}}, l[27][9] = { // 9 Cell positions for 27 Units { 0, 1, 2, 3, 4, 5, 6, 7, 8}, { 9,10,11,12,13,14,15,16,17}, {18,19,20,21,22,23,24,25,26}, {27,28,29,30,31,32,33,34,35}, {36,37,38,39,40,41,42,43,44}, {45,46,47,48,49,50,51,52,53}, {54,55,56,57,58,59,60,61,62}, {63,64,65,66,67,68,69,70,71}, {72,73,74,75,76,77,78,79,80}, { 0, 9,18,27,36,45,54,63,72}, { 1,10,19,28,37,46,55,64,73}, { 2,11,20,29,38,47,56,65,74}, { 3,12,21,30,39,48,57,66,75}, { 4,13,22,31,40,49,58,67,76}, { 5,14,23,32,41,50,59,68,77}, { 6,15,24,33,42,51,60,69,78}, { 7,16,25,34,43,52,61,70,79}, { 8,17,26,35,44,53,62,71,80}, { 0, 1, 2, 9,10,11,18,19,20}, { 3, 4, 5,12,13,14,21,22,23}, { 6, 7, 8,15,16,17,24,25,26}, {27,28,29,36,37,38,45,46,47}, {30,31,32,39,40,41,48,49,50}, {33,34,35,42,43,44,51,52,53}, {54,55,56,63,64,65,72,73,74}, {57,58,59,66,67,68,75,76,77}, {60,61,62,69,70,71,78,79,80}}, h[246][9] = { // 36 pairs/84 triplets/126 quads and other Cell positions for each Unit { 0, 1, 2, 3, 4, 5, 6, 7, 8}, { 0, 2, 1, 3, 4, 5, 6, 7, 8}, { 0, 3, 1, 2, 4, 5, 6, 7, 8}, { 0, 4, 1, 2, 3, 5, 6, 7, 8}, { 0, 5, 1, 2, 3, 4, 6, 7, 8}, { 0, 6, 1, 2, 3, 4, 5, 7, 8}, { 0, 7, 1, 2, 3, 4, 5, 6, 8}, { 0, 8, 1, 2, 3, 4, 5, 6, 7}, { 1, 2, 0, 3, 4, 5, 6, 7, 8}, { 1, 3, 0, 2, 4, 5, 6, 7, 8}, { 1, 4, 0, 2, 3, 5, 6, 7, 8}, { 1, 5, 0, 2, 3, 4, 6, 7, 8}, { 1, 6, 0, 2, 3, 4, 5, 7, 8}, { 1, 7, 0, 2, 3, 4, 5, 6, 8}, { 1, 8, 0, 2, 3, 4, 5, 6, 7}, { 2, 3, 0, 1, 4, 5, 6, 7, 8}, { 2, 4, 0, 1, 3, 5, 6, 7, 8}, { 2, 5, 0, 1, 3, 4, 6, 7, 8}, { 2, 6, 0, 1, 3, 4, 5, 7, 8}, { 2, 7, 0, 1, 3, 4, 5, 6, 8}, { 2, 8, 0, 1, 3, 4, 5, 6, 7}, { 3, 4, 0, 1, 2, 5, 6, 7, 8}, { 3, 5, 0, 1, 2, 4, 6, 7, 8}, { 3, 6, 0, 1, 2, 4, 5, 7, 8}, { 3, 7, 0, 1, 2, 4, 5, 6, 8}, { 3, 8, 0, 1, 2, 4, 5, 6, 7}, { 4, 5, 0, 1, 2, 3, 6, 7, 8}, { 4, 6, 0, 1, 2, 3, 5, 7, 8}, { 4, 7, 0, 1, 2, 3, 5, 6, 8}, { 4, 8, 0, 1, 2, 3, 5, 6, 7}, { 5, 6, 0, 1, 2, 3, 4, 7, 8}, { 5, 7, 0, 1, 2, 3, 4, 6, 8}, { 5, 8, 0, 1, 2, 3, 4, 6, 7}, { 6, 7, 0, 1, 2, 3, 4, 5, 8}, { 6, 8, 0, 1, 2, 3, 4, 5, 7}, { 7, 8, 0, 1, 2, 3, 4, 5, 6}, { 0, 1, 2, 3, 4, 5, 6, 7, 8}, { 0, 1, 3, 2, 4, 5, 6, 7, 8}, { 0, 1, 4, 2, 3, 5, 6, 7, 8}, { 0, 1, 5, 2, 3, 4, 6, 7, 8}, { 0, 1, 6, 2, 3, 4, 5, 7, 8}, { 0, 1, 7, 2, 3, 4, 5, 6, 8}, { 0, 1, 8, 2, 3, 4, 5, 6, 7}, { 0, 2, 3, 1, 4, 5, 6, 7, 8}, { 0, 2, 4, 1, 3, 5, 6, 7, 8}, { 0, 2, 5, 1, 3, 4, 6, 7, 8}, { 0, 2, 6, 1, 3, 4, 5, 7, 8}, { 0, 2, 7, 1, 3, 4, 5, 6, 8}, { 0, 2, 8, 1, 3, 4, 5, 6, 7}, { 0, 3, 4, 1, 2, 5, 6, 7, 8}, { 0, 3, 5, 1, 2, 4, 6, 7, 8}, { 0, 3, 6, 1, 2, 4, 5, 7, 8}, { 0, 3, 7, 1, 2, 4, 5, 6, 8}, { 0, 3, 8, 1, 2, 4, 5, 6, 7}, { 0, 4, 5, 1, 2, 3, 6, 7, 8}, { 0, 4, 6, 1, 2, 3, 5, 7, 8}, { 0, 4, 7, 1, 2, 3, 5, 6, 8}, { 0, 4, 8, 1, 2, 3, 5, 6, 7}, { 0, 5, 6, 1, 2, 3, 4, 7, 8}, { 0, 5, 7, 1, 2, 3, 4, 6, 8}, { 0, 5, 8, 1, 2, 3, 4, 6, 7}, { 0, 6, 7, 1, 2, 3, 4, 5, 8}, { 0, 6, 8, 1, 2, 3, 4, 5, 7}, { 0, 7, 8, 1, 2, 3, 4, 5, 6}, { 1, 2, 3, 0, 4, 5, 6, 7, 8}, { 1, 2, 4, 0, 3, 5, 6, 7, 8}, { 1, 2, 5, 0, 3, 4, 6, 7, 8}, { 1, 2, 6, 0, 3, 4, 5, 7, 8}, { 1, 2, 7, 0, 3, 4, 5, 6, 8}, { 1, 2, 8, 0, 3, 4, 5, 6, 7}, { 1, 3, 4, 0, 2, 5, 6, 7, 8}, { 1, 3, 5, 0, 2, 4, 6, 7, 8}, { 1, 3, 6, 0, 2, 4, 5, 7, 8}, { 1, 3, 7, 0, 2, 4, 5, 6, 8}, { 1, 3, 8, 0, 2, 4, 5, 6, 7}, { 1, 4, 5, 0, 2, 3, 6, 7, 8}, { 1, 4, 6, 0, 2, 3, 5, 7, 8}, { 1, 4, 7, 0, 2, 3, 5, 6, 8}, { 1, 4, 8, 0, 2, 3, 5, 6, 7}, { 1, 5, 6, 0, 2, 3, 4, 7, 8}, { 1, 5, 7, 0, 2, 3, 4, 6, 8}, { 1, 5, 8, 0, 2, 3, 4, 6, 7}, { 1, 6, 7, 0, 2, 3, 4, 5, 8}, { 1, 6, 8, 0, 2, 3, 4, 5, 7}, { 1, 7, 8, 0, 2, 3, 4, 5, 6}, { 2, 3, 4, 0, 1, 5, 6, 7, 8}, { 2, 3, 5, 0, 1, 4, 6, 7, 8}, { 2, 3, 6, 0, 1, 4, 5, 7, 8}, { 2, 3, 7, 0, 1, 4, 5, 6, 8}, { 2, 3, 8, 0, 1, 4, 5, 6, 7}, { 2, 4, 5, 0, 1, 3, 6, 7, 8}, { 2, 4, 6, 0, 1, 3, 5, 7, 8}, { 2, 4, 7, 0, 1, 3, 5, 6, 8}, { 2, 4, 8, 0, 1, 3, 5, 6, 7}, { 2, 5, 6, 0, 1, 3, 4, 7, 8}, { 2, 5, 7, 0, 1, 3, 4, 6, 8}, { 2, 5, 8, 0, 1, 3, 4, 6, 7}, { 2, 6, 7, 0, 1, 3, 4, 5, 8}, { 2, 6, 8, 0, 1, 3, 4, 5, 7}, { 2, 7, 8, 0, 1, 3, 4, 5, 6}, { 3, 4, 5, 0, 1, 2, 6, 7, 8}, { 3, 4, 6, 0, 1, 2, 5, 7, 8}, { 3, 4, 7, 0, 1, 2, 5, 6, 8}, { 3, 4, 8, 0, 1, 2, 5, 6, 7}, { 3, 5, 6, 0, 1, 2, 4, 7, 8}, { 3, 5, 7, 0, 1, 2, 4, 6, 8}, { 3, 5, 8, 0, 1, 2, 4, 6, 7}, { 3, 6, 7, 0, 1, 2, 4, 5, 8}, { 3, 6, 8, 0, 1, 2, 4, 5, 7}, { 3, 7, 8, 0, 1, 2, 4, 5, 6}, { 4, 5, 6, 0, 1, 2, 3, 7, 8}, { 4, 5, 7, 0, 1, 2, 3, 6, 8}, { 4, 5, 8, 0, 1, 2, 3, 6, 7}, { 4, 6, 7, 0, 1, 