TopCoder Statistics - Problem Statement

Problem Statement

There are two teams A and B, each with exactly n members, that will compete in a contest to decide which team is better. The contest consists of n one-on-one fights, where a member of team A fights a member of team B. A valid fight arrangement of the teams assigns each member of team A to a distinct member of team B. All valid pairings are equally likely to be chosen. For example, if each team has 2 fighters (A1, A2 and B1, B2), there are two possible assignments: (A1 vs. B2, A2 vs. B1) and (A1 vs. B1, A2 vs. B2). Each of those assignments has a 50% chance of being chosen.

Each fighter has a non-negative integer strength. If fighters with strengths X and Y are matched in a fight, the team of the fighter with the greater strength is awarded (X-Y)² points. If both have equal strength, the fight ends in a tie and no team is awarded any points. After all the fights are finished, each team adds up their points. The winning margin of team A is their point total minus team B's point total. You must calculate and return the expected value of that number.

To keep the input small, it will be codified in the following way. You will be given two int[]s A and B representing team A and B, respectively. Use the following pseudo-code on each of the int[]s to generate the strengths of that team's members (array indices are 0-based):

input array: X
output array: R (of size n)
j := 0
m := size of X
for i := 0 to n-1
	R[i] := X[j]
	s := (j+1)%m
	X[j] := ( ( X[j] ^ X[s] ) + 13 ) % 49999
	j := s

This code, along with the constraints, ensures that each member's strength is between 0 and 49998, inclusive. In the above code, % is the modulo operator and ^ is the bitwise XOR binary operator. See the notes section for information on performing XOR in your language.

Definition

Class:: RandomFights
Method:: expectedNrOfPoints
Parameters:: int[], int[], int
Returns:: double
Method signature:: double expectedNrOfPoints(int[] A, int[] B, int n)
(be sure your method is public)

Notes

The input is only coded for convenience. The intended solution does not rely at all in a property of the way it is generated, it just generates both arrays and works on them.
The returned value must have an absolute or relative error less than 1e-9.
If x and y are ints, (x^y) represents the bitwise XOR operation on them in C++, Java, C# and Python. In VB.Net (x BitXor y) does it.

Constraints

A and B will each contain between 1 and 50 elements, inclusive.
Each element of A and B will be between 0 and 49998, inclusive.
n will be between 1 and 50000, inclusive.

Examples

{6}

{4}

1

Returns: 4.0

The winning margin of A is always (6-4)2=4.
{1,7}

{3,5}

2

Returns: 0.0

There are two possible assignments here: (1 vs. 3) and (7 vs. 5), or (1 vs. 5) and (7 vs. 3). In the first case, each team gets 4 points, so the winning margin of A is 0. In the second case, each team gets 16 points, so the winning margin is also 0. Since the winning margin is 0 in every case, the expected value is, of course, 0.
{3,7}

{1,5}

2

Returns: 20.0

The two possible assignments in this case are: (3 vs. 1) and (7 vs. 5), or (3 vs. 5) and (7 vs. 1). The winning margin in the first case is 4+4=8, and in the second case, it is 36-4=32. Since both assignments are equally likely to be chosen, the expected value is the average of the two margins.
{1,2,3,5}

{3,1,5,2}

6

Returns: -35.666666666666664
{45,35,236,2342,5543,21,32,2,6,23,24,23,41,1}

{2345,45,2345,345}

50

Returns: 1.2721986164E8

A and B can have different lengths. Each one is generated separately.
{34,3245,2534,53,53,46,346,246,346,2,624,624,6,245,6324,6542,624,6}

{345,234,523,4624,6,2456,345,634,634,7,3457,376,34,6234,62,523,52,35,32}

7

Returns: -9713701.714285715

You can have extra unused elements in the input.
{1,2,3,4}

{1,2,3,4}

50000

Returns: 0.0

If both teams are that even, neither of them can take advantage.
{5,6,6,7,54,46,432,2}

{7,6,434,345,7,45,12,3}

8

Returns: -111828.5
{25832,32711,1780,29957,23097,4619,46201,5138,5372,37779,39501,3080,32090,41322,11592,46982,34128,6754,5787,19084,24425,215,36529,18645,34704,40115,34250,22098,27000,939,22517,47023,26616,16270,48033,3231,34296,5213,24447,3151,44386,44157,30260,10410,41961,29234}

{18671,23054,39089,45596,27664,47508,46482,22208,37526,48442,27290,19555,40412,42744,41555,31044,27437,30755,21304,20311,21710,11167,19806,44430,41904,37160,40058,17637,27404,42854,23060,46274,38358,38872,45933,25363,26841,41610,33415,5075}

