Problem Statement
The time limit for this problem is 4 seconds.
Bob has been dating Alice for a long time now and feels this is the right time to propose her. The city where they live is represented as a grid of size R x C. Bob lives in top-left cell (0, 0), while Alice lives in the bottom-right cell (R-1, C-1). All the other cells in the grid are owned by various florists.
Bob is planning a surprise visit to her place and greeting her with a bouquet of flowers. He is going to walk from his home to Alice's home along one of the shortest paths. I.e., in each step he will either move one row down or one column to the right.
The florist in cell (i, j) has exactly roses[i*C+j] roses and tulips[i*C+j] tulips. The florist is only willing to sell all the flowers together, for a combined price of costs[i*C+j]. Bob is going to purchase all the flowers from all florists he encounters on his path.
Bob's bouquet will be formed by all the flowers he bought along the way. He knows that Alice loves roses much more than she likes tulips, so he would like to maximize the ratio of roses to tulips in the bouquet. Bob also knows that Alice does not like wasting money, so he would like to give her a bouquet with a total cost at most K.
Help Bob maximize his chances with Alice: Compute and return the largest possible ratio between the number of roses and the number of tulips in a bouquet that is cheap enough. If he cannot give Alice any bouquet that would cost K or less, return -1 instead.
Definition
- Class:
- ProposalOptimization
- Method:
- bestPath
- Parameters:
- int, int, int, int[], int[], int[]
- Returns:
- double
- Method signature:
- double bestPath(int R, int C, int K, int[] roses, int[] tulips, int[] costs)
- (be sure your method is public)
Notes
- Your answer will be accepted if it has an absolute or a relative error at most 1e-9.
- While the actual city is a 2D grid, the arrays roses, tulips and costs that describe it are 1D arrays. You may note that the order of elements in these arrays corresponds to listing all the cells in the city in row major order.
Constraints
- R and C will be positive.
- R*C will be between 4 and 300, inclusive.
- K will be between 1 and 10^9, inclusive.
- roses, tulips and costs will each have R*C elements.
- The first and the last element of roses, tulips and costs will be 0.
- Each other element of roses, tulips and costs will be between 1 and 10^6, inclusive.
Examples
2
2
100
{0, 2, 3, 0}
{0, 3, 5, 0}
{0, 70, 80, 0}
Returns: 0.6666666666666667
Bob has two possible paths: He can go right, purchase 2 roses and 3 tulips for 70, and then go down to Alice's house. He can go down, purchase 3 roses and 5 tulips for 80, and then go right to Alice's house. In the first option Bob will give Alice a bouquet in which the ratio of roses to tulips is 2/3 = 0.66666. In the second option Bob will give Alice a bouquet in which the ratio of roses to tulips is 3/5 = 0.6. The first option is better.
2
2
100
{0, 2, 3, 0}
{0, 3, 5, 0}
{0, 170, 100, 0}
Returns: 0.6
The first bouquet is now too expensive. Bob has to go with the second option.
3
3
98
{0, 1, 1, 1, 1, 1, 1, 1, 0}
{0, 1, 1, 1, 1, 1, 1, 1, 0}
{0, 33, 33, 33, 33, 33, 33, 33, 0}
Returns: -1.0
All possible ways produce bouquets that cost 99, so all possible bouquets are too expensive.
5
9
622
{0, 2, 12, 1, 6, 10, 10, 24, 3, 1, 7, 4, 4, 1, 37, 4, 6, 8, 2, 20, 5, 20, 6, 7, 22, 3, 2, 8, 31, 18, 5, 28, 11, 1, 34, 1, 4, 2, 6, 1, 6, 9, 5, 7, 0}
{0, 4, 37, 22, 3, 14, 10, 6, 5, 6, 5, 17, 4, 7, 12, 3, 1, 3, 3, 1, 5, 1, 11, 37, 6, 24, 6, 3, 21, 1, 2, 27, 7, 1, 8, 1, 8, 1, 26, 20, 6, 6, 6, 7, 0}
{0, 19, 70, 79, 18, 43, 49, 65, 16, 38, 61, 69, 43, 12, 62, 11, 44, 35, 7, 62, 40, 88, 60, 57, 65, 38, 46, 18, 69, 87, 28, 80, 47, 5, 64, 1, 15, 3, 86, 41, 86, 21, 56, 28, 0}
Returns: 2.161290322580645
3
3
100
{0, 10, 1000, 222, 1, 10, 223, 224, 0}
{0, 1, 2000, 333, 1000000, 1, 334, 332, 0}
{0, 1, 1, 33, 1, 1, 33, 33, 0}
Returns: 0.6696696696696696
3
2
14
{0, 1, 1, 1, 1, 0}
{0, 1, 1, 1, 1, 0}
{0, 5, 2, 1, 5, 0}
Returns: 1.0
2
3
15
{0, 1, 3, 1, 1, 0}
{0, 1, 2, 6, 1, 0}
{0, 1, 18, 9, 1, 0}
Returns: 1.0
Bob has three possible paths: He can go right, right, down. On this path, he would get 4 roses and 3 tulips for cost 19 but his budget is only 15 so he cannot take this path. He can go right, down, right. On this path, he would get 2 roses and 2 tulips for cost 2. He can go down, right, right. On this path, he would get 2 roses and 7 tulips for cost 10. The last two options are only feasible and while he gets 2 roses in both the paths, it's better to go right, down, right since the number of tulips acquired is lesser so, better the ratio. Hence, the answer is 2/2 = 1.0 .