2, 3, 5, 8}, { 4, 6, 8, 0, 1, 2, 3, 5, 7}, { 4, 7, 8, 0, 1, 2, 3, 5, 6}, { 5, 6, 7, 0, 1, 2, 3, 4, 8}, { 5, 6, 8, 0, 1, 2, 3, 4, 7}, { 5, 7, 8, 0, 1, 2, 3, 4, 6}, { 6, 7, 8, 0, 1, 2, 3, 4, 5}, { 0, 1, 2, 3, 4, 5, 6, 7, 8}, { 0, 1, 2, 4, 3, 5, 6, 7, 8}, { 0, 1, 2, 5, 3, 4, 6, 7, 8}, { 0, 1, 2, 6, 3, 4, 5, 7, 8}, { 0, 1, 2, 7, 3, 4, 5, 6, 8}, { 0, 1, 2, 8, 3, 4, 5, 6, 7}, { 0, 1, 3, 4, 2, 5, 6, 7, 8}, { 0, 1, 3, 5, 2, 4, 6, 7, 8}, { 0, 1, 3, 6, 2, 4, 5, 7, 8}, { 0, 1, 3, 7, 2, 4, 5, 6, 8}, { 0, 1, 3, 8, 2, 4, 5, 6, 7}, { 0, 1, 4, 5, 2, 3, 6, 7, 8}, { 0, 1, 4, 6, 2, 3, 5, 7, 8}, { 0, 1, 4, 7, 2, 3, 5, 6, 8}, { 0, 1, 4, 8, 2, 3, 5, 6, 7}, { 0, 1, 5, 6, 2, 3, 4, 7, 8}, { 0, 1, 5, 7, 2, 3, 4, 6, 8}, { 0, 1, 5, 8, 2, 3, 4, 6, 7}, { 0, 1, 6, 7, 2, 3, 4, 5, 8}, { 0, 1, 6, 8, 2, 3, 4, 5, 7}, { 0, 1, 7, 8, 2, 3, 4, 5, 6}, { 0, 2, 3, 4, 1, 5, 6, 7, 8}, { 0, 2, 3, 5, 1, 4, 6, 7, 8}, { 0, 2, 3, 6, 1, 4, 5, 7, 8}, { 0, 2, 3, 7, 1, 4, 5, 6, 8}, { 0, 2, 3, 8, 1, 4, 5, 6, 7}, { 0, 2, 4, 5, 1, 3, 6, 7, 8}, { 0, 2, 4, 6, 1, 3, 5, 7, 8}, { 0, 2, 4, 7, 1, 3, 5, 6, 8}, { 0, 2, 4, 8, 1, 3, 5, 6, 7}, { 0, 2, 5, 6, 1, 3, 4, 7, 8}, { 0, 2, 5, 7, 1, 3, 4, 6, 8}, { 0, 2, 5, 8, 1, 3, 4, 6, 7}, { 0, 2, 6, 7, 1, 3, 4, 5, 8}, { 0, 2, 6, 8, 1, 3, 4, 5, 7}, { 0, 2, 7, 8, 1, 3, 4, 5, 6}, { 0, 3, 4, 5, 1, 2, 6, 7, 8}, { 0, 3, 4, 6, 1, 2, 5, 7, 8}, { 0, 3, 4, 7, 1, 2, 5, 6, 8}, { 0, 3, 4, 8, 1, 2, 5, 6, 7}, { 0, 3, 5, 6, 1, 2, 4, 7, 8}, { 0, 3, 5, 7, 1, 2, 4, 6, 8}, { 0, 3, 5, 8, 1, 2, 4, 6, 7}, { 0, 3, 6, 7, 1, 2, 4, 5, 8}, { 0, 3, 6, 8, 1, 2, 4, 5, 7}, { 0, 3, 7, 8, 1, 2, 4, 5, 6}, { 0, 4, 5, 6, 1, 2, 3, 7, 8}, { 0, 4, 5, 7, 1, 2, 3, 6, 8}, { 0, 4, 5, 8, 1, 2, 3, 6, 7}, { 0, 4, 6, 7, 1, 2, 3, 5, 8}, { 0, 4, 6, 8, 1, 2, 3, 5, 7}, { 0, 4, 7, 8, 1, 2, 3, 5, 6}, { 0, 5, 6, 7, 1, 2, 3, 4, 8}, { 0, 5, 6, 8, 1, 2, 3, 4, 7}, { 0, 5, 7, 8, 1, 2, 3, 4, 6}, { 0, 6, 7, 8, 1, 2, 3, 4, 5}, { 1, 2, 3, 4, 0, 5, 6, 7, 8}, { 1, 2, 3, 5, 0, 4, 6, 7, 8}, { 1, 2, 3, 6, 0, 4, 5, 7, 8}, { 1, 2, 3, 7, 0, 4, 5, 6, 8}, { 1, 2, 3, 8, 0, 4, 5, 6, 7}, { 1, 2, 4, 5, 0, 3, 6, 7, 8}, { 1, 2, 4, 6, 0, 3, 5, 7, 8}, { 1, 2, 4, 7, 0, 3, 5, 6, 8}, { 1, 2, 4, 8, 0, 3, 5, 6, 7}, { 1, 2, 5, 6, 0, 3, 4, 7, 8}, { 1, 2, 5, 7, 0, 3, 4, 6, 8}, { 1, 2, 5, 8, 0, 3, 4, 6, 7}, { 1, 2, 6, 7, 0, 3, 4, 5, 8}, { 1, 2, 6, 8, 0, 3, 4, 5, 7}, { 1, 2, 7, 8, 0, 3, 4, 5, 6}, { 1, 3, 4, 5, 0, 2, 6, 7, 8}, { 1, 3, 4, 6, 0, 2, 5, 7, 8}, { 1, 3, 4, 7, 0, 2, 5, 6, 8}, { 1, 3, 4, 8, 0, 2, 5, 6, 7}, { 1, 3, 5, 6, 0, 2, 4, 7, 8}, { 1, 3, 5, 7, 0, 2, 4, 6, 8}, { 1, 3, 5, 8, 0, 2, 4, 6, 7}, { 1, 3, 6, 7, 0, 2, 4, 5, 8}, { 1, 3, 6, 8, 0, 2, 4, 5, 7}, { 1, 3, 7, 8, 0, 2, 4, 5, 6}, { 1, 4, 5, 6, 0, 2, 3, 7, 8}, { 1, 4, 5, 7, 0, 2, 3, 6, 8}, { 1, 4, 5, 8, 0, 2, 3, 6, 7}, { 1, 4, 6, 7, 0, 2, 3, 5, 8}, { 1, 4, 6, 8, 0, 2, 3, 5, 7}, { 1, 4, 7, 8, 0, 2, 3, 5, 6}, { 1, 5, 6, 7, 0, 2, 3, 4, 8}, { 1, 5, 6, 8, 0, 2, 3, 4, 7}, { 1, 5, 7, 8, 0, 2, 3, 4, 6}, { 1, 6, 7, 8, 0, 2, 3, 4, 5}, { 2, 3, 4, 5, 0, 1, 6, 7, 8}, { 2, 3, 4, 6, 0, 1, 5, 7, 8}, { 2, 3, 4, 7, 0, 1, 5, 6, 8}, { 2, 3, 4, 8, 0, 1, 5, 6, 7}, { 2, 3, 5, 6, 0, 1, 4, 7, 8}, { 2, 3, 5, 7, 0, 1, 4, 6, 8}, { 2, 3, 5, 8, 0, 1, 4, 6, 7}, { 2, 3, 6, 7, 0, 1, 4, 5, 8}, { 2, 3, 6, 8, 0, 1, 4, 5, 7}, { 2, 3, 7, 8, 0, 1, 4, 5, 6}, { 2, 4, 5, 6, 0, 1, 3, 7, 8}, { 2, 4, 5, 7, 0, 1, 3, 6, 8}, { 2, 4, 5, 8, 0, 1, 3, 6, 7}, { 2, 4, 6, 7, 0, 1, 3, 5, 8}, { 2, 4, 6, 8, 0, 1, 3, 5, 7}, { 2, 4, 7, 8, 0, 1, 3, 5, 6}, { 2, 5, 6, 7, 0, 1, 3, 4, 8}, { 2, 5, 6, 8, 0, 1, 3, 4, 7}, { 2, 5, 7, 8, 0, 1, 3, 4, 6}, { 2, 6, 7, 8, 0, 1, 3, 4, 5}, { 3, 4, 5, 6, 0, 1, 2, 7, 8}, { 3, 4, 5, 7, 0, 1, 2, 6, 8}, { 3, 4, 5, 8, 0, 1, 2, 6, 7}, { 3, 4, 6, 7, 0, 1, 2, 5, 8}, { 3, 4, 6, 8, 0, 1, 2, 5, 7}, { 3, 4, 7, 8, 0, 1, 2, 5, 6}, { 3, 5, 6, 7, 0, 1, 2, 4, 8}, { 3, 5, 6, 8, 0, 1, 2, 4, 7}, { 3, 5, 7, 8, 0, 1, 2, 4, 6}, { 3, 6, 7, 8, 0, 1, 2, 4, 5}, { 4, 5, 6, 7, 0, 1, 2, 3, 8}, { 4, 5, 6, 8, 0, 1, 2, 3, 7}, { 4, 5, 7, 8, 0, 1, 2, 3, 6}, { 4, 6, 7, 8, 0, 1, 2, 3, 5}, { 5, 6, 7, 8, 0, 1, 2, 3, 4}}, j[54][15] = { // 3 Intersection and affected 6 Line + 6 Box Cell positions for 54 Box-Line { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,18,19,20}, { 3, 4, 5, 0, 1, 2, 6, 7, 8,12,13,14,21,22,23}, { 6, 7, 8, 0, 1, 2, 3, 4, 5,15,16,17,24,25,26}, { 9,10,11,12,13,14,15,16,17, 0, 1, 2,18,19,20}, {12,13,14, 9,10,11,15,16,17, 3, 4, 5,21,22,23}, {15,16,17, 9,10,11,12,13,14, 6, 