Statistics

Problem Statement for "Egalitarianism2"

Problem Statement

There are N cities in the plane. For convenience, the cities are numbered 0 through N-1. For each i, the city number i is represented by the point at coordinates (x[i], y[i]).


The king wants to connect all cities by building exactly N-1 roads. Each road must connect two cities. All roads must be straight. Hence, the length of a road is equal to the Euclidean distance between the two points it connects. The roads are allowed to cross and even overlap arbitrarily. (You cannot change roads at a crossing. Hence, the N-1 roads connect all cities if and only if their topology is a tree.)


The king does not care about roads being short. However, people often complain if some roads are short and others are long. Therefore, the king would like to select a set of N-1 roads such that they connect all cities, and the standard deviation of the sequence of their lengths is as small as possible.


Formally, given a sequence of real numbers (a1,...,aS) we can compute their standard deviation as follows. First, let b = ((a1+...+aS) / S) be their mean - i.e., the average of our numbers. Next, let c = (sum_i (b-ai)^2) be the sum of squared distances of all values from the mean. Finally, the standard deviation of our sequence is computed as sqrt(c/S). Note that our sequence will contain exactly N-1 road lengths, hence in the above formulas S will be equal to N-1.


You are given the int[]s x and y with N elements each: the coordinates of the N points. Compute and return the smallest possible value of the standard deviation of lengths of selected roads.

Definition

Class:
Egalitarianism2
Method:
minStdev
Parameters:
int[], int[]
Returns:
double
Method signature:
double minStdev(int[] x, int[] y)
(be sure your method is public)

Notes

  • The Euclidean distance between points (a,b) and (c,d) equals sqrt( (a-c)^2 + (b-d)^2 ).
  • Your return value must have an absolute or a relative error of less than 1e-9.

Constraints

  • x will contain between 3 and 20 elements, inclusive.
  • x and y will contain same number of elements.
  • Each element in x will be between -1,000,000 and 1,000,000, inclusive.
  • Each element in y will be between -1,000,000 and 1,000,000, inclusive.
  • No two cities will be located in the same place.

Examples

  1. {0,0,1,1}

    {0,1,0,1}

    Returns: 0.0

    We can build these roads: 0-1, 1-3, 3-2.

  2. {0,0,0}

    {0,9,10}

    Returns: 0.5

    The optimal solution is to build the roads with lengths 9 and 10. (Note that these two roads overlap, but that is allowed.)

  3. {12,46,81,56}

    {0,45,2,67}

    Returns: 6.102799971320928

  4. {0,0,0,0,0,0,0}

    {0,2,3,9,10,15,16}

    Returns: 0.9428090415820632

  5. {167053, 536770, -590401, 507047, 350178, -274523, -584679, -766795, -664177, 267757, -291856, -765547, 604801, -682922, -404590, 468001, 607925, 503849, -499699, -798637}

    {-12396, -66098, -56843, 20270, 81510, -23294, 10423, 24007, -24343, -21587, -6318, -7396, -68622, 56304, -85680, -14890, -38373, -25477, -38240, 11736}

    Returns: 40056.95946451828

  6. {-306880, 169480, -558404, -193925, 654444, -300247, -456420, -119436, -620920, -470018, -914272, -691256, -49418, -21054, 603373, -23656, 891691, 258986, -453793, -782940}

    {-77318, -632629, -344942, -361706, 191982, 349424, 676536, 166124, 291342, -268968, 188262, -537953, -70432, 156803, 166174, 345128, 58614, -671747, 508265, 92324}

    Returns: 36879.15127634308

  7. {5777, -5301, 6209, -6600, -715, -2810, 1923, 1950, 2502, 3038, 2936, -5287, -1280, 5698, 2592, 2409}

    {-166, -103, -131, 64, 147, -121, -164, 17, -60, 71, -170, -86, 129, -82, -39, 155}

    Returns: 271.259608558745

  8. {660, 7165, 509, -6666, 4966, -122, -7359, -6902, -5171, 1325, -5220, 8406, -4782, 1965, 4746, -2681, 5972, -6278}

    {23128, -38655, -33294, 14425, -58156, -80729, -24803, -34471, 9942, 15048, 45109, 68997, -29260, -20727, 77070, -86194, -76561, -70561}