3
3
28
{0, 2, 2, 1, 1, 4, 1, 2, 0}
{0, 3, 1, 1, 2, 2, 1, 1, 0}
{0, 8, 5, 4, 4, 10, 1, 8, 0}
Returns: 1.3333333333333333
6
1
259
{0, 9, 1, 14, 41, 0}
{0, 5, 4, 24, 6, 0}
{0, 26, 8, 74, 85, 0}
Returns: 1.6666666666666667
3
3
225
{0, 2, 9, 10, 22, 4, 2, 15, 0}
{0, 5, 2, 1, 4, 7, 13, 12, 0}
{0, 11, 14, 85, 77, 26, 63, 51, 0}
Returns: 3.0
1
30
1000000000
{0, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 0}
{0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0}
{0, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 0}
Returns: 1000000.0
20
15
180498
{0, 340, 631, 602, 1862, 850, 603, 979, 12, 3219, 89, 32, 1617, 594, 116, 713, 576, 2891, 180, 67, 898, 1227, 1550, 657, 1, 543, 7, 1060, 5374, 924, 2165, 956, 1054, 2549, 714, 1096, 819, 1318, 583, 2349, 4386, 2502, 168, 546, 3309, 708, 52, 766, 1352, 7, 1531, 2564, 461, 781, 636, 3757, 3728, 2240, 127, 1718, 605, 288, 2120, 2343, 28, 12, 1750, 462, 2618, 2260, 619, 1031, 2160, 2526, 588, 1688, 1808, 21, 368, 1501, 1309, 380, 272, 439, 1469, 3086, 2037, 3073, 558, 971, 1955, 1289, 1411, 369, 54, 610, 1905, 1433, 438, 17, 190, 716, 565, 573, 1078, 140, 1326, 761, 1164, 934, 2315, 1154, 3594, 1317, 13, 2492, 72, 61, 1656, 1231, 72, 796, 144, 388, 18, 1157, 60, 3736, 16, 1537, 450, 1834, 852, 78, 324, 379, 524, 1120, 4315, 854, 1882, 713, 565, 3417, 4, 135, 135, 152, 26, 1871, 1365, 198, 3180, 728, 2760, 1131, 1176, 104, 598, 1198, 796, 297, 128, 1139, 82, 1803, 2, 1779, 1290, 507, 409, 377, 196, 37, 1766, 525, 436, 393, 22, 189, 171, 329, 2495, 2370, 2937, 2567, 1111, 2068, 535, 795, 168, 1213, 1208, 508, 579, 153, 3879, 20, 1217, 352, 341, 1476, 1397, 560, 387, 709, 272, 3842, 25, 503, 416, 8, 448, 1025, 1132, 2713, 361, 1148, 477, 1079, 2140, 68, 1541, 942, 436, 1053, 588, 1267, 1789, 386, 4881, 1120, 268, 583, 262, 140, 2537, 1071, 1166, 2406, 270, 587, 81, 1969, 2052, 11, 871, 357, 3010, 214, 2172, 1497, 264, 884, 457, 3856, 4358, 42, 687, 84, 157, 2294, 396, 646, 233, 2056, 4158, 1162, 250, 587, 1790, 3472, 758, 307, 2394, 101, 2425, 1872, 4512, 332, 45, 297, 3580, 115, 19, 364, 271, 6028, 1626, 50, 1553, 507, 1517, 377, 55, 3479, 578, 2788, 535, 0}
{0, 290, 5471, 192, 1359, 413, 668, 11, 621, 2993, 95, 4023, 162, 56, 1163, 38, 1506, 888, 74, 84, 2072, 115, 2584, 545, 490, 1668, 38, 302, 176, 1155, 1952, 1032, 1843, 2117, 100, 1218, 1748, 1375, 1466, 2625, 483, 4041, 3951, 74, 1968, 324, 961, 2910, 2057, 2638, 1492, 351, 195, 3095, 1819, 476, 492, 904, 5002, 1740, 5146, 1682, 2460, 247, 108, 128, 1219, 318, 776, 192, 1760, 1831, 546, 427, 562, 3299, 3047, 4111, 4435, 1124, 2352, 1182, 82, 3601, 1101, 516, 1301, 388, 183, 2666, 3117, 570, 2792, 2009, 2218, 290, 253, 296, 2745, 171, 4293, 1637, 2779, 1367, 2791, 1252, 2598, 226, 1223, 309, 258, 1247, 1478, 1650, 825, 487, 3266, 1169, 611, 2934, 107, 1207, 3589, 999, 614, 92, 173, 1355, 64, 366, 247, 61, 414, 3, 4240, 1461, 20, 812, 1846, 1083, 1085, 343, 1035, 59, 34, 840, 227, 134, 28, 2507, 1773, 532, 926, 2222, 1735, 65, 3623, 1224, 1362, 3628, 475, 2340, 19, 2818, 92, 403, 27, 2997, 448, 336, 1441, 172, 1284, 132, 623, 4820, 3065, 3052, 58, 1396, 24, 130, 2064, 226, 2505, 349, 373, 3872, 1414, 153, 2089, 425, 2406, 2107, 1074, 869, 69, 49, 306, 2048, 907, 2042, 2271, 879, 2, 492, 348, 366, 201, 196, 172, 8, 1237, 150, 741, 1106, 721, 1687, 1175, 968, 2367, 654, 422, 407, 269, 3054, 77, 101, 1977, 193, 4, 3406, 4033, 1649, 1416, 2109, 327, 439, 1588, 951, 952, 2122, 305, 715, 2821, 106, 4211, 2637, 1121, 1408, 466, 1346, 160, 3448, 1457, 2208, 52, 139, 218, 798, 331, 32, 1522, 362, 1443, 1820, 63, 652, 225, 3667, 21, 213, 315, 64, 924, 557, 240, 1310, 1761, 678, 198, 1127, 1253, 226, 196, 7020, 1201, 1403, 263, 671, 1969, 193, 1625, 154, 1724, 592, 701, 1123, 569, 0}