7, 8,24,25,26}, {18,19,20,21,22,23,24,25,26, 0, 1, 2, 9,10,11}, {21,22,23,18,19,20,24,25,26, 3, 4, 5,12,13,14}, {24,25,26,18,19,20,21,22,23, 6, 7, 8,15,16,17}, {27,28,29,30,31,32,33,34,35,36,37,38,45,46,47}, {30,31,32,27,28,29,33,34,35,39,40,41,48,49,50}, {33,34,35,27,28,29,30,31,32,42,43,44,51,52,53}, {36,37,38,39,40,41,42,43,44,27,28,29,45,46,47}, {39,40,41,36,37,38,42,43,44,30,31,32,48,49,50}, {42,43,44,36,37,38,39,40,41,33,34,35,51,52,53}, {45,46,47,48,49,50,51,52,53,27,28,29,36,37,38}, {48,49,50,45,46,47,51,52,53,30,31,32,39,40,41}, {51,52,53,45,46,47,48,49,50,33,34,35,42,43,44}, {54,55,56,57,58,59,60,61,62,63,64,65,72,73,74}, {57,58,59,54,55,56,60,61,62,66,67,68,75,76,77}, {60,61,62,54,55,56,57,58,59,69,70,71,78,79,80}, {63,64,65,66,67,68,69,70,71,54,55,56,72,73,74}, {66,67,68,63,64,65,69,70,71,57,58,59,75,76,77}, {69,70,71,63,64,65,66,67,68,60,61,62,78,79,80}, {72,73,74,75,76,77,78,79,80,54,55,56,63,64,65}, {75,76,77,72,73,74,78,79,80,57,58,59,66,67,68}, {78,79,80,72,73,74,75,76,77,60,61,62,69,70,71}, { 0, 9,18,27,36,45,54,63,72, 1, 2,10,11,19,20}, {27,36,45, 0, 9,18,54,63,72,28,29,37,38,46,47}, {54,63,72, 0, 9,18,27,36,45,55,56,64,65,73,74}, { 1,10,19,28,37,46,55,64,73, 0, 2, 9,11,18,20}, {28,37,46, 1,10,19,55,64,73,27,29,36,38,45,47}, {55,64,73, 1,10,19,28,37,46,54,56,63,65,72,74}, { 2,11,20,29,38,47,56,65,74, 0, 1, 9,10,18,19}, {29,38,47, 2,11,20,56,65,74,27,28,36,37,45,46}, {56,65,74, 2,11,20,29,38,47,54,55,63,64,72,73}, { 3,12,21,30,39,48,57,66,75, 4, 5,13,14,22,23}, {30,39,48, 3,12,21,57,66,75,31,32,40,41,49,50}, {57,66,75, 3,12,21,30,39,48,58,59,67,68,76,77}, { 4,13,22,31,40,49,58,67,76, 3, 5,12,14,21,23}, {31,40,49, 4,13,22,58,67,76,30,32,39,41,48,50}, {58,67,76, 4,13,22,31,40,49,57,59,66,68,75,77}, { 5,14,23,32,41,50,59,68,77, 3, 4,12,13,21,22}, {32,41,50, 5,14,23,59,68,77,30,31,39,40,48,49}, {59,68,77, 5,14,23,32,41,50,57,58,66,67,75,76}, { 6,15,24,33,42,51,60,69,78, 7, 8,16,17,25,26}, {33,42,51, 6,15,24,60,69,78,34,35,43,44,52,53}, {60,69,78, 6,15,24,33,42,51,61,62,70,71,79,80}, { 7,16,25,34,43,52,61,70,79, 6, 8,15,17,24,26}, {34,43,52, 7,16,25,61,70,79,33,35,42,44,51,53}, {61,70,79, 7,16,25,34,43,52,60,62,69,71,78,80}, { 8,17,26,35,44,53,62,71,80, 6, 7,15,16,24,25}, {35,44,53, 8,17,26,62,71,80,33,34,42,43,51,52}, {62,71,80, 8,17,26,35,44,53,60,61,69,70,78,79}}, J[20] = { // Bit positions 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536,131072,262144,524288}; bool solve (int p) { int a = p, // Unsolved Cell position x = a, // Unsolved Cell position for least Candidates y = 0, // 0 Represent Naked Single z = g[r[a]]; // 512 Represent greatest value for first time least Candidates checking for (; a < q; ++a) // Search Naked/Hidden Single or Guess Candidate for each unsolved Cell position { if (B[z] > B[g[r[a]]]) // Check unsolved Cell position for least Candidates if (B[z = g[r[x = a]]] == 1) goto NHSCF; // Found Naked Single Candidate int K = g[r[a]] & (g[r[a]] ^ (g[w[r[a]][0]] | g[w[r[a]][1]] | g[w[r[a]][2]] | g[w[r[a]][3]] | g[w[r[a]][4]] | g[w[r[a]][5]] | g[w[r[a]][6]] | g[w[r[a]][7]])); // Assign Hidden Candidates Row wise if (B[K] == 1) // Check Hidden Single Candidate Row wise z = K; // Assign Hidden Single Candidate else { // Assign Hidden Candidates Column wise K = g[r[a]] & (g[r[a]] ^ (g[w[r[a]][12]] | g[w[r[a]][13]] | g[w[r[a]][14]] | g[w[r[a]][15]] | g[w[r[a]][16]] | g[w[r[a]][17]] | g[w[r[a]][18]] | g[w[r[a]][19]])); if (B[K] == 1) // Check Hidden Single Candidate Column wise z = K; // Assign Hidden Single Candidate else { // Assign Hidden Candidates Box wise K = g[r[a]] & (g[r[a]] ^ (g[w[r[a]][6]] | g[w[r[a]][7]] | g[w[r[a]][8]] | g[w[r[a]][9]] | g[w[r[a]][10]] | g[w[r[a]][11]] | g[w[r[a]][12]] | g[w[r[a]][13]])); if (B[K] == 1) // Check Hidden Single Candidate Box wise z = K; // Assign Hidden Single Candidate else continue; } } x = a; // Assign Hidden Single Cell position y = 1; // 1 Represent Hidden Single goto NHSCF; } for (; y < 27; ++y) // Search Naked/Hidden Tuples for each Unit { int X = (g[l[y][0]] ? 1 : 0) + (g[l[y][1]] ? 1 : 0) + (g[l[y][2]] ? 1 : 0) + (g[l[y][3]] ? 1 : 0) + (g[l[y][4]] ? 1 : 0) + (g[l[y][5]] ? 1 : 0) + (g[l[y][6]] ? 1 : 0) + (g[l[y][7]] ? 1 : 0) + (g[l[y][8]] ? 