    Returns: 3986.967988700865

  9. {-629414, -324391, -264311}

    {-2, 21, 18}

    Returns: 30039.999840321456

  10. {583, 0, 530, -160, -172, 182, 332, 338, -330, 347, -810, -538}

    {46, 8, 41, -45, 46, 30, -34, 7, -11, -35, 3, 16}

    Returns: 31.397307185989142

  11. {-5246, 2266, -6759, 5016}

    {208, -674, -504, 450}

    Returns: 1104.0529049413371

  12. {-559, 468, -6892, -2632, -2319, -1793, -6530, 1778, 6026, 6515, -6178, 5411, 468, -4751, 2038}

    {-637294, 443117, -87256, -705996, 821966, 541804, -772249, 75092, 287311, -909574, 324143, -51544, -321445, 264267, 476149}

    Returns: 47754.58395460869

  13. {17985, 331605, 258697, -414591, 44635, -335501}

    {2134, 903, 104, 2557, 1825, -269}

    Returns: 64546.86633308984

  14. {11554, 3481, 9490, 13255}

    {3, 7, -1, -2}

    Returns: 1539.4337319269196

  15. {-578, -581, 464, 71}

    {3, 4, 0, -7}

    Returns: 121.4035489434658

  16. {675989, -129070, 215161, -313826, -137988, 617477, -503052, -440999, -483456, -543934, -36837, -134270}

    {967, 5499, 675, 3222, -4923, 4022, 2126, 3862, -4959, 4951, -4457, 3619}

    Returns: 46378.70549960345

  17. {518755, -63434, 314925, 65781, 387170, 398239}

    {-1529, -4217, -1366, -2722, -1381, 4027}

    Returns: 50862.126160609325

  18. {-19643, -427, 5670, -8029, 756, 7090, -17990, 19740, -5207, 8418}

    {15, 23, -2, 17, -12, 22, 11, 5, 12, 20}

    Returns: 1441.7279427836413

  19. {-227, 536, 189, -280}

    {-1645, -2151, -929, -1396}

    Returns: 105.21606633264568

  20. {-24871, 3846, -25617, 28938, -28825, 25764, -14199}

    {-791, -167, 721, -834, -427, 736, -623}

    Returns: 4907.988204398708

  21. {-30, -58, -67, 5}

    {-22, 1, 5, -6}

    Returns: 4.085178115097297

  22. {-3, -3, 2, -5, -5, 10, -8, -7, 2, -3, 3, 9, -6, 4, -2, -1, 0, 3, 1}

    {6, -4, -6, -1, -6, -5, -6, 4, -1, -5, -5, -6, 0, 4, 5, 2, -6, 1, 3}

    Returns: 0.3174988430662238

  23. {5719, 16856, -13397, 56534, -58532, -56351, 28280, -26647, 42654, 22693, 43889, -38401, -31330, -13579}

    {60712, 35854, -63556, -48027, -28724, 49009, -57960, -64409, -44125, 47853, 44119, -78325, 46269, 74534}

    Returns: 3860.305210015256

  24. {31288, 281486, 169052, 3189, -31667, 254526, 31158, -144597, 272930, -131861, -191124, -261308, -127665, 240879, 62095, 162131, 294705, -65105, -84333, 285539}

    {-8, -7, -11, 0, 12, -3, -8, 7, -14, 10, 1, -8, -10, -15, -7, -10, -2, 11, -7, -15}

    Returns: 12506.074501228519

  25. {78, -146, 136}

    {-1450, -3429, -3695}

    Returns: 127.05616572118299

  26. {5, 6, -2, 2, 3, 5, 0, -5, -5, 0, 1, -1, 7, -4, -3, 3, -5, -6, -7}

    {518652, 455484, 162487, 350249, 238253, -280881, 511955, -72432, 540300, 205295, -405408, -273113, 257991, 307359, -161323, -279997, 120713, 141586, 515045}

    Returns: 23101.651869488327

  27. {-373136, -466850, -260427, 217507, 508573, 56112, 396835, 340228, 185147, 113716}