{0, 1505, 9702, 5583, 5530, 8618, 7078, 3018, 1949, 8447, 1768, 5327, 9072, 1041, 2325, 1545, 5077, 8887, 543, 300, 7661, 3760, 7740, 7700, 1253, 2999, 105, 3199, 8581, 7223, 6791, 3775, 5419, 9704, 5786, 6242, 4150, 5130, 5945, 8970, 7653, 9698, 7967, 4153, 6896, 4893, 7305, 8549, 9770, 6243, 7312, 6304, 1931, 5558, 8290, 5784, 8572, 6570, 9643, 8965, 7970, 4138, 6555, 6073, 1346, 1109, 9006, 4582, 7284, 5900, 3617, 7907, 3566, 8245, 5588, 8126, 7924, 5483, 6673, 3733, 9788, 4133, 1661, 5385, 8316, 5177, 7069, 9571, 1379, 9644, 9337, 3666, 7077, 8824, 5732, 5326, 4181, 3815, 4984, 670, 7537, 4026, 7896, 5668, 6005, 6899, 5051, 1698, 4911, 1660, 5884, 8148, 6880, 3996, 4638, 4289, 9293, 6499, 8161, 9520, 881, 4714, 9265, 6487, 2456, 2890, 790, 7000, 425, 2858, 2080, 6571, 3993, 211, 6527, 3641, 1351, 3415, 8911, 2612, 4366, 6179, 2083, 5111, 362, 3755, 3098, 703, 504, 7456, 9172, 3556, 5574, 3966, 5834, 3617, 7250, 2240, 4065, 9706, 9063, 4899, 232, 9932, 286, 9948, 246, 7342, 5428, 1159, 9860, 2469, 4152, 1159, 9834, 9013, 7460, 6495, 109, 3502, 1386, 1344, 7242, 4081, 7036, 5228, 6089, 9072, 8124, 3002, 4003, 2885, 6550, 3306, 3213, 2520, 6285, 128, 3029, 3245, 6666, 5412, 6081, 3140, 1047, 2309, 804, 7057, 1177, 887, 3781, 122, 2601, 5380, 4058, 6372, 1930, 4263, 5906, 6259, 8600, 4157, 5140, 6966, 925, 6209, 2635, 1783, 6896, 753, 8095, 7982, 6021, 3384, 8569, 3384, 5825, 6434, 4180, 5130, 4033, 7407, 1359, 4378, 6634, 677, 7962, 4080, 7135, 5234, 8297, 9330, 742, 6022, 2593, 9088, 6296, 481, 1236, 5066, 3063, 5445, 6295, 7548, 2212, 9414, 9047, 5888, 3996, 8561, 7765, 7293, 3200, 780, 6967, 1378, 4889, 7636, 9484, 3159, 1473, 4024, 8039, 1464, 443, 9758, 2393, 9403, 9060, 5998, 5248, 5671, 9957, 3111, 2720, 5679, 9242, 5863, 1900, 0}
Returns: 2.4341584717983498
15
20
178007
{0, 4423, 65, 245, 399, 767, 515, 5950, 859, 1068, 1349, 3545, 153, 136, 3, 1066, 5426, 2325, 242, 452, 1543, 9, 677, 1313, 902, 2545, 2825, 182, 845, 175, 484, 1547, 838, 208, 426, 154, 697, 829, 814, 1036, 558, 79, 1, 986, 470, 108, 2953, 625, 634, 10, 408, 2176, 2546, 816, 1320, 433, 1192, 45, 2573, 3744, 860, 1124, 1250, 927, 17, 3487, 1405, 59, 83, 1791, 2588, 1212, 813, 11, 50, 307, 2234, 3144, 408, 390, 154, 265, 617, 1680, 291, 322, 1183, 960, 1470, 1878, 1639, 94, 3120, 19, 555, 1978, 2330, 2852, 621, 1301, 4405, 134, 664, 797, 73, 35, 1131, 6078, 1110, 279, 1179, 217, 2205, 690, 56, 1371, 3043, 129, 538, 676, 347, 119, 747, 514, 379, 161, 111, 996, 39, 64, 200, 476, 1252, 358, 243, 32, 92, 10, 169, 552, 26, 946, 3795, 861, 312, 120, 511, 1356, 323, 3780, 5723, 2714, 86, 2535, 71, 38, 2252, 3954, 815, 952, 792, 610, 64, 993, 82, 2258, 556, 1439, 477, 195, 519, 1530, 1580, 1275, 2990, 173, 861, 683, 1230, 1026, 89, 665, 48, 2313, 929, 54, 432, 165, 198, 501, 1831, 264, 670, 250, 263, 83, 2270, 1625, 3293, 1373, 1495, 719, 557, 637, 1683, 151, 12, 466, 23, 1825, 179, 265, 92, 611, 1216, 170, 302, 1826, 3566, 110, 470, 1687, 394, 389, 193, 280, 1016, 797, 1614, 2201, 19, 167, 101, 749, 244, 278, 88, 1175, 849, 15, 897, 419, 2069, 1922, 2382, 415, 3752, 935, 522, 1190, 1759, 1353, 1817, 684, 688, 1580, 1402, 1131, 1288, 279, 957, 2375, 1235, 375, 232, 436, 1218, 2709, 480, 543, 36, 562, 1418, 259, 3524, 1258, 138, 447, 307, 138, 1274, 333, 864, 5, 64, 482, 4499, 330, 1024, 4373, 1893, 1294, 1087, 517, 1327, 619, 151, 20, 26, 0}
{0, 1487, 63, 677, 6512, 811, 1743, 1143, 859, 2082, 119, 2823, 727, 415, 4, 2107, 371, 1109, 309, 7, 2198, 1681, 2364, 1920, 2732, 518, 539, 823, 2311, 674, 359, 2649, 251, 1255, 1115, 3169, 214, 1729, 2197, 620, 141, 1280, 472, 714, 208, 1686, 2028, 2986, 818, 4412, 423, 3026, 2628, 1564, 2216, 1474, 256, 4, 1974, 1065, 1144, 323, 788, 2200, 73, 2163, 3401, 723, 732, 1340, 1930, 2268, 3840, 11, 679, 119, 1786, 304, 108, 658, 428, 2363, 2336, 228, 234, 281, 448, 1248, 1517, 383, 3975, 283, 2388, 3, 662, 251, 1315, 1753, 976, 1033, 269, 46, 600, 92, 583, 1911, 1112, 737, 766, 260, 2722, 769, 1023, 1906, 180, 647, 1878, 2968, 5325, 450, 685, 103, 457, 3770, 467, 19, 2949, 1117, 1109, 69, 235, 646, 515, 693, 5175, 2371, 283, 821, 1047, 2377, 767, 1223, 426, 2313, 69, 97, 1261, 2383, 131, 719, 850, 1824, 326, 2411, 387, 6, 921, 613, 3016, 2406, 130, 858, 