1 : 0); // Count Unit unsolved Cell positions if (X < 4) continue; // Skip Unit for less than 4 unsolved Cell positions for (a = 0; a < 36; ++a) // Search Naked/Hidden pair Candidates for each Unit 36 pair Cell positions { if (!g[l[y][h[a][0]]] || !g[l[y][h[a][1]]]) { // Skip solved Cell positions if (!g[l[y][h[a][0]]]) a += 7 - h[a][0]; continue; } int K[2] = {g[l[y][h[a][0]]] | g[l[y][h[a][1]]], g[l[y][h[a][2]]] | g[l[y][h[a][3]]] | g[l[y][h[a][4]]] | g[l[y][h[a][5]]] | g[l[y][h[a][6]]] | g[l[y][h[a][7]]] | g[l[y][h[a][8]]]}; // Assign Candidates in Unit pair and other Cell positions if (B[K[0]] == 2) // Check Naked pair Candidates in Unit pair Cell positions { if (K[0] & K[1]) // Check Naked pair Candidates in Unit other Cell positions { int k[7] = {g[l[y][h[a][2]]], g[l[y][h[a][3]]], g[l[y][h[a][4]]], g[l[y][h[a][5]]], g[l[y][h[a][6]]], g[l[y][h[a][7]]], g[l[y][h[a][8]]]}; // Backup and remove Naked pair Candidates from Unit other Cell positions g[l[y][h[a][2]]] &= ~K[0]; g[l[y][h[a][3]]] &= ~K[0]; g[l[y][h[a][4]]] &= ~K[0]; g[l[y][h[a][5]]] &= ~K[0]; g[l[y][h[a][6]]] &= ~K[0]; g[l[y][h[a][7]]] &= ~K[0]; g[l[y][h[a][8]]] &= ~K[0]; #ifdef RJ printf ("%d) Found Naked pair Candidates %d at Unit %d Cells %d %d\n", a, b[K[0]], y, l[y][h[a][0]], l[y][h[a][1]]); #endif if (solve (p)) return 1; #ifdef RJ printf ("%d) Restore Naked pair Candidates %d at Unit %d Cells %d %d\n", a, b[K[0]], y, l[y][h[a][0]], l[y][h[a][1]]); #endif g[l[y][h[a][2]]] = k[0]; g[l[y][h[a][3]]] = k[1]; g[l[y][h[a][4]]] = k[2]; g[l[y][h[a][5]]] = k[3]; g[l[y][h[a][6]]] = k[4]; g[l[y][h[a][7]]] = k[5]; g[l[y][h[a][8]]] = k[6]; return 0; // Restore Naked pair Candidates to Unit other Cell positions } continue; } K[0] &= K[0] ^ K[1]; // Assign Hidden Candidates in Unit pair Cell positions if (B[K[0]] == 2) // Check Unit pair Cell positions for Hidden pair Candidates { int k[2] = {g[l[y][h[a][0]]], g[l[y][h[a][1]]]}; // Backup and remove other than Hidden pair Candidates from Unit pair Cell positions g[l[y][h[a][0]]] &= K[0]; g[l[y][h[a][1]]] &= K[0]; #ifdef RJ printf ("%d) Found Hidden pair Candidates %d at Unit %d Cells %d %d\n", a, b[K[0]], y, l[y][h[a][0]], l[y][h[a][1]]); #endif if (solve (p)) return 1; #ifdef RJ printf ("%d) Restore Hidden pair Candidates %d at Unit %d Cells %d %d\n", a, b[K[0]], y, l[y][h[a][0]], l[y][h[a][1]]); #endif g[l[y][h[a][0]]] = k[0]; g[l[y][h[a][1]]] = k[1]; return 0; // Restore other than Hidden pair Candidates to Unit pair Cell positions } } if (X < 6) continue; // Skip triplets and quads for less than 6 unsolved Cell positions for (; a < 120; ++a) // Search Naked/Hidden triplet Candidates for each Unit 84 triplet Cell positions { if (!g[l[y][h[a][0]]] || !g[l[y][h[a][1]]] || !g[l[y][h[a][2]]]) { // Skip solved Cell positions if (!g[l[y][h[a][0]]]) { int A[7] = {27,20,14, 9, 5, 2, 0}; a += A[h[a][0]]; } else if (!g[l[y][h[a][1]]]) a += 7 - h[a][1]; continue; } int K[2] = {g[l[y][h[a][0]]] | g[l[y][h[a][1]]] | g[l[y][h[a][2]]], g[l[y][h[a][3]]] | g[l[y][h[a][4]]] | g[l[y][h[a][5]]] | g[l[y][h[a][6]]] | g[l[y][h[a][7]]] | g[l[y][h[a][8]]]}; if (B[K[0]] == 3) // Check Naked triplet Candidates in Unit triplet Cell positions { if (K[0] & K[1]) // Check Naked triplet Candidates in Unit other Cell positions { int k[6] = {g[l[y][h[a][3]]], g[l[y][h[a][4]]], g[l[y][h[a][5]]], g[l[y][h[a][6]]], g[l[y][h[a][7]]], g[l[y][h[a][8]]]}; // Backup and remove Naked triplet Candidates from Unit other Cell positions g[l[y][h[a][3]]] &= ~K[0]; g[l[y][h[a][4]]] &= ~K[0]; g[l[y][h[a][5]]] &= ~K[0]; g[l[y][h[a][6]]] &= ~K[0]; g[l[y][h[a][7]]] &= ~K[0]; g[l[y][h[a][8]]] &= ~K[0]; #ifdef RJ printf ("%d) Found Naked triplet Candidates %d at Unit %d Cells %d %d %d\n", a, b[K[0]], y, l[y][h[a][0]], l[y][h[a][1]], l[y][h[a][2]]); #endif if (solve (p)) return 1; #ifdef RJ printf ("%d) Restore Naked triplet Candidates %d at Unit %d Cells %d %d %d\n", a, b[K[0]], y, l[y][h[a][0]], l[y][h[a][1]], l[y][h[a][2]]); #endif g[l[y][h[a][3]]] = k[0]; g[l[y][h[a][4]]] = k[1]; g[l[y][h[a][5]]] = k[2]; g[l[y][h[a][6]]] = k[3]; g[l[y][h[a][7]]] = k[4]; g[l[y][h[a][8]]] = k[5]; return 0; // Restore Naked triplet Candidates to Unit other Cell positions } continue; } K[0] &= K[0] ^ K[1]; // Assign Hidden Candidates in Unit triplet Cell positions if (B[K[0]] == 3) // Check Hidden triplet Candidates in Unit triplet Cell positions { int k[3] = {g[l[y][h[a][0]]], g[l[y][h[a][1]]], g[l[y][h[a][2]]]}; // Backup and remove other than Hidden triplet Candidates from Unit