    {-4146, -3457, 2513, 52, -2028, 4577, -796, 3502, -374, -4674}

    Returns: 54326.5882145463

  28. {-7, -5, -4, 1, 7, -3, 0, -7, -8, -7, -1, 6, -6}

    {218, 6, 484, -173, -310, -438, 267, 135, 348, 5, 550, 538, -239}

    Returns: 31.88098407932375

  29. {55334, -53329, -453, -463, 11432, 13497, -27968, -19648, -38279, -59383}

    {-19, 11, -3, 16, -18, -23, 3, 16, -11, 11}

    Returns: 4362.233711419435

  30. {4067, -1141, -1046, 3357, 3174, 4574, 5913, 1642, -6090, 4691, 4788, -190, -2792, 1150, -44, 893, 3131, -613, 3597}

    {25, 31, -28, 47, -13, -40, 54, -26, -24, 13, -51, 1, 53, 57, 52, -48, 61, 11, 59}

    Returns: 276.5646333474226

  31. {-81, -1152, 1311, -1085, -1032, 341, -1391, 1135, 1670, -609, 1274, 871, 291, -1407, 432, 5, -715, 1528, 354}

    {-5, 4, -5, 6, -6, -4, -3, 5, -3, 4, -5, 4, -1, 5, -1, 1, -4, 6, -2}

    Returns: 50.84126016319136

  32. {16, 8, 13, -18, 10, 11, -6, 7, -12, 21, -6, 12, -3, -25, 26, -21, -25}

    {-180982, 253920, 129821, 232794, -146413, 98212, 23196, 217773, -238410, -264418, 52727, -23917, 288917, 212, -224013, 34060, -188537}

    Returns: 13329.321834323295

  33. {104, -52, -72, -6, -9, 147, 35, -120, -87, 91, 118, -114, -149, -85, -2, 59, 133, -107, -71}

    {-793847, -28114, 301276, 703332, 200356, -325993, 745990, -122855, -515289, 563078, -550450, -747678, -381183, 785498, 324581, -417918, -290279, -524431, 290843}

    Returns: 34161.43218733342

  34. {4519, 7714, -7202, -7112, -2335, 3171, 4904, -4610, -823, 2831, -609, -5991}

    {-570, -259, 33, 344, 154, -626, -82, -299, 661, 70, 396, -204}

    Returns: 455.93254037562724

  35. {3, -7, -8, -45, -84, 57, 65, 4}

    {38376, -26351, -3067, -127039, -201438, 119941, -123102, 109810}

    Returns: 15339.351941858564

  36. {-5, -5, 0, -2}

    {-6, -5, 2, -9}

    Returns: 1.0743256160550643

  37. {29, 55, -84, 100, 13}

    {-408, 4836, -5793, -2109, 3415}

    Returns: 682.819159263403

  38. {-33, 42, -17}

    {313, 6029, -18250}

    Returns: 2858.032395962411

  39. {9, 2, -3, 10, -12, 12, 5, 7, -12, 4, -1, 10, 12, 1, 11, 12}

    {190245, 446093, -545896, -564485, 354160, 112958, -571300, 478828, 489759, -297167, 401402, -262135, 381307, 12391, 175812, -101609}

    Returns: 24525.64498225122

  40. {3715, -5780, -1523, -10188, 4205, 4499, -9296, 2244, -6781, 4509, 8129, -8352, -6711}

    {-318, 563, 52, 421, 222, -241, 405, -312, 586, 816, -84, -664, 177}

    Returns: 553.4992577714017

  41. {72567, 256129, 6257, 40569, 206621, 271687, -177844, 79825, 104203, 156697, -43152, 128483, -109169}

    {20, -20, 12, -15, 37, 38, 34, -4, 1, -13, -11, -9, 29}

    Returns: 9019.180671772212

  42. {-27918, -38483, 19387, 36788, 11262, -54997, -7326, 3726, -25038, -17528, 29182, 57105}