1019, 172, 3480, 339, 77, 4557, 78, 2170, 824, 371, 379, 54, 222, 633, 266, 2632, 398, 135, 46, 205, 46, 335, 675, 38, 49, 94, 67, 437, 1591, 1718, 660, 537, 1947, 478, 2632, 3254, 2059, 179, 75, 2036, 2884, 3588, 254, 1929, 14, 3235, 2034, 4, 870, 2300, 272, 444, 793, 542, 2615, 2619, 445, 427, 26, 38, 549, 145, 908, 2119, 470, 19, 2278, 2611, 48, 3326, 106, 265, 397, 4975, 5, 1091, 1039, 17, 56, 3795, 680, 92, 438, 152, 3, 37, 272, 377, 994, 297, 2735, 925, 742, 381, 2414, 116, 1927, 2150, 144, 1271, 1685, 888, 928, 104, 595, 303, 297, 1704, 161, 1091, 1585, 2577, 285, 1583, 1419, 391, 4844, 90, 157, 2325, 3710, 114, 2786, 436, 173, 119, 3681, 2128, 1199, 3906, 2602, 218, 2479, 2512, 1251, 308, 2625, 0}
{0, 8694, 493, 8262, 8713, 4659, 7322, 9914, 4188, 4331, 6770, 8667, 2561, 751, 9, 9148, 7572, 4332, 761, 640, 5681, 2837, 8186, 5299, 6718, 7891, 5196, 3097, 7511, 2176, 2925, 8362, 5939, 2164, 5343, 8545, 1249, 4516, 3806, 6278, 6529, 5591, 2846, 5048, 5700, 3752, 8199, 7221, 2956, 5946, 3169, 8948, 8268, 6984, 9545, 8401, 3624, 135, 5833, 9262, 2674, 5082, 2667, 6208, 115, 8771, 8573, 4303, 4790, 8938, 7478, 5024, 9709, 48, 1401, 1456, 8695, 9149, 4740, 3468, 1671, 6080, 5503, 4996, 691, 4478, 2703, 4819, 8492, 6356, 8474, 1834, 8937, 28, 3875, 4849, 6401, 8949, 2322, 3763, 7499, 230, 2116, 3395, 5829, 9829, 4291, 8903, 4480, 956, 6975, 6962, 5216, 6993, 696, 6726, 6551, 5781, 8281, 1621, 1538, 458, 9742, 5753, 5955, 1414, 5128, 2970, 2955, 528, 1094, 1645, 3559, 2619, 9005, 8385, 837, 1887, 5043, 5238, 2513, 7373, 8644, 7811, 494, 893, 2577, 5742, 1276, 5675, 9205, 5900, 638, 7562, 875, 192, 8123, 7532, 7385, 8709, 1497, 6618, 4252, 3214, 4940, 5369, 4186, 9820, 2790, 7460, 2298, 6589, 5105, 3152, 5498, 1770, 6481, 4946, 2505, 7469, 1210, 1408, 257, 4212, 2297, 405, 835, 1962, 447, 4340, 7516, 3504, 2668, 4550, 7768, 1604, 8543, 9797, 8850, 2292, 5553, 7362, 6531, 6470, 2480, 7909, 118, 9528, 8826, 2317, 6399, 5031, 547, 1899, 3713, 1008, 9229, 8921, 7037, 4434, 1909, 9383, 5429, 1152, 4027, 8030, 2143, 2793, 7804, 8238, 250, 5815, 619, 8236, 1016, 7429, 438, 2922, 7467, 44, 4772, 5842, 3616, 4383, 4108, 2189, 7844, 5078, 4860, 9526, 9308, 3371, 7340, 3903, 5637, 3311, 7804, 5812, 6547, 4223, 1509, 6957, 4081, 8995, 9153, 1050, 6855, 9042, 5120, 3100, 674, 2499, 4299, 5218, 5573, 7662, 3867, 3244, 8652, 1116, 2020, 4450, 9931, 265, 6655, 1669, 6574, 1331, 7507, 8933, 9886, 8828, 6052, 6439, 7439, 6664, 4621, 3044, 6148, 0}
Returns: 2.1307673449374844
10
30
1724
{0, 4, 1, 1, 5, 1, 2, 7, 3, 2, 3, 6, 21, 9, 8, 18, 1, 1, 1, 10, 1, 13, 10, 4, 10, 1, 4, 42, 2, 24, 18, 9, 2, 21, 4, 2, 27, 12, 17, 2, 12, 1, 11, 3, 18, 29, 2, 1, 4, 38, 19, 3, 20, 6, 4, 5, 14, 25, 1, 55, 5, 37, 9, 1, 26, 42, 16, 8, 11, 3, 3, 12, 9, 24, 54, 3, 7, 3, 15, 6, 20, 14, 12, 1, 1, 26, 4, 39, 7, 9, 4, 2, 29, 6, 1, 2, 13, 23, 4, 21, 3, 6, 1, 9, 10, 6, 4, 21, 58, 23, 5, 5, 8, 1, 7, 23, 1, 1, 1, 16, 9, 1, 15, 27, 23, 12, 9, 10, 3, 38, 2, 2, 4, 1, 41, 5, 5, 1, 6, 3, 15, 2, 2, 1, 10, 1, 1, 8, 1, 24, 7, 8, 2, 5, 2, 2, 2, 1, 12, 12, 7, 4, 1, 7, 6, 4, 7, 30, 9, 7, 1, 1, 2, 1, 30, 1, 12, 10, 2, 5, 7, 10, 18, 47, 1, 6, 17, 23, 3, 8, 1, 8, 14, 3, 4, 44, 35, 6, 6, 2, 4, 2, 2, 4, 10, 4, 8, 2, 2, 4, 12, 4, 14, 4, 11, 1, 2, 4, 1, 3, 5, 24, 13, 4, 48, 17, 45, 15, 1, 1, 35, 32, 5, 4, 4, 1, 12, 38, 16, 1, 7, 5, 9, 1, 57, 2, 22, 27, 16, 1, 8, 34, 7, 7, 3, 7, 37, 13, 13, 30, 17, 24, 6, 2, 46, 6, 1, 7, 6, 9, 8, 1, 7, 7, 3, 14, 15, 5, 29, 34, 2, 35, 4, 57, 7, 2, 7, 14, 5, 28, 11, 13, 8, 23, 5, 10, 1, 15, 8, 0}