43406

Returns: 1.2778477372164968E12
{10772,2055,20542,22205,21418,46963,36881,18539,6090,14830,49110,34705,24994,46399,44168,17113,30887,39036,41220,40378,1883,39039,16257,33133,17389,16443,46132,49070,17978,49357,48606,16647,34145,45415,28470,25287,30708,33150,27061,38326,47535}

{36946,42278,24819,15464,4378,15762,583,26898,40604,48312,21365,32206,25365,37977,5645,43084}

43997

Returns: 2.4299645684013525E12
{44415,24764,49143,33491,44211,26415,9819,32124,25537,19433,7955,37808}

{29304,8372,49857,46922,46853,3017,37440,1352,32816,24676,8328,21646,9439,25089,34995,23207,42711,38920,42602,2711,22474,47182,25817,24345,41143,10233,37980,47552,33477,42329,16318,4223,47033,43136,15798,43642,26663,49396,8657,17659,33765,7331,18545,28036,39742}

43713

Returns: -3.7997811109193857E12
{39182,43686,331,7441,5666,26290,22589,36850,18417,8960,45187,4398,25629,25906,23068,49600,15175,38151,18213,34317,46968,25803,14716,18255,21343,31135}

{21468,35099,28080,14305,1458,3869,27425,21822,13886,41200,25908,26350,36728,37269,29179,16066,1443,23225,6162,42648,36667,49705,16803,13618,5721,17745,5901,1880,30168,43706,8550,33877,9902,29651}

42006

Returns: 1.3367887221860583E12
{5064,18013,600,17062,49024,30542,45977,27736,21549,48394,9181,44060,46226,47870,32159,42068,49751,33599,10276,48569,5592,11074,27144,42013,18742,18057,13016,28040,34549,24617,19263,37833,41570,4181,5714,18443}

{37085,31056,49437,37991,48280,46440,47312,14750,17177,37695,48188,49428,42732,36297,23422,29648,4327,2757,19738,40337,12220,25621,31242,23166,10010,12866,8587,17419,8980,10535,36557,12471,28296,18622,4078,8483,7239,13821,11478,11697,12924,2904,49074,37338}

46657

Returns: -5.037546726287212E12
{11533,47325,13655,44715,10447,39502,30513,40681,5012,36562,26920,10217,4162,1299,25642,26688,3255,30333,15790,46062,6687,5322,16020,15160,15741,19377,16594,46431}

{6587,27858,3515,24176,9883,32104,45100,38951,37952,2218,12965,32318,31919,15057,32501,33471,18491,39215,47512,23807,46295,25667,41608,13170,45298,21245,6298,4915,7836,11689,42000,39231,10861,20553,9388,3992,10672,46512,34276,8134,47098}

46822

Returns: 1.035772633160808E13
{15316,38779,11169,18668,24137,47811,39806}

{9776,26779,20280,18627,46036,16698,15291,1643,31884,4786,27464,39464,7822,32025,13675,5580,14313,14024,17642,41879,31465,45202,48888,20046,10444,18021,39653,26950,40663,14930,2668,34997}

43120

Returns: 1.9909510919632778E12
{38017,34136,41445,6619,25518,17719,12641,40161,39644,1174,42691,27120}

{9739,35011,41878,38231,31884,22305,20959,1528,44607,49408,35923,40535,44172,32101,13969,21191,37188,3409,22154,43503,20636,21304,7446,32110,23204,35269,4377,23543,30981,46439,49627,29200,1743,20558,22238,43045,28830,34761,22128,39115}

45420

Returns: -2.4557648006351733E12
{26547,37925,19340,30620,47280,11621,1698,29427,21628,6151,17216,796,1747,10301,40457,3082,49372,305,36419,9909,28751,24143,10191,5334,6088,48193,8985,2941,13169,8158,46068,37631,39471,13170,14596,5214,37699,39186,35814,38472,36999,13723,1674}

{46643,17757,21029,8020,17890,38023,34553,24863,27107,9623,2341,27307,20861,13818,39801,28651,26884}

45578

Returns: 5.342630313601904E12
{39511,3368,27763,19325,31579,379,48970,11325,43731,28256,7927,6062,13,7355,14815,7721,9325,806,4828,43510,33200,1078,42923,48389,7992,24512,9572,29246,5865,21806,25121,30962,16142,41092,34971,42766,32815,23157,15696,46057,25912,27980,5140,22936,23711,4034,18208,6432}