triplet Cell positions g[l[y][h[a][0]]] &= K[0]; g[l[y][h[a][1]]] &= K[0]; g[l[y][h[a][2]]] &= K[0]; #ifdef RJ printf ("%d) Found Hidden triplet Candidates %d at Unit %d Cells %d %d %d\n", a, b[K[0]], y, l[y][h[a][0]], l[y][h[a][1]], l[y][h[a][2]]); #endif if (solve (p)) return 1; #ifdef RJ printf ("%d) Restore Hidden triplet Candidates %d at Unit %d Cells %d %d %d\n", a, b[K[0]], y, l[y][h[a][0]], l[y][h[a][1]], l[y][h[a][2]]); #endif g[l[y][h[a][0]]] = k[0]; g[l[y][h[a][1]]] = k[1]; g[l[y][h[a][2]]] = k[2]; return 0; // Restore other than Hidden triplet Candidates to Unit triplet Cell positions } } if (X < 8) continue; // Skip quads for less than 8 unsolved Cell positions for (; a < 246; ++a) // Search Naked/Hidden quad Candidates for each Unit 126 quad Cell positions { if (!g[l[y][h[a][0]]] || !g[l[y][h[a][1]]] || !g[l[y][h[a][2]]] || !g[l[y][h[a][3]]]) { // Skip solved Cell positions if (!g[l[y][h[a][0]]]) { int A[6] = {55,34,19, 9, 3, 0}; a += A[h[a][0]]; } else if (!g[l[y][h[a][1]]]) { int A[7] = {27,20,14, 9, 5, 2, 0}; a += A[h[a][1]]; } else if (!g[l[y][h[a][2]]]) a += 7 - h[a][2]; continue; } int K[2] = {g[l[y][h[a][0]]] | g[l[y][h[a][1]]] | g[l[y][h[a][2]]] | g[l[y][h[a][3]]], g[l[y][h[a][4]]] | g[l[y][h[a][5]]] | g[l[y][h[a][6]]] | g[l[y][h[a][7]]] | g[l[y][h[a][8]]]}; if (B[K[0]] == 4) // Check Naked quad Candidates in Unit quad Cell positions { if (K[0] & K[1]) // Check Naked quad Candidates in Unit other Cell positions { int k[5] = {g[l[y][h[a][4]]], g[l[y][h[a][5]]], g[l[y][h[a][6]]], g[l[y][h[a][7]]], g[l[y][h[a][8]]]}; // Backup and remove Naked quad Candidates from Unit other Cell positions g[l[y][h[a][4]]] &= ~K[0]; g[l[y][h[a][5]]] &= ~K[0]; g[l[y][h[a][6]]] &= ~K[0]; g[l[y][h[a][7]]] &= ~K[0]; g[l[y][h[a][8]]] &= ~K[0]; #ifdef RJ printf ("%d) Found Naked quad Candidates %d at Unit %d Cells %d %d %d %d\n", a, b[K[0]], y, l[y][h[a][0]], l[y][h[a][1]], l[y][h[a][2]], l[y][h[a][3]]); #endif if (solve (p)) return 1; #ifdef RJ printf ("%d) Restore Naked quad Candidates %d at Unit %d Cells %d %d %d %d\n", a, b[K[0]], y, l[y][h[a][0]], l[y][h[a][1]], l[y][h[a][2]], l[y][h[a][3]]); #endif g[l[y][h[a][4]]] = k[0]; g[l[y][h[a][5]]] = k[1]; g[l[y][h[a][6]]] = k[2]; g[l[y][h[a][7]]] = k[3]; g[l[y][h[a][8]]] = k[4]; return 0; // Restore Naked quad Candidates to Unit other Cell positions } continue; } K[0] &= K[0] ^ K[1]; // Assign Hidden Candidates in Unit quad Cell positions if (B[K[0]] == 4) // Check Hidden quad Candidates in Unit quad Cell positions { int k[4] = {g[l[y][h[a][0]]], g[l[y][h[a][1]]], g[l[y][h[a][2]]], g[l[y][h[a][3]]]}; // Backup and remove other than Hidden quad Candidates from Unit quad Cell positions g[l[y][h[a][0]]] &= K[0]; g[l[y][h[a][1]]] &= K[0]; g[l[y][h[a][2]]] &= K[0]; g[l[y][h[a][3]]] &= K[0]; #ifdef RJ printf ("%d) Found Hidden quad Candidates %d at Unit %d Cells %d %d %d %d\n", a, b[K[0]], y, l[y][h[a][0]], l[y][h[a][1]], l[y][h[a][2]], l[y][h[a][3]]); #endif if (solve (p)) return 1; #ifdef RJ printf ("%d) Restore Hidden quad Candidates %d at Unit %d Cells %d %d %d %d\n", a, b[K[0]], y, l[y][h[a][0]], l[y][h[a][1]], l[y][h[a][2]], l[y][h[a][3]]); #endif g[l[y][h[a][0]]] = k[0]; g[l[y][h[a][1]]] = k[1]; g[l[y][h[a][2]]] = k[2]; g[l[y][h[a][3]]] = k[3]; return 0; // Restore other than Hidden quad Candidates to Unit quad Cell positions } } } for (y = 0; y < 54; ++y) // Search Intersection Removal for 54 Box-Line 3 Cell positions for (int K = g[j[y][0]] | g[j[y][1]] | g[j[y][2]]; a = K & -K; K &= K - 1) { // Search Box-Line 3 Cell positions for each Intersection Removal Candidate if (g[j[y][3]] & a || g[j[y][4]] & a || g[j[y][5]] & a || g[j[y][6]] & a || g[j[y][7]] & a || g[j[y][8]] & a) { // Found Intersection Removal Candidate in Line other Cell positions if (!