#include <iostream>							
const uint_fast64_t s = 1296;
const uint_fast64_t Valids[1296] = { 1111,1112,1113,1114,1115,1116,1121,1122,1123,1124,1125,1126,1131,1132,1133,1134,1135,1136,1141,1142,1143,1144,1145,1146,1151,1152,1153,1154,1155,1156,1161,1162,1163,1164,1165,1166,1211,1212,1213,1214,1215,1216,1221,1222,1223,1224,1225,1226,1231,1232,1233,1234,1235,1236,1241,1242,1243,1244,1245,1246,1251,1252,1253,1254,1255,1256,1261,1262,1263,1264,1265,1266,1311,1312,1313,1314,1315,1316,1321,1322,1323,1324,1325,1326,1331,1332,1333,1334,1335,1336,1341,1342,1343,1344,1345,1346,1351,1352,1353,1354,1355,1356,1361,1362,1363,1364,1365,1366,1411,1412,1413,1414,1415,1416,1421,1422,1423,1424,1425,1426,1431,1432,1433,1434,1435,1436,1441,1442,1443,1444,1445,1446,1451,1452,1453,1454,1455,1456,1461,1462,1463,1464,1465,1466,1511,1512,1513,1514,1515,1516,1521,1522,1523,1524,1525,1526,1531,1532,1533,1534,1535,1536,1541,1542,1543,1544,1545,1546,1551,1552,1553,1554,1555,1556,1561,1562,1563,1564,1565,1566,1611,1612,1613,1614,1615,1616,1621,1622,1623,1624,1625,1626,1631,1632,1633,1634,1635,1636,1641,1642,1643,1644,1645,1646,1651,1652,1653,1654,1655,1656,1661,1662,1663,1664,1665,1666,
	2111,2112,2113,2114,2115,2116,2121,2122,2123,2124,2125,2126,2131,2132,2133,2134,2135,2136,2141,2142,2143,2144,2145,2146,2151,2152,2153,2154,2155,2156,2161,2162,2163,2164,2165,2166,2211,2212,2213,2214,2215,2216,2221,2222,2223,2224,2225,2226,2231,2232,2233,2234,2235,2236,2241,2242,2243,2244,2245,2246,2251,2252,2253,2254,2255,2256,2261,2262,2263,2264,2265,2266,2311,2312,2313,2314,2315,2316,2321,2322,2323,2324,2325,2326,2331,2332,2333,2334,2335,2336,2341,2342,2343,2344,2345,2346,2351,2352,2353,2354,2355,2356,2361,2362,2363,2364,2365,2366,2411,2412,2413,2414,2415,2416,2421,2422,2423,2424,2425,2426,2431,2432,2433,2434,2435,2436,2441,2442,2443,2444,2445,2446,2451,2452,2453,2454,2455,2456,2461,2462,2463,2464,2465,2466,2511,2512,2513,2514,2515,2516,2521,2522,2523,2524,2525,2526,2531,2532,2533,2534,2535,2536,2541,2542,2543,2544,2545,2546,2551,2552,2553,2554,2555,2556,2561,2562,2563,2564,2565,2566,2611,2612,2613,2614,2615,2616,2621,2622,2623,2624,2625,2626,2631,2632,2633,2634,2635,2636,2641,2642,2643,2644,2645,2646,2651,2652,2653,2654,2655,2656,2661,2662,2663,2664,2665,2666,
	3111,3112,3113,3114,3115,3116,3121,3122,3123,3124,3125,3126,3131,3132,3133,3134,3135,3136,3141,3142,3143,3144,3145,3146,3151,3152,3153,3154,3155,3156,3161,3162,3163,3164,3165,3166,3211,3212,3213,3214,3215,3216,3221,3222,3223,3224,3225,3226,3231,3232,3233,3234,3235,3236,3241,3242,3243,3244,3245,3246,3251,3252,3253,3254,3255,3256,3261,3262,3263,3264,3265,3266,3311,3312,3313,3314,3315,3316,3321,3322,3323,3324,3325,3326,3331,3332,3333,3334,3335,3336,3341,3342,3343,3344,3345,3346,3351,3352,3353,3354,3355,3356,3361,3362,3363,3364,3365,3366,3411,3412,3413,3414,3415,3416,3421,3422,3423,3424,3425,3426,3431,3432,3433,3434,3435,3436,3441,3442,3443,3444,3445,3446,3451,3452,3453,3454,3455,3456,3461,3462,3463,3464,3465,3466,3511,3512,3513,3514,3515,3516,3521,3522,3523,3524,3525,3526,3531,3532,3533,3534,3535,3536,3541,3542,3543,3544,3545,3546,3551,3552,3553,3554,3555,3556,3561,3562,3563,3564,3565,3566,3611,3612,3613,3614,3615,3616,3621,3622,3623,3624,3625,3626,3631,3632,3633,3634,3635,3636,3641,3642,3643,3644,3645,3646,3651,3652,3653,3654,3655,3656,3661,3662,3663,3664,3665,3666,