{0, 3, 35, 1, 7, 12, 2, 8, 15, 2, 1, 2, 21, 1, 61, 5, 4, 27, 5, 6, 10, 9, 34, 28, 22, 5, 15, 5, 5, 12, 7, 8, 8, 18, 3, 1, 7, 26, 36, 9, 7, 1, 2, 4, 9, 10, 15, 1, 23, 6, 23, 31, 5, 5, 9, 9, 1, 6, 4, 14, 29, 17, 23, 3, 5, 7, 1, 2, 7, 2, 3, 33, 21, 13, 9, 4, 27, 1, 35, 3, 1, 24, 8, 1, 2, 15, 22, 9, 4, 13, 4, 6, 3, 6, 9, 4, 17, 3, 3, 1, 6, 6, 11, 53, 3, 17, 1, 13, 9, 13, 7, 39, 4, 1, 43, 13, 1, 3, 1, 34, 38, 1, 15, 23, 33, 6, 12, 1, 5, 18, 1, 1, 25, 1, 4, 20, 1, 12, 1, 3, 8, 5, 3, 1, 10, 10, 6, 1, 1, 31, 1, 5, 12, 3, 6, 19, 2, 6, 22, 23, 22, 20, 2, 28, 2, 5, 27, 3, 2, 2, 1, 1, 5, 1, 20, 1, 15, 5, 41, 1, 2, 12, 38, 9, 1, 4, 12, 28, 2, 5, 11, 22, 1, 28, 5, 12, 9, 8, 11, 7, 22, 52, 10, 22, 6, 5, 1, 7, 17, 26, 3, 3, 10, 3, 37, 9, 1, 2, 10, 1, 4, 7, 4, 5, 12, 22, 17, 1, 10, 6, 4, 36, 7, 7, 10, 6, 24, 8, 3, 2, 8, 12, 8, 6, 6, 13, 19, 12, 41, 1, 17, 20, 19, 6, 4, 10, 2, 6, 10, 5, 21, 3, 15, 4, 13, 2, 1, 7, 24, 47, 9, 5, 4, 11, 1, 6, 2, 2, 1, 16, 21, 7, 1, 3, 19, 1, 23, 8, 13, 5, 17, 43, 10, 1, 1, 10, 59, 9, 15, 0}
{0, 20, 83, 5, 52, 22, 19, 80, 56, 17, 8, 68, 66, 72, 89, 32, 10, 44, 25, 38, 20, 78, 64, 52, 57, 49, 38, 89, 37, 52, 85, 55, 86, 95, 15, 6, 47, 61, 83, 22, 95, 9, 21, 40, 66, 57, 31, 5, 87, 68, 68, 68, 48, 55, 18, 51, 83, 61, 34, 96, 71, 86, 46, 14, 45, 65, 27, 56, 44, 11, 14, 63, 46, 82, 83, 52, 68, 15, 62, 58, 80, 70, 58, 2, 5, 63, 47, 75, 19, 80, 12, 22, 100, 16, 33, 7, 57, 77, 16, 52, 11, 40, 46, 99, 44, 45, 26, 78, 92, 49, 57, 84, 31, 3, 92, 48, 1, 6, 4, 91, 73, 1, 88, 81, 88, 57, 28, 32, 18, 71, 12, 11, 74, 1, 91, 32, 20, 92, 42, 9, 34, 9, 13, 2, 25, 35, 50, 19, 14, 77, 14, 17, 56, 17, 39, 64, 6, 25, 58, 56, 75, 68, 11, 51, 34, 12, 62, 54, 17, 23, 2, 1, 56, 5, 67, 4, 39, 84, 86, 8, 12, 82, 69, 79, 7, 88, 56, 73, 11, 28, 87, 50, 70, 100, 23, 93, 59, 29, 55, 69, 39, 69, 45, 92, 30, 84, 68, 17, 52, 90, 35, 27, 39, 11, 73, 84, 10, 47, 45, 24, 58, 61, 31, 17, 85, 99, 93, 26, 37, 12, 62, 91, 34, 26, 27, 21, 90, 65, 37, 12, 43, 22, 91, 14, 96, 47, 80, 69, 94, 1, 93, 72, 39, 77, 41, 30, 59, 74, 95, 61, 60, 58, 42, 9, 77, 71, 3, 42, 100, 82, 30, 10, 18, 96, 5, 24, 64, 53, 66, 65, 35, 60, 10, 93, 76, 21, 41, 46, 51, 73, 55, 75, 42, 43, 32, 81, 97, 40, 68, 0}
Returns: 2.15234375
30
10
2166
{0, 1, 2, 31, 8, 10, 36, 1, 30, 37, 4, 1, 11, 9, 23, 32, 4, 2, 23, 4, 2, 48, 6, 27, 44, 46, 4, 19, 18, 15, 7, 2, 31, 3, 1, 7, 28, 4, 5, 10, 3, 34, 8, 7, 29, 3, 1, 21, 2, 8, 13, 10, 5, 10, 4, 8, 1, 2, 1, 2, 6, 4, 13, 28, 27, 4, 3, 4, 6, 4, 5, 23, 4, 1, 4, 35, 17, 13, 2, 2, 4, 6, 2, 8, 16, 11, 40, 20, 20, 29, 8, 1, 13, 5, 5, 25, 1, 14, 6, 31, 5, 24, 5, 14, 9, 1, 3, 6, 28, 6, 13, 43, 4, 4, 8, 3, 11, 19, 11, 22, 1, 3, 3, 11, 3, 14, 1, 2, 2, 18, 11, 6, 1, 4, 13, 16, 6, 8, 27, 2, 31, 2, 1, 5, 24, 10, 6, 16, 6, 5, 3, 20, 12, 39, 4, 60, 2, 20, 1, 4, 1, 3, 5, 13, 20, 1, 3, 22, 1, 1, 6, 1, 2, 3, 2, 4, 1, 5, 5, 15, 10, 4, 1, 23, 1, 7, 21, 41, 7, 1, 15, 4, 5, 1, 7, 8, 6, 1, 2, 28, 4, 25, 5, 9, 20, 36, 2, 5, 28, 8, 16, 1, 10, 3, 19, 2, 3, 32, 1, 1, 1, 5, 4, 23, 11, 28, 4, 34, 4, 1, 17, 9, 2, 22, 1, 9, 20, 4, 19, 2, 21, 20, 6, 68, 8, 1, 3, 5, 19, 38, 6, 18, 22, 3, 9, 2, 55, 10, 9, 10, 34, 10, 27, 5, 35, 5, 12, 6, 45, 1, 3, 14, 11, 1, 6, 27, 11, 3, 1, 1, 4, 22, 1, 21, 7, 26, 9, 63, 1, 5, 2, 3, 3, 4, 1, 21, 2, 7, 8, 0}
{0, 10, 1, 2, 46, 13, 7, 9, 19, 7, 2, 1, 43, 4, 21, 13, 3, 11, 7, 2, 20, 12, 17, 7, 5, 6, 20, 4, 17, 5, 30, 1, 1, 1, 1, 17, 11, 24, 3, 19, 8, 21, 1, 1, 6, 5, 9, 10, 1, 8, 7, 21, 4, 17, 4, 3, 26, 6, 1, 1, 2, 29, 10, 3, 13, 2, 5, 2, 4, 2, 4, 24, 32, 1, 60, 44, 5, 14, 2, 9, 2, 1, 39, 4, 7, 15, 14, 9, 7, 1, 1, 1, 9, 12, 13, 41, 1, 4, 24, 4, 17, 3, 13, 13, 12, 4, 5, 11, 17, 1, 44, 11, 2, 2, 38, 3, 6, 8, 23, 10, 2, 37, 11, 12, 3, 23, 1, 17, 3, 9, 10, 4, 1, 9, 13, 3, 5, 8, 5, 16, 5, 1, 5, 7, 2, 2, 3, 21, 53, 1, 14, 32, 9, 8, 3, 8, 2, 12, 3, 9, 12, 14, 1, 14, 2, 1, 6, 3, 14, 1, 17, 1, 11, 5, 1, 1, 1, 19, 6, 4, 1, 3, 20, 9, 2, 3, 4, 6, 4, 15, 12, 3, 1, 3, 13, 8, 3, 22, 5, 3, 8, 43, 34, 2, 15, 10, 1, 6, 1, 16, 25, 3, 13, 7, 1, 12, 20, 12, 14, 1, 2, 1, 36, 8, 41, 7, 3, 9, 4, 4, 8, 15, 14, 5, 13, 25, 19, 1, 2, 1, 21, 25, 20, 1, 11, 29, 16, 1, 12, 8, 8, 3, 8, 16, 2, 12, 5, 1, 5, 9, 5, 6, 10, 10, 15, 20, 6, 2, 24, 9, 6, 11, 14, 1, 13, 8, 3, 23, 19, 11, 37, 18, 6, 4, 21, 17, 3, 1, 1, 29, 5, 16, 3, 19, 19, 11, 1, 2, 24, 0}