    {2239, 226, 325, 3422, -2274, -2287, 2662, 115, -674, 2504, -1738, 243}

    Returns: 2370.6025386873685

  43. {-11731, -17552, 21046, 18166, -5758, -17175, -20775, -19762, 5751, 884}

    {31752, 52235, 39177, 55599, -8713, 34385, -23093, -50281, 48680, 48219}

    Returns: 6086.550337820554

  44. {-123, 185, -4, -269, -241, -276, -202, -144}

    {-6707, 11010, 7317, -7157, 15883, -16447, -7381, 8868}

    Returns: 2567.535942756141

  45. {-2787, -6188, -12883, 8575, -15396, -8788, -10130, 18900, -10760}

    {509, -2480, 2118, -3522, -4689, 2556, 891, -4173, -3155}

    Returns: 1303.9821046930265

  46. {-122, 230, -436, -141, 34, -188, 264, 211, -126, 122}

    {-38159, 332388, -384664, -298616, -271400, 287617, 238745, 56862, 365977, 369226}

    Returns: 30881.916843845047

  47. {-4692, -1384, -4255, 305, 4480, -4428, 5927, 6935, 3672, -707, -7401, 129, 3952, 7040, -6681, -947, 5215}

    {5832, 14941, 18561, -12736, -26451, -2721, 11694, -3923, 5063, 27501, -26785, 7362, 10199, -23384, 11542, 9636, 22439}

    Returns: 782.0204506797977

  48. {-9981, -5247, -4594, -2261, 3367, -6360, 9068, -7982, 3773, 10251, -10923}

    {54, 36, -55, 48, -19, 26, 19, 34, -12, 9, -4}

    Returns: 654.260255402633

  49. {60594, 208549, 206883, 71030, 99317, -115131, -80241, -8834, 104375, 185312, -109180}

    {4639, 1140, 8172, -6553, -606, 78, 3499, -6559, -6562, -7160, 8377}

    Returns: 12690.590210478462

  50. {-4, -8, 3, 10, 7, 2, -14, 14, -4, -12}

    {-6, 0, -4, 5, -4, -1, 7, 1, -2, 7}

    Returns: 0.9883136782273713

  51. {123, 115, -688, 732, -503, 742, 448, 687, -180, -606, -198, -334, 528, 492, -157}

    {-56, -62, 63, 1, -28, -27, 50, -9, -1, 25, -10, -58, -2, -61, -45}

    Returns: 43.975699436668414

  52. {7, -31, -72, 17, 69, 78, 93, 77, -33, 17, 3, 48, 71, -41, 13, 23, -3, 49}

    {-534432, -754240, 93761, 334955, 112192, 253421, -782977, 383925, -309163, 165545, -745042, 726792, -599625, 255438, 790978, 608011, 613883, -329714}

    Returns: 57890.52400814554

  53. {-4, -8, 3, -1, -7}

    {47664, -32765, -5689, 11390, -36580}

    Returns: 6218.585841490388

  54. {3198, 1807, -2286, -8112, -944, -6092, 2478, 8568, 4504}

    {500032, 458071, -476706, 273366, -183794, 228252, 591660, 274981, -193425}

    Returns: 52734.74242051689

  55. {8084, 4503, 35021, 17225, -36518, -9408, -1597, -4001}

    {-409523, 179829, -245025, -224622, 701657, -488185, -454264, -553777}

    Returns: 105536.69247585024

  56. {-22, -15, 18, -24, 52, -18, 32, 33, 53, -35, -53, -55, -15, -9, -26, -36}

    {8, 8, -1, 1, -3, 4, -7, -1, 4, 2, -4, -6, 2, -3, 2, 1}

    Returns: 2.840728315715467

  57. {-3, -1, 1, -2, 2, -4, 2, 1, 1, -4, 1, -1, 0, 4, -5, 5, 4, 1, 1}

    {3752, -3303, 3499, 2274, -742, 43, -1805, -2588, -4654, -2916, 692, -531, 4540, -2601, 3760, 1983, -2055, -3011, 211}

    Returns: 200.28281228188717

  58. {-2, -5, 4, -4, 2, 3, 6, 6, -6, 4, 1, -5, -2, -2, -5, -5}

    {88056, -22347, -24631, -38255, -8698, -77730, -63559, 16928, 16342, -7349, -28443, -80915, -35432, 73587, -32302, 6038}

    Returns: 6452.650627768802

  59. {101113, -66638, -47895, 315942, 331196, -3435, 197558, 251374, -113250, 113169, -218597, -147313, 140724, 313698, 288334}