	4111,4112,4113,4114,4115,4116,4121,4122,4123,4124,4125,4126,4131,4132,4133,4134,4135,4136,4141,4142,4143,4144,4145,4146,4151,4152,4153,4154,4155,4156,4161,4162,4163,4164,4165,4166,4211,4212,4213,4214,4215,4216,4221,4222,4223,4224,4225,4226,4231,4232,4233,4234,4235,4236,4241,4242,4243,4244,4245,4246,4251,4252,4253,4254,4255,4256,4261,4262,4263,4264,4265,4266,4311,4312,4313,4314,4315,4316,4321,4322,4323,4324,4325,4326,4331,4332,4333,4334,4335,4336,4341,4342,4343,4344,4345,4346,4351,4352,4353,4354,4355,4356,4361,4362,4363,4364,4365,4366,4411,4412,4413,4414,4415,4416,4421,4422,4423,4424,4425,4426,4431,4432,4433,4434,4435,4436,4441,4442,4443,4444,4445,4446,4451,4452,4453,4454,4455,4456,4461,4462,4463,4464,4465,4466,4511,4512,4513,4514,4515,4516,4521,4522,4523,4524,4525,4526,4531,4532,4533,4534,4535,4536,4541,4542,4543,4544,4545,4546,4551,4552,4553,4554,4555,4556,4561,4562,4563,4564,4565,4566,4611,4612,4613,4614,4615,4616,4621,4622,4623,4624,4625,4626,4631,4632,4633,4634,4635,4636,4641,4642,4643,4644,4645,4646,4651,4652,4653,4654,4655,4656,4661,4662,4663,4664,4665,4666,
	5111,5112,5113,5114,5115,5116,5121,5122,5123,5124,5125,5126,5131,5132,5133,5134,5135,5136,5141,5142,5143,5144,5145,5146,5151,5152,5153,5154,5155,5156,5161,5162,5163,5164,5165,5166,5211,5212,5213,5214,5215,5216,5221,5222,5223,5224,5225,5226,5231,5232,5233,5234,5235,5236,5241,5242,5243,5244,5245,5246,5251,5252,5253,5254,5255,5256,5261,5262,5263,5264,5265,5266,5311,5312,5313,5314,5315,5316,5321,5322,5323,5324,5325,5326,5331,5332,5333,5334,5335,5336,5341,5342,5343,5344,5345,5346,5351,5352,5353,5354,5355,5356,5361,5362,5363,5364,5365,5366,5411,5412,5413,5414,5415,5416,5421,5422,5423,5424,5425,5426,5431,5432,5433,5434,5435,5436,5441,5442,5443,5444,5445,5446,5451,5452,5453,5454,5455,5456,5461,5462,5463,5464,5465,5466,5511,5512,5513,5514,5515,5516,5521,5522,5523,5524,5525,5526,5531,5532,5533,5534,5535,5536,5541,5542,5543,5544,5545,5546,5551,5552,5553,5554,5555,5556,5561,5562,5563,5564,5565,5566,5611,5612,5613,5614,5615,5616,5621,5622,5623,5624,5625,5626,5631,5632,5633,5634,5635,5636,5641,5642,5643,5644,5645,5646,5651,5652,5653,5654,5655,5656,5661,5662,5663,5664,5665,5666,
	6111,6112,6113,6114,6115,6116,6121,6122,6123,6124,6125,6126,6131,6132,6133,6134,6135,6136,6141,6142,6143,6144,6145,6146,6151,6152,6153,6154,6155,6156,6161,6162,6163,6164,6165,6166,6211,6212,6213,6214,6215,6216,6221,6222,6223,6224,6225,6226,6231,6232,6233,6234,6235,6236,6241,6242,6243,6244,6245,6246,6251,6252,6253,6254,6255,6256,6261,6262,6263,6264,6265,6266,6311,6312,6313,6314,6315,6316,6321,6322,6323,6324,6325,6326,6331,6332,6333,6334,6335,6336,6341,6342,6343,6344,6345,6346,6351,6352,6353,6354,6355,6356,6361,6362,6363,6364,6365,6366,6411,6412,6413,6414,6415,6416,6421,6422,6423,6424,6425,6426,6431,6432,6433,6434,6435,6436,6441,6442,6443,6444,6445,6446,6451,6452,6453,6454,6455,6456,6461,6462,6463,6464,6465,6466,6511,6512,6513,6514,6515,6516,6521,6522,6523,6524,6525,6526,6531,6532,6533,6534,6535,6536,6541,6542,6543,6544,6545,6546,6551,6552,6553,6554,6555,6556,6561,6562,6563,6564,6565,6566,6611,6612,6613,6614,6615,6616,6621,6622,6623,6624,6625,6626,6631,6632,6633,6634,6635,6636,6641,6642,6643,6644,6645,6646,6651,6652,6653,6654,6655,6656,6661,6662,6663,6664,6665,6666 };