(g[j[y][9]] & a || g[j[y][10]] & a || g[j[y][11]] & a || g[j[y][12]] & a || g[j[y][13]] & a || g[j[y][14]] & a)) { // Not found Intersection Removal Candidate in Box other Cell positions int k[6] = {g[j[y][3]], g[j[y][4]], g[j[y][5]], g[j[y][6]], g[j[y][7]], g[j[y][8]]}; // Backup and remove Intersection Removal Candidate from Line other Cell positions g[j[y][3]] &= ~a; g[j[y][4]] &= ~a; g[j[y][5]] &= ~a; g[j[y][6]] &= ~a; g[j[y][7]] &= ~a; g[j[y][8]] &= ~a; #ifdef RJ printf ("%d) Found Pointing and Claiming Intersection Removal Candidate %d at Cells %d %d %d\n", y, b[a], j[y][0], j[y][1], j[y][2]); #endif if (solve (p)) return 1; #ifdef RJ printf ("%d) Restore Pointing and Claiming Intersection Removal Candidate %d at Cells %d %d %d\n", y, b[a], j[y][0], j[y][1], j[y][2]); #endif g[j[y][3]] = k[0]; // Restore Intersection Removal Candidate to Line other Cell positions g[j[y][4]] = k[1]; g[j[y][5]] = k[2]; g[j[y][6]] = k[3]; g[j[y][7]] = k[4]; g[j[y][8]] = k[5]; return 0; } continue; } // Not found Intersection Removal Candidate in Line other Cell positions if (g[j[y][9]] & a || g[j[y][10]] & a || g[j[y][11]] & a || g[j[y][12]] & a || g[j[y][13]] & a || g[j[y][14]] & a) { // Found Intersection Removal Candidate in Box other Cell positions int k[6] = {g[j[y][9]], g[j[y][10]], g[j[y][11]], g[j[y][12]], g[j[y][13]], g[j[y][14]]}; // Backup and remove Intersection Removal Candidate from Box other Cell positions g[j[y][9]] &= ~a; g[j[y][10]] &= ~a; g[j[y][11]] &= ~a; g[j[y][12]] &= ~a; g[j[y][13]] &= ~a; g[j[y][14]] &= ~a; #ifdef RJ printf ("%d) Found Box-Line Reduction Intersection Removal Candidate %d at Cells %d %d %d\n", y, b[a], j[y][0], j[y][1], j[y][2]); #endif if (solve (p)) return 1; #ifdef RJ printf ("%d) Restore Box-Line Reduction Intersection Removal Candidate %d at Cells %d %d %d\n", y, b[a], j[y][0], j[y][1], j[y][2]); #endif g[j[y][9]] = k[0]; // Restore Intersection Removal Candidate to Box other Cell positions g[j[y][10]] = k[1]; g[j[y][11]] = k[2]; g[j[y][12]] = k[3]; g[j[y][13]] = k[4]; g[j[y][14]] = k[5]; return 0; } } for (int Y = 0; Y < 10; Y += 9) // Search Basic Fishes for Row and Column wise for (y = 0; y < 9; ++y) // Search Basic Fishes for each Candidate { int k[9]; // Backup Basic Fish Candidate for Line Cell positions for (a = Y; a < Y + 9; ++a) k[a - Y] = (g[l[a][0]] & J[y] ? 1 : 0) | (g[l[a][1]] & J[y] ? 2 : 0) | (g[l[a][2]] & J[y] ? 4 : 0) | (g[l[a][3]] & J[y] ? 8 : 0) | (g[l[a][4]] & J[y] ? 16 : 0) | (g[l[a][5]] & J[y] ? 32 : 0) | (g[l[a][6]] & J[y] ? 64 : 0) | (g[l[a][7]] & J[y] ? 128 : 0) | (g[l[a][8]] & J[y] ? 256 : 0); for (a = 0; a < 36; ++a) { // Search X-Wing Candidate for Line 36 pair Cell positions int A = k[h[a][0]], K[2], X[2] = {-1,-1}; if (B[A] != 2 || A != k[h[a][1]]) { // Skip for X-Wing Candidate not found in Lines pair Cell positions if (B[A] != 2) a += 7 - h[a][0]; continue; } for (int L = A, Z = 0; K[Z] = L & -L; L &= L - 1, ++Z) { // Search opposite Line other Cell positions for X-Wing Candidate if (!(k[h[a][2]] & K[Z] || k[h[a][3]] & K[Z] || k[h[a][4]] & K[Z] || k[h[a][5]] & K[Z] || k[h[a][6]] & K[Z] || k[h[a][7]] & K[Z] || k[h[a][8]] & K[Z])) continue; // Skip for X-Wing Candidate not found in opposite Line other Cell positions X[Z] = b[K[Z]] - Y + 8; g[l[X[Z]][h[a][2]]] &= ~J[y]; g[l[X[Z]][h[a][3]]] &= ~J[y]; g[l[X[Z]][h[a][4]]] &= ~J[y]; g[l[X[Z]][h[a][5]]] &= ~J[y]; g[l[X[Z]][h[a][6]]] &= ~J[y]; g[l[X[Z]][h[a][7]]] &= ~J[y]; g[l[X[Z]][h[a][8]]] &= ~J[y]; } // Remove X-Wing Candidate from opposite Line other Cell positions if (X[0] + X[1] == -2) continue; // Skip for X-Wing Candidate not found in opposite Lines other Cell positions #ifdef RJ printf ("%d) Found %s wise X-Wing for Candidate %d at r%d%dc%d%d\n", a, Y ? "Column" : "Row", y + 1, Y ? b[K[0]] : h[a][0] + 1, Y ? b[K[1]] : h[a][1] + 1, Y ? h[a][0] + 1 : b[K[0]], Y ? h[a][1] + 1 : b[K[1]]); #endif if (solve (p)) return 1; #ifdef RJ printf ("%d) Restore %s wise X-Wing for Candidate %d at r%d%dc%d%d\n", a, Y ? "Column" : "Row", y + 1, Y ? b[K[0]] : h[a][0] + 1, Y ? b[K[1]] : h[a][1] + 1, Y ? h[a][0] + 1 : b[K[0]], Y ? h[a][1] + 1 : b[K[1]]); #endif for (int Z = 0; Z < 2; ++Z) { // Restore X-Wing Candidate to opposite Lines other Cell positions if (X[Z] == -1) continue; g[l[X[Z]][h[a][2]]] |= k[h[a][2]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][3]]] |= k[h[a][3]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][4]]] |= k[h[a][4]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][5]]] |= k[h[a][5]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][6]]] |= k[h[a][6]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][7]]] |= k[h[a][7]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][8]]] |= k[h[a][8]] & K[Z] ? J[y] : 0; } return 0; } for (; a < 120; ++a) // Search Sword Fish Candidate in Line 84 triplet Cell positions { int A = k[h[a][0]] | k[h[a][1]] | k[h[a][2]], K[3], X[3] = {-1,-1,-1}; if (!k[h[a][0]] || !k[h[a][1]] || !k[h[a][2]] || B[A] != 3) { // Skip for either solved Cell positions or Sord Fish Candidate not found in Lines triplet Cell positions if (!k[h[a][0]] || B[k[h[a][0]]] > 3) { int A[7] = {27,20,14, 9, 5, 2, 0}; a += A[h[a][0]]; } else if (!k[h[a][1]] || B[k[h[a][1]]] > 3) a += 7 - h[a][1]; continue; } for (int L = A, Z = 0; K[Z] = L & -L; L &= L - 1, ++Z) { // Search opposite Line other Cell positions for Sword Fish Candidate if (!