{0, 93, 15, 59, 73, 72, 59, 21, 63, 84, 31, 5, 70, 96, 95, 69, 17, 100, 70, 10, 84, 93, 91, 55, 69, 88, 33, 32, 86, 63, 50, 6, 79, 10, 8, 67, 96, 39, 46, 58, 23, 92, 37, 26, 68, 34, 24, 72, 4, 35, 53, 48, 37, 89, 49, 25, 39, 18, 2, 5, 32, 91, 71, 64, 62, 30, 54, 33, 31, 28, 21, 69, 78, 6, 84, 100, 77, 95, 30, 71, 54, 16, 63, 33, 98, 64, 71, 45, 87, 46, 70, 6, 39, 46, 22, 98, 5, 96, 89, 45, 65, 49, 23, 61, 31, 25, 52, 32, 79, 24, 78, 78, 10, 9, 64, 9, 88, 36, 46, 61, 8, 70, 30, 57, 26, 73, 7, 38, 13, 67, 44, 40, 12, 60, 40, 68, 88, 23, 66, 50, 77, 4, 55, 48, 76, 16, 45, 62, 79, 12, 93, 98, 77, 82, 25, 99, 10, 61, 5, 35, 35, 40, 16, 63, 45, 3, 59, 42, 52, 2, 57, 5, 59, 11, 3, 44, 9, 57, 93, 48, 24, 35, 34, 85, 12, 44, 56, 67, 60, 30, 39, 17, 30, 17, 40, 58, 43, 33, 10, 61, 16, 88, 68, 37, 78, 87, 10, 16, 38, 89, 58, 33, 74, 32, 54, 20, 34, 94, 47, 1, 19, 10, 79, 51, 76, 85, 17, 59, 21, 7, 81, 29, 49, 59, 20, 60, 67, 24, 36, 14, 100, 95, 56, 97, 42, 93, 68, 15, 63, 97, 57, 66, 67, 28, 62, 38, 85, 30, 21, 82, 86, 93, 84, 22, 74, 46, 26, 28, 92, 24, 14, 41, 35, 3, 78, 64, 42, 46, 34, 37, 63, 75, 47, 78, 98, 67, 56, 87, 3, 82, 10, 54, 12, 73, 90, 49, 7, 74, 46, 0}
Returns: 2.566371681415929
28
10
1932
{0, 10, 23, 25, 18, 4, 25, 5, 33, 67, 2, 3, 4, 13, 37, 37, 9, 13, 24, 38, 45, 1, 17, 4, 23, 1, 3, 53, 21, 1, 6, 1, 7, 2, 6, 10, 20, 8, 5, 5, 1, 8, 3, 1, 1, 1, 50, 20, 5, 2, 18, 3, 4, 16, 28, 10, 6, 28, 5, 19, 15, 6, 1, 7, 5, 3, 7, 4, 2, 6, 1, 11, 1, 4, 1, 4, 1, 19, 9, 45, 73, 6, 34, 20, 20, 35, 4, 11, 1, 12, 8, 2, 5, 6, 2, 20, 2, 10, 1, 1, 2, 1, 2, 1, 28, 27, 2, 14, 13, 1, 9, 13, 17, 1, 6, 4, 30, 5, 3, 3, 27, 7, 10, 5, 14, 19, 1, 1, 12, 3, 4, 6, 13, 55, 37, 36, 4, 9, 23, 1, 14, 2, 11, 5, 14, 1, 12, 15, 9, 3, 5, 4, 2, 6, 3, 3, 3, 1, 4, 11, 11, 5, 1, 25, 11, 5, 28, 3, 19, 5, 20, 31, 4, 30, 4, 33, 8, 4, 12, 3, 15, 2, 19, 5, 29, 9, 8, 24, 13, 5, 2, 12, 8, 46, 12, 8, 23, 11, 5, 1, 1, 11, 1, 2, 4, 3, 4, 2, 69, 15, 21, 2, 3, 1, 10, 5, 3, 7, 3, 1, 29, 4, 1, 23, 1, 39, 11, 30, 15, 14, 11, 22, 14, 2, 2, 6, 4, 17, 19, 9, 1, 10, 2, 18, 4, 6, 18, 5, 2, 8, 3, 8, 2, 15, 5, 3, 4, 13, 22, 28, 12, 4, 17, 20, 2, 2, 29, 36, 13, 30, 5, 1, 4, 9, 6, 4, 1, 6, 3, 0}
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{0, 39, 50, 47, 45, 13, 66, 22, 58, 88, 31, 45, 11, 65, 97, 52, 65, 60, 63, 83, 98, 30, 89, 82, 45, 10, 97, 97, 54, 1, 46, 18, 42, 22, 42, 38, 64, 99, 35, 13, 7, 91, 10, 17, 82, 13, 86, 40, 64, 35, 36, 20, 36, 91, 76, 51, 82, 76, 49, 68, 50, 74, 63, 69, 27, 33, 76, 65, 8, 62, 2, 43, 1, 77, 1, 47, 3, 71, 61, 71, 95, 70, 80, 54, 66, 89, 59, 63, 13, 76, 22, 21, 81, 37, 19, 89, 49, 28, 22, 12, 6, 43, 4, 4, 79, 61, 17, 84, 76, 2, 82, 34, 59, 69, 14, 20, 89, 49, 14, 51, 74, 68, 97, 45, 78, 64, 12, 11, 90, 31, 15, 92, 28, 92, 71, 89, 14, 70, 95, 1, 20, 17, 26, 50, 75, 26, 30, 67, 57, 82, 31, 86, 90, 19, 39, 16, 18, 8, 11, 22, 22, 15, 56, 53, 41, 11, 92, 89, 57, 53, 99, 76, 15, 90, 58, 77, 31, 80, 70, 58, 40, 59, 45, 76, 49, 60, 20, 100, 63, 12, 14, 25, 46, 64, 76, 58, 92, 80, 38, 12, 1, 62, 3, 12, 41, 64, 8, 5, 90, 78, 65, 4, 19, 38, 42, 25, 84, 26, 9, 28, 40, 55, 1, 87, 11, 94, 47, 95, 25, 37, 66, 56, 68, 90, 17, 39, 39, 65, 94, 33, 7, 76, 31, 66, 9, 16, 82, 95, 89, 33, 19, 17, 71, 69, 13, 32, 7, 81, 56, 59, 72, 53, 94, 91, 4, 99, 87, 77, 75, 91, 58, 15, 67, 17, 9, 20, 2, 76, 15, 0}
Returns: 2.1574803149606296
10
28
16964035
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Returns: 2.3055768424613707
28
10
17517147
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Returns: 2.4192776934213778
10
29
181466
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Returns: 2.229211186472173
10
29
2222
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Returns: 2.693798449612403
29
10
21524569
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Returns: 2.6705433845277917
10
29
190052
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Returns: 2.603955007256894
10
29
20726668
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Returns: 2.0455870687840965
32
8
231263
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Returns: 2.809679907443116
17
17
1673
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Returns: 2.168316831683168