const double coef[14] = { 1.10, 1.07, 1.04, 0.81, 0.62, 1.02, 0.95, 1.05, 0.88, 0.92, 0.79, 1.02, 0.80, 1.93 }; //magic entropy coefficients

int main()
{
	uint_fast64_t imark[14] = { 0 };
	uint_fast64_t i, j, k, l, m, n = 0, o, p, sum = 0, best = 8192;
	
	uint_fast64_t a[5], b[5];
	typedef uint_fast64_t(mark_)[s];
	mark_* mark = new mark_[s]; // pre-determine all signs of all possible comparisons
	k = 0;
	for (i = 0; i < 4; i++) for (j = 0; j <= (4 - i); j++) { imark[k] = i * 10 + j; k++; } imark[13] = 40;
	for (i = 0; i < s - 1; i++) {
		for (j = 1; j < s; j++) {a[0] = Valids[i]; b[0] = Valids[j]; p = 0; m = 0;
		for (k = 1; k < 4; k++){
			a[k] = a[0] % 10; b[k] = b[0] % 10; a[0] = (a[0] - a[k]) / 10; b[0] = (b[0] - b[k]) / 10;
		}
		a[4] = a[0]; b[4] = b[0];
		for (k = 1; k <= 4; k++) if (a[k] == b[k]) { p++; a[k] = 0; b[k] = 9; }
		for (k = 1; k <= 4; k++) {
			for (l = 1; l <= 4; l++)  if (a[k] == b[l]) { m++; b[l] = 9; break; }
		}
			mark[i][j] = -0.5 * p * p + 5.5 * p + m; mark[j][i] = mark[i][j]; // signs meaningful indices
		}
	}
	for (i = 0; i < s; i++) mark[i][i] = 13; //score by itself is always ++++
	
	uint_fast64_t iValid[s] = { 0 };
	
	sum = 0;
	for (o = 0; o < s; o++) //for all 1296 elements in the Set
	
	{
		n = 0;
		for (i = 0; i < s; i++) {iValid[n] = i; n++; }
				
		for (l = 1; l < 7; l++) //game levels 2 to "never to be reached" 7
		{
			uint_fast64_t pure[s][14] = { 0 };
			
			for (j = 0; j < s; j++) { //populate next sign remains
				for (i = 0; i < n; i++) { pure[j][mark[j][iValid[i]]]++; }
			}

			double scoreE[s][14] = { 0.0 };
			double scoreGur[s] = { 0.0 };
			double scoremax = { 0.0 }; 
			
			for (i = 0; i < s; i++) {
				
				for (j = 0; j < 14; j++) {

					if (pure[i][j] > 0) { scoreE[i][j] += -((double)pure[i][j] / (double)n) * log2((double)pure[i][j] / (double)n); } //Entropy

					scoreGur[i] += scoreE[i][j] * coef[j]; //Weighted Entropy

				}

				if (scoreGur[i] > scoremax) { scoremax = scoreGur[i]; k = i; } //Save the best score

			}

			//for (i = k + 1; i < (s * (pure[k][13] != 1)); i++)  if (pure[i][13] && (scoreGur[i] == scoremax)) { k = i; break; } //checks if a consistent guess has the same score - not necessary for optimized coefficients

			m = mark[k][o];			
			if (m==13)	{
				std::cout << l << "." << Valids[o] << "\n";
				sum += l; break;
			}
			
			std::cout << l << "." << Valids[k] << " ";

			p = n; n = 0;

			for (i = 0; i < p; i++) {

				if (mark[iValid[i]][k]== m) { iValid[n] = iValid[i]; n++; } //find next set of consistents
			}

			if (n == 1) {
				std::cout << l + 1 << "." << Valids[o] << "\n";
				sum += l + 1; break;
			}

		}

	}
	
	std::cout << Valids[8] << ":" << sum << " / " << (double)sum / 1296 << " best:" << "\n"; //populate game tree
	std::cout << "\a\a\a";
	system("pause");

	return 0;
}