(k[h[a][3]] & K[Z] || k[h[a][4]] & K[Z] || k[h[a][5]] & K[Z] || k[h[a][6]] & K[Z] || k[h[a][7]] & K[Z] || k[h[a][8]] & K[Z])) continue; // Skip for Sword Fish Candidate not found in opposite Line other Cell positions X[Z] = b[K[Z]] - Y + 8; g[l[X[Z]][h[a][3]]] &= ~J[y]; g[l[X[Z]][h[a][4]]] &= ~J[y]; g[l[X[Z]][h[a][5]]] &= ~J[y]; g[l[X[Z]][h[a][6]]] &= ~J[y]; g[l[X[Z]][h[a][7]]] &= ~J[y]; g[l[X[Z]][h[a][8]]] &= ~J[y]; } // Remove Sword Fish Candidate from opposite Line other Cell positions if (X[0] + X[1] + X[2] == -3) continue; // Skip for Sword Fish Candidate not found in opposite Lines other Cell positions #ifdef RJ printf ("%d) Found %s wise Sword Fish for Candidate %d at r%d%d%dc%d%d%d\n", a, Y ? "Column" : "Row", y + 1, Y ? b[K[0]] : h[a][0] + 1, Y ? b[K[1]] : h[a][1] + 1, Y ? b[K[2]] : h[a][2] + 1, Y ? h[a][0] + 1 : b[K[0]], Y ? h[a][1] + 1 : b[K[1]], Y ? h[a][2] + 1 : b[K[2]]); #endif if (solve (p)) return 1; #ifdef RJ printf ("%d) Restore %s wise Sword Fish for Candidate %d at r%d%d%dc%d%d%d\n", a, Y ? "Column" : "Row", y + 1, Y ? b[K[0]] : h[a][0] + 1, Y ? b[K[1]] : h[a][1] + 1, Y ? b[K[2]] : h[a][2] + 1, Y ? h[a][0] + 1 : b[K[0]], Y ? h[a][1] + 1 : b[K[1]], Y ? h[a][2] + 1 : b[K[2]]); #endif for (int Z = 0; Z < 3; ++Z) { // Restore Sword Fish Candidate to opposite Lines other Cell positions if (X[Z] == -1) continue; g[l[X[Z]][h[a][3]]] |= k[h[a][3]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][4]]] |= k[h[a][4]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][5]]] |= k[h[a][5]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][6]]] |= k[h[a][6]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][7]]] |= k[h[a][7]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][8]]] |= k[h[a][8]] & K[Z] ? J[y] : 0; } return 0; } for (; a < 246; ++a) // Search Jelly Fish Candidate in Line 126 quad Cell positions { int A = k[h[a][0]] | k[h[a][1]] | k[h[a][2]] | k[h[a][3]], K[4], X[4] = {-1,-1,-1,-1}; if (!k[h[a][0]] || !k[h[a][1]] || !k[h[a][2]] || !k[h[a][3]] || B[A] != 4) { // Skip for either solved Cell positions or Jelly Fish Candidate not found in Line quad Cell positions if (!k[h[a][0]] || B[k[h[a][0]]] > 4) { int A[6] = {55,34,19, 9, 3, 0}; a += A[h[a][0]]; } else if (!k[h[a][1]] || B[k[h[a][1]]] > 4) { int A[7] = {27,20,14, 9, 5, 2, 0}; a += A[h[a][1]]; } else if (!k[h[a][2]] || B[k[h[a][2]]] > 4) a += 7 - h[a][2]; continue; } for (int L = A, Z = 0; K[Z] = L & -L; L &= L - 1, ++Z) { // Search opposite Line other Cell positions for Jelly Fish Candidate if (!(k[h[a][4]] & K[Z] || k[h[a][5]] & K[Z] || k[h[a][6]] & K[Z] || k[h[a][7]] & K[Z] || k[h[a][8]] & K[Z])) continue; // Skip for Jelly Fish Candidate not found in opposite Line other Cell positions X[Z] = b[K[Z]] - Y + 8; g[l[X[Z]][h[a][4]]] &= ~J[y]; g[l[X[Z]][h[a][5]]] &= ~J[y]; g[l[X[Z]][h[a][6]]] &= ~J[y]; g[l[X[Z]][h[a][7]]] &= ~J[y]; g[l[X[Z]][h[a][8]]] &= ~J[y]; } // Remove Jelly Fish Candidate from opposite Line other Cell positions if (X[0] + X[1] + X[2] + X[3] == -4) continue; // Skip for Jelly Fish Candidate not found in opposite Lines other Cell positions #ifdef RJ printf ("%d) Found %s wise Jelly Fish for Candidate %d at r%d%d%d%dc%d%d%d%d\n", a, Y ? "Column" : "Row", y + 1, Y ? b[K[0]] : h[a][0] + 1, Y ? b[K[1]] : h[a][1] + 1, Y ? b[K[2]] : h[a][2] + 1, Y ? b[K[3]] : h[a][3] + 1, Y ? h[a][0] + 1 : b[K[0]], Y ? h[a][1] + 1 : b[K[1]], Y ? h[a][2] + 1 : b[K[2]], Y ? h[a][3] + 1 : b[K[3]]); #endif if (solve (p)) return 1; #ifdef RJ printf ("%d) Restore %s wise Jelly Fish for Candidate %d at r%d%d%d%dc%d%d%d%d\n", a, Y ? "Column" : "Row", y + 1, Y ? b[K[0]] : h[a][0] + 1, Y ? b[K[1]] : h[a][1] + 1, Y ? b[K[2]] : h[a][2] + 1, Y ? b[K[3]] : h[a][3] + 1, Y ? h[a][0] + 1 : b[K[0]], Y ? h[a][1] + 1 : b[K[1]], Y ? h[a][2] + 1 : b[K[2]], Y ? h[a][3] + 1 : b[K[3]]); #endif for (int Z = 0; Z < 4; ++Z) { // Restore Jelly Fish Candidate to opposite Lines other Cell positions if (X[Z] == -1) continue; g[l[X[Z]][h[a][4]]] |= k[h[a][4]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][5]]] |= k[h[a][5]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][6]]] |= k[h[a][6]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][7]]] |= k[h[a][7]] & K[Z] ? J[y] : 0; g[l[X[Z]][h[a][8]]] |= k[h[a][8]] & K[Z] ? J[y] : 0; } return 0; } } y = 2; // 2 Represent Guess NHSCF: if (x > p) // Check current Cell position for sorting and eliminating { a = r[p]; r[p] = r[x]; r[x] = a; } int K = g[r[p]]; // Backup Candidates from current Cell position for (g[r[p]] = 0; s[r[p]] = b[z & -z]; z &= z - 1) { // Clear current Cell Candidates and solve current Cell position for each Candidate int k = 0; for (++n[y], a = 0; a < 20; ++a) if (g[w[r[p]][a]] & J[s[r[p]] - 1]) { k |= J[a]; // Backup 20 affected Cell positions current Candidate g[w[r[p]][a]] &= ~J[s[r[p]] - 1]; } // Remove current Candidate from 20 affected Cell positions #ifdef RJ printf ("%d) Apply %s Candidate %d from Candidates %d at Cell %d\n", p, y ? (y == 2 ? "Trial and Error" : "Hidden Single") : "Naked Single", s[r[p]], b[K], r[p]); #endif if (a == 20 && (p + 1 == q || solve (p + 1))) return 1; // Check either all Cell positions solved or recursive solve for next unsolved Cell position #ifdef RJ printf ("%d) Restore %s Candidate %d from Candidates %d at Cell %d\n", p, y ? (y == 2 ? "Trial and Error" : "Hidden Single") : "Naked Single", s[r[p]], b[K], r[p]); #endif while (a) // Restore current Candidate to 20 affected Cell positions if (k & J[--a]) g[w[r[p]][a]] |= J[s[r[p]] - 1]; } g[r[p]] = K; // Restore Candidates to current Cell position return 0; } bool check (int p, int q) { for (int a = 0; a < 20; ++a) if (s[w[p][a]] == q) // Check duplicate Candidate in 20 affected clue Cell positions return 0; return 1; } bool invalid (void) { for (int p = 0; p < 81; ++p) if (!s[p]) // Check unsolved Cell position { for (int a = 0; a < 9; ++a) g[p] |= check (p, a + 1) ? J[a] : 0; // Check constraint and assign Candidate for unsolved Cell position if (!g[p]) // Check no Candidate assigned return 1; r[q++] = p; // Assign unsolved Cell position for sorting and eliminating } else if (!check (p, s[p])) // Check constraint for clue Cell position return 1; return 0; } int main (void) { int a = -1, m, i = 0, t = 0, u = 0, v = 0, y = 0; float c, d = 0, e = 0, f = 0, k = 0; FILE *o = fopen ("sudoku.txt", "r"); if (o == NULL) printf ("Unable to open sudoku.txt file for read !!\n"); else do { if ((m = fgetc (o)) != 10 && m != EOF && a < 80) s[++a] = m > 48 && m < 58 ? m - 48 : 0; else // Assign clue Cell positions if (m == 10 || m == EOF) { #ifdef RJ printf ("\n"); #endif while (a < 80) // Clear remaining unsolved Cell positions s[++a] = 0; q = n[0] = n[1] = n[2] = 0; c = clock (); if (invalid ()) { c = (clock () - c) / CLOCKS_PER_SEC; d += c; printf ("%ld) Error: Invalid Sudoku! # I%ld", ++t, ++i); } else if (!q) { c = (clock () - c) / CLOCKS_PER_SEC; k += c; printf ("%ld) Valid Sudoku # V%ld", ++t, ++y); } else if (solve (0)) { c = (clock () - c) / CLOCKS_PER_SEC; e += c; printf ("%ld) ", ++t); for (a = 0; a < 81; ++a) printf ("%c", s[a] + '0'); printf (" # S%ld", ++v); } else { c = (clock () - c) / CLOCKS_PER_SEC; f += c; printf ("%ld) Error: Unsolvable Sudoku! # U%ld", ++t, ++u); } printf (" # N%ld # H%ld # G%ld # %f\n", n[0], n[1], n[2], c); a = -1; } #ifdef RJ if (m != EOF) printf ("%c", m); #endif } while (m != EOF); printf ("=======================================\n"); printf ("Total Sudoku puzzle read : %ld\n", t); printf ("Total time for all puzzles : %f\n", d + e + f + y); printf ("Average time per puzzle : %f\n", t ? (d + e + f + y) / t : 0); printf ("Number of valid puzzles : %ld\n", y); printf ("Time for valid puzzles : %f\n", k); printf ("Average time per valid : %f\n", y ? k / y : 0); printf ("Number of invalid puzzles : %ld\n", i); printf ("Time for invalid puzzles : %f\n", d); printf ("Average time per invalid : %f\n", i ? d / i : 0); printf ("Number of solved puzzles : %ld\n", v); printf ("Time for solved puzzles : %f\n", e); printf ("Average time per solved : %f\n", v ? e / v : 0); printf ("Number of unsolved puzzle : %ld\n", u); printf ("Time for unsolved puzzles : %f\n", f); printf ("Average time per unsolved : %f\n", u ? f / u : 0); if (fclose (o) == EOF) printf ("Unable to close sudoku.txt file !!"); }