    {-4, -4, 6, -2, 3, -7, 4, -4, -9, -5, 6, 8, 3, 8, -6}

    Returns: 15983.64901861192

  60. {16633, -1399, 35025}

    {688, 4006, 297}

    Returns: 30.715258444794017

  61. {-20, -11, -41, 58, -54, 73, -41, 48, -46}

    {73, -124, 369, -302, -176, 35, 324, -43, 145}

    Returns: 18.716359651737125

  62. {44, -60, -65, 52, -53, -41, -30, -48, 38, -33, 18, 51}

    {8, 2, -6, 6, -1, 6, 4, 2, 3, -5, 6, -10}

    Returns: 4.940494945846833

  63. {-12256, -8057, 2129, -12575, 10612, 5418, -10932, -8658, -10127, 992, -722, -3139, -7790, 10568, -8046}

    {-7, 2, -7, -5, -6, 1, -4, -2, 0, 7, 4, 4, 7, -6, -3}

    Returns: 653.8232578487263

  64. {-39182, 32037, -2046, -28292, -1944, -46070, 44572, 16328, 31713}

    {-53567, -421640, -104611, 306737, 376583, -20512, 228524, 224713, -425644}

    Returns: 26747.30501844281

  65. {209916, -69137, 139347, -334841}

    {50, -7, 54, 13}

    Returns: 30609.19746367781

  66. {19, -23, 27, 30, 17, -26, -7, -9, 16, 4, 1, -3, 9, -5, 6, 27, -20, -30, 17, 34}

    {-33, -13, 2, -27, 30, -35, -23, -32, -31, -3, -3, 16, 18, -35, -17, -14, -17, 31, 19, 24}

    Returns: 1.4258296863314457

  67. {12021, -602007, 472608, 188120, 232778, -461903, -140675, 374605, 98432, -82222, 654564, 291397}

    {-18320, 14439, -1825, 1297, -5754, -14689, -10583, -5187, 4077, -16884, -5383, -5405}

    Returns: 40186.42711761184

  68. {-68, 680, 495}

    {23, -27, 23}

    Returns: 93.334630203774

  69. {-3598, -3148, 961, -6911, 1912, -2763, 3994, 5610}

    {5, 7830, -223, 14989, -16993, 1630, -7249, 7971}

    Returns: 964.0940678016851

  70. {-3, -42, 5, -60, -32, -39, 1, 59, -30, 0, -46, 42, 45, 41, 45, -53, -43, -36, 30, 29}

    {-38746, -8219, 81076, -80419, 65149, -82469, -61184, -20632, -60840, 71631, 88119, -39603, -60948, 42563, 18502, 75803, 39578, 81931, 49543, 26075}

    Returns: 3469.2932985720186

  71. {910, -59167, -9690, 13097, 23505, -41278, 30296, 41950, 23950, -26711, 26981, -1455, -57095, -38014, -73216}

    {311, 8450, 7919, 1659, -4987, -2322, 7062, 5882, 3125, 8640, -288, -5382, 5485, -1719, -602}

    Returns: 1624.5641392976736

  72. {33, 35, 16, -34, 23, 2}

    {-170, 849, -502, -365, -45, 611}

    Returns: 111.33534005695503

  73. {-487, -826, 539, 107, -300, -528, -168, 637, 328, -751}

    {-10855, 10595, -5510, 10771, 3947, 10436, 4754, 1140, -7156, -3314}

    Returns: 790.0497582441524

  74. {314, -178, -622, 494}

    {-5, 0, -5, 7}

    Returns: 98.14699984088487

  75. {38, -31, -51, -17, -1, 9}

    {-84532, -99190, 385500, 92735, -250321, 308880}

    Returns: 45239.60458300168

  76. {338, -226, -364, 165, -63, 538, 405, 235, -447, -107, 191, 580, 385, -473, 125, -160, 130}

    {-904, 4954, -5510, -778, -134, 832, -824, 5532, 4879, 2935, 994, -1893, -3191, 1832, 5577, -827, 336}