17
17
18385005
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Returns: 3.386505406850197
98
2
45740959
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Returns: 1.1518840109184874
2
130
5801
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Returns: -1.0
3
11
60
{0, 1, 1, 1, 3, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 2, 3, 2, 2, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 0}
{0, 1, 4, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 7, 1, 5, 1, 4, 1, 1, 1, 1, 1, 6, 1, 1, 2, 2, 1, 2, 1, 1, 0}
{0, 3, 7, 10, 8, 5, 2, 2, 6, 8, 4, 2, 2, 10, 4, 9, 4, 10, 5, 2, 10, 7, 1, 9, 3, 2, 3, 6, 7, 9, 6, 5, 0}
Returns: 1.125
3
4
113
{0, 1, 2, 3, 6, 3, 8, 3, 6, 1, 2, 0}
{0, 19, 1, 3, 4, 1, 4, 7, 1, 1, 2, 0}
{0, 30, 14, 7, 28, 11, 22, 21, 15, 2, 6, 0}
Returns: 1.875
5
9
622
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{0, 4, 37, 22, 3, 14, 10, 6, 5, 6, 5, 17, 4, 7, 12, 3, 1, 3, 3, 1, 5, 1, 11, 37, 6, 24, 6, 3, 21, 1, 2, 27, 7, 1, 8, 1, 8, 1, 26, 20, 6, 6, 6, 7, 0}
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Returns: 2.161290322580645
280
1
168720521
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Returns: 1.034163639869071
8
8
703
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Returns: 3.8541666666666665
5
5
3463524
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{0, 230000, 241978, 66472, 1222, 17345, 17304, 441, 54033, 21415, 57415, 8156, 77030, 56242, 5892, 325200, 3122, 985, 6600, 65822, 68849, 148664, 10270, 6136, 0}
{0, 371688, 413064, 355998, 11395, 534832, 280117, 123750, 572064, 422357, 220135, 842485, 324663, 878719, 140184, 584778, 9303, 42901, 594966, 396852, 249278, 509800, 740026, 20893, 0}
Returns: 15.508717900123187
15
15
16759336
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Returns: 4.054848906129444
16
16
1634
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Returns: 2.775
1
256
1550040
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{0, 3782, 9805, 7592, 1270, 4036, 9140, 3206, 5876, 5699, 8562, 8287, 5440, 3095, 8027, 5482, 2794, 3853, 4458, 2225, 2785, 5910, 5950, 5684, 1456, 7927, 1878, 5681, 2992, 9006, 2178, 7359, 6828, 8745, 1633, 6063, 3987, 3652, 7978, 8073, 3030, 2613, 4296, 3878, 3065, 4585, 183, 2215, 3053, 6926, 7079, 7106, 7451, 5219, 6647, 5541, 9333, 8192, 8827, 3280, 24, 6475, 8892, 8623, 3070, 6526, 758, 7350, 8148, 6188, 8265, 2563, 1067, 5960, 4674, 3256, 3753, 170, 4060, 1402, 1991, 6473, 2473, 9169, 8640, 8957, 4101, 7969, 4258, 5454, 4899, 8798, 3408, 1569, 7413, 7010, 5398, 7953, 5160, 321, 4749, 5670, 920, 3820, 345, 2123, 6132, 1477, 3155, 1444, 2864, 5868, 2374, 7223, 5015, 7267, 2945, 9644, 5825, 8638, 852, 9392, 6355, 2510, 6725, 7722, 5773, 990, 5551, 5475, 8012, 6736, 6798, 3653, 9616, 9207, 2752, 1073, 7810, 8829, 922, 1772, 6408, 3935, 5336, 2511, 3659, 7136, 4481, 5047, 5882, 6816, 931, 8788, 6187, 5324, 3018, 4767, 800, 5731, 2484, 3780, 9452, 788, 5540, 7661, 9282, 8996, 9171, 6232, 8936, 3931, 2722, 7840, 8939, 8587, 6470, 9419, 7394, 2737, 3682, 2999, 1153, 6924, 6151, 885, 7857, 7761, 8060, 7779, 7405, 6202, 9471, 6054, 5590, 3973, 775, 5649, 8506, 3816, 4944, 9144, 9263, 760, 6527, 304, 1718, 9530, 3520, 9695, 1634, 8250, 1049, 7416, 7078, 6802, 5661, 8459, 474, 7507, 2032, 8950, 9666, 657, 5130, 7625, 8204, 6334, 6081, 364, 8283, 3864, 1735, 7374, 4899, 8945, 1512, 8204, 3851, 79, 4859, 1582, 6043, 5964, 1336, 6902, 2154, 9396, 1616, 989, 575, 6586, 8931, 669, 5408, 0}
Returns: 0.9454010161278781
2
2
14
{0, 3, 1, 0}
{0, 1, 1, 0}
{0, 5, 3, 0}
Returns: 3.0
2
2
57
{0, 6, 1, 0}
{0, 3, 1, 0}
{0, 21, 5, 0}
Returns: 2.0
2
2
37
{0, 1, 3, 0}
{0, 1, 3, 0}
{0, 5, 11, 0}
Returns: 1.0
1
4
1000
{0, 1000000, 1000000, 0}
{0, 1, 1, 0}
{0, 1, 1, 0}
Returns: 1000000.0
1
300
150500000
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Returns: -1.0
300
1
150500000
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Returns: -1.0
2
150
76000000
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Returns: 1.104229109594719
150
2
76000000
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Returns: 1.1894817112788878
3
100
51500000
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Returns: 1.08919551463658
100
3
51500000
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Returns: 1.1798629035098438
4
75
39500000
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Returns: 1.2620109433181101
75
4
39500000
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Returns: 1.2017444954073118
5
60
32500000
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Returns: 1.3380929519173603
60
5
32500000
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Returns: 1.4858808146711098
6
50
28000000
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Returns: 1.2430506752485075
50
6
28000000
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Returns: 1.4915883872475992
7
42
24500000
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Returns: 1.4892309255515508
42
7
24500000
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Returns: 1.3218232980689022
8
37
22500000
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Returns: 1.5391372376500578
37
8
22500000
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Returns: 1.6697607120414903
9
33
21000000
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Returns: 1.6059523932123851
33
9
21000000
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Returns: 1.8252104445486474
10
30
20000000
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Returns: 1.5949311522718974
30
10
20000000
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Returns: 1.8848511693749908
11
27
19000000
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Returns: 1.6972864771697138
27
11
19000000
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Returns: 1.7672276253595307
12
25
18500000
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Returns: 2.0055362561064434
25
12
18500000
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Returns: 1.7813938688959774
13
23
18000000
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Returns: 1.6644938742359794
23
13
18000000
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Returns: 1.5844748529724937
14
21
17500000
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Returns: 1.9570951888033048
21
14
17500000
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Returns: 1.9769702960992153
15
20
17500000
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Returns: 2.18867655576717
20
15
17500000
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Returns: 1.815311823088673
16
18
17000000
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Returns: 1.924685337620233
18
16
17000000
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Returns: 2.0537725073947937
17
17
17000000
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Returns: 2.2478364550404395
17
17
17000000
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Returns: 2.2478364550404395
17
17
1000000000
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Returns: 1.9064153687582448
17
17
13000000
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Returns: 1.6561069701683804
17
17
613838932
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Returns: 1.8808875385440367
9
33
1000000000
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Returns: 1.494844705226343
17
17
864283461
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Returns: 2.0244396094849657
36
2
130691676
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Returns: 1.0562678489483488
15
20
1000000000
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Returns: 1.8715210824096977
15
20
1000000000
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Returns: 715540.4375
3
3
1000000000
{0, 100, 1, 1, 1, 1000, 1, 1, 0 }
{0, 9999, 1, 100, 1, 1, 1, 1, 0 }
{0, 1, 111, 1, 1, 1, 111, 111, 0 }
Returns: 9.823529411764705
17
17
1000000000
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Returns: 1.0