    Returns: 247.0636123820364

  77. {21, 10, -17, 23}

    {-471, 762, -647, 199}

    Returns: 117.03070640024201

  78. {47, 80, -51, 50, 7, -38, 19, 38, 8, 23, 29, -42, 71, 63, 20, 66}

    {-35, -13, 18, -74, -67, -78, 28, 69, 20, 1, 77, 49, 92, -46, 27, -90}

    Returns: 4.756050698962774

  79. {-56982, -35986, 48643, 75905}

    {362, 3422, 857, -4439}

    Returns: 11659.973317761363

  80. {-116, 7, 12, -63, 47, 7, 8, -70, -16, -21, -6, 80}

    {171, -383, -496, -142, -501, 141, 271, 387, 70, -488, 326, -459}

    Returns: 44.977576840453324

  81. {5, 0, -9, -7, -1, -10, -5, 4}

    {12802, 15924, 13563, -6676, 5540, -33077, 6414, 29930}

    Returns: 2950.2627347348434

  82. {-121, 740, -229, 63, 720, 516, 171, -119, 733, 635, 255}

    {21, 11, -13, 3, -5, 21, 22, 7, -5, -9, -21}

    Returns: 49.06952534665129

  83. {-26014, -10955, 3183, -9950, 22519, -12672, 10513, 13522, 20690, -21117}

    {-6, 3, -3, 4, -2, -4, 3, -3, -1, 1}

    Returns: 1607.7058190487292

  84. {-1, 4, -7, 9}

    {-9, 0, -2, 3}

    Returns: 1.902450811000772

  85. {-511, -1316, 1327}

    {-50222, 199025, 176180}

    Returns: 11419.41968235925

  86. {402511, -239793, 274104, -144845, 285214, 334198, 182271, -391262, 330159, -32561, 194093, 58729, -366921, -214115, -202942, -406001, -34514, -369544, -254530}

    {157237, -196317, -730035, -310805, 498206, 772345, 309935, 621940, 722067, -1044, -335322, 616718, 73795, -559890, 443353, -249812, -38640, -614699, -398416}

    Returns: 22416.750368492936

  87. {-42, -74, -47, 60, -59, 62, 73, -54, -37, 64, -12, -27, -73, 16, -59}

    {-1386, 996, 426, 1347, -159, 1406, 427, -1374, -489, -206, 397, -769, -1394, -720, 861}

    Returns: 73.64154383915121

  88. {326445, -126203, -462519, -506667, -223701, 549159, 616900, 568399, -413449, 382645, 483944, 334476, -113513}

    {-445, 19, -400, 96, 159, 320, -261, -93, -420, -112, 420, 289, 34}

    Returns: 50456.85605823142

  89. {-284, -261, -1071, 1869, -646, -1221, 880, 278, -1327, 35, 1154, 1845}

    {-3, -10, 61, 68, -53, 44, -4, -78, 43, 44, -62, -45}

    Returns: 94.9057892512618

  90. {6, 1, 1, 6, 4, 1, -8, 0, -5, -3, 1, 4, 5, 2}

    {246438, -93882, 132226, 132105, 41405, 214028, -39313, 313777, -167531, -80845, 80900, 236778, 201018, -201875}

    Returns: 12058.130123886818

  91. {-168756, 57895, 161917, 118426, 261598, -27669, -45307, -259626, -120362, 70381, -214016, -187684}

    {194, -169, -64, -127, 92, 227, -213, -25, -162, 220, -232, -224}

    Returns: 12692.569778005216

  92. {-683, -361, -187, -310, 270, -501, -181, -235}

    {85099, 11676, -23406, 67697, -59331, 20679, 21958, -26308}

    Returns: 7945.558353095844

  93. {1017, 3052, -433, 360, 3506, 2434, 5245, 7167, -5609, 6376}

    {-657045, 31253, -948219, 109272, -447712, -687506, 942821, 109764, 888207, -632835}

    Returns: 99289.95568816655

  94. {5, -3, 5, 0, 8, 1, 1, -8, 1}

    {-3868, -3746, 8718, 9122, -1533, 7116, 6520, 5042, -4735}

    Returns: 737.6897324964402

  95. {-2771, 5152, -4015, -5156, 3733, 316, -211, 2365, -3498, 5705, 1004, 834, -5358, -4832, -5205, 2847, 5113, 4016, -3558, 4307}

    {-9, 6, 7, -4, 2, -3, -5, -5, -2, -8, -7, -3, 4, -1, -5, -2, 10, 10, -9, 7}

    Returns: 309.7420782875239

  96. {25, -39, 33}

    {-70744, 22639, -65183}

    Returns: 2780.496208472141

  97. {7, 4, 3}

    {539002, 764062, -614171}

    Returns: 112529.99999671266

  98. {70, -3429, 2750, 778, 1710, 718, -3777, 1363, -700, 2095, -723, 2581, 2790, -685, 1661, -1532, -2033, -1861, 64, 3302}

    {578, -1576, -70, 1575, 1734, -1211, -3825, 4017, -173, 2909, 2281, -3951, 158, 4123, 2910, 2178, 1938, 3985, 3761, -4209}

    Returns: 208.71631676355224

  99. {810, -333, -186, 716, -92, -520, -372, 495, 463, -595, 33}

    {8, -5, -5, 1, 0, -4, 4, 1, -3, -8, 5}

    Returns: 58.81550909602877

  100. {213, -195, -200}

    {5094, 994, 4876}

    Returns: 119.12362891727935

  101. {560, -446, 315, 356, 512, -666}

    {-178626, -216109, -166205, -15226, 223131, -202477}

    Returns: 30587.43908919246

  102. {67421, 303854, 86204, 371411, 156683, -219608, -2436, -184243, -187497, -35863, -278636, -231282, -205522, 94086, 276369, 172652, 244576, 227845}

    {253, -248, -232, -205, 83, -9, 238, -256, 217, -34, 194, 199, -27, -213, -165, -177, -130, 63}

    Returns: 19721.832806291663

  103. {33892, -63756, -11965, 28553}

    {-13116, 5384, 13377, -6197}

    Returns: 3629.2100064310353

  104. {7, -12, -1, -8, -12, -9, -4, -3, 14, -7, 0, -1}

    {31, -75, -39, -65, -31, -51, 40, -44, -79, -84, -3, 66}

    Returns: 3.2083802594859416

  105. {12405, -5382, -12544}

    {-1, 5, -5}

    Returns: 3580.9996543395628

  106. {0, 0, 0, 0, 0, 0, 0 }

    {0, 2, 3, 9, 10, 15, 16 }

    Returns: 0.9428090415820632

  107. {167053, 536770, -590401, 507047, 350178, -274523, -584679, -766795, -664177, 267757, -291856, -765547, 604801, -682922, -404590, 468001, 607925, 503849, -499699, -798637 }

    {-12396, -66098, -56843, 20270, 81510, -23294, 10423, 24007, -24343, -21587, -6318, -7396, -68622, 56304, -85680, -14890, -38373, -25477, -38240, 11736 }

    Returns: 40056.95946451828

  108. {-306880, 169480, -558404, -193925, 654444, -300247, -456420, -119436, -620920, -470018, -914272, -691256, -49418, -21054, 603373, -23656, 891691, 258986, -453793, -782940 }

    {-77318, -632629, -344942, -361706, 191982, 349424, 676536, 166124, 291342, -268968, 188262, -537953, -70432, 156803, 166174, 345128, 58614, -671747, 508265, 92324 }

    Returns: 36879.15127634308

  109. {780865, 787933, 707858, 262619, 732752, 767083, 257365, 405035, 175539, 428723, 128352, 564498, 465343, 413344, 787975, 272256, 297810, 553397, 849476, 503261 }

    {593736, 587774, 541152, 430560, 273673, 547167, 298482, 590044, 543428, 338002, 95150, 587003, 131741, 713425, 218571, 908209, 689135, 268316, 225042, 340568 }

    Returns: 12273.393230483718

  110. {2671, 1984, 761, 7270, 3343, 7107, 1848, 1969, 3143, 14, 9492, 2596, 875, 6195, 2111, 4953, 8376, 3908, 2492, 5528 }

    {1515, 5357, 621, 9051, 32, 5702, 6576, 6665, 9233, 8696, 641, 5341, 7734, 7823, 3714, 2063, 7317, 1516, 1908, 5354 }

    Returns: 224.1387848162398

  111. {10, 5, 7, 7, 2, 5, 7, 8, 9 }

    {4, 5, 1, 7, 9, 10, 4, 9, 3 }

    Returns: 0.2332299158027406

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