{31852,39166,43590,30574,19422,26097,40025,9592,30691,4200,43298,44446,22293,31242,39781,12912,41402,22230,27115,222,8923,12688,29508,3442,37318,26505,8876,22619,35103,49264}

42349

Returns: 7.66311512595364E11
{11859,20857,17186,34101,46939,24026,39926,18363,38304,40123,49808,24391,40784,49602,48793,14545,30881,21156,43846,42213,6233,10338,7795,1493,41821,21933,23414,35438,46897,15239,33490,47099,44697,7556,44980,10778,42828,39926,41652,42891,40651,6438,28720,25902,15720,11305,26410,4275,46293}

{19052,26146,41859,17194,40608,38179,47753,30490,20542,6354,47524,41802,6607,32817,12730,15723,15375,31548,45610,6652,20298,9527,12511,28941,39761,35392,47352,14815,13898,46841,21443,40524,33349,26832,30010,16221,45081,15852,15281,40477,30964,40144,18789,648,24720,30637,14269,23784,8826,2640}

46843

Returns: -3.807347935340935E10
{31278,34598,38313,30059,38261,48841,39881,4543,48170,16113,46092,45192,3825,46689,19517,11907,46672,7467,9326,7911,23697,42585,30812,33177,17403,41427,20816,16568,15579,35918,21950,26325,35377,4080,33812,35915,10540,46332,47510,25618,6220,47408,34347,35229,33667,27143,22967,30813}

{17465,9079,18297,17039,34101,26829,23648,12700,19649,1229,46299,28017,2286,43150,23060,31664,8048,36006,41018,28370,23638,24828,43991,24283,34166,23256,11210,36108,27479,6921,39576,49315,45151,37763,37704,497,20267,19351,24198,7959,29335,24015,8339,10771,15416,10774,14778,45976,2666}

43181

Returns: 3.616079401725667E12
{11832,3679,18683,18014,24872,38936,41857,5268,47959,33606,9062,25879,18251,15535,17543,36697,10788,26370,14445,27967,12124,43409,18538,49769,27523,48337,26662,37997,16517,23407,15931,39401,7589,22364,38934,46104,14917,16218,16676,39197,34104,47226,22720,4821,31561,11735,42159,28658,20303}

{2304,11139,14201,27206,14851,16077,12611,5299,24647,46021,32518,7644,6089,5529,37603,15200,30031,15814,24336,45659,9750,16378,29800,23518,44087,41974,2469,32969,7743,13244,23302,10173,14019,18384,33344,24515,23463,1497,12114,24492,16484,10278,29539,34201,16694,19349,30563,14352}

47608

Returns: 1.8832848423902695E12
{13048,10226,21983,31429,43047,46983,23660,49106,4935,2474,22816,33205,12078,17623,48040,47493,5570,15320,34598,14596,34562,44348,39319,28758,27634,28442,13069,11332,4443,26664,3175,9101,28868,32942,17402,10891,11373,6888,32589,20431,43837,38366,39798,27224,37571,20618,13581,31007,3073,47251}

{18704,12447,40831,33327,36294,12942,38425,31288,21634,8812,40064,10424,7612,5172,10775,40714,28762,49137,20877,30865,48805,35854,19384,14337,31305,38135,18330,24445,37924,11518,27909,26392,10641,3061,24249,46055,5555,16252,22923,10791,22624,19247,48908,35290,16556,14925,11189,23933,24437,30208}

49244

Returns: 3.1656744671623125E12
{11514,9445,5595,37966,2029,17412,42774,15811,19744,9584,11267,13923,26043,13538,49947,1753,12090,29915,11988,13547,19848,26199,1800,42467,26152,16688,40332,18213,22490,23097,40585,26273,1286,13296,35956,23922,37646,22665,41083,18465,44190,18350,46255,16452,497,23694,7640,10505,20579}

{3602,3017,26457,38125,32395,10381,45133,15694,20136,10291,8036,13218,5169,45429,5781,47906,14980,24654,28109,4481,30105,47299,26591,32805,18176,29236,29417,40932,8761,2082,19231,4062,30016,49118,1192,46811,3164,21130,29339,13480,25343,30480,15365,6746,8410,47847,43543,14619,16969,49981}

40103

Returns: 1.2197924619763647E12
{12641,2048,5360,5912,43526,8139,8779,41599,38047,5685,40526,22092,40552,16830,40459,27448,3209,24886,35290,268,22972,41535,8820,47023,317,5651,23921,4999,34366,22694,41120,1586,1002,44465,45768,17235,47651,15311,27914,30728,14214,24518,1681,8189,234,31720,12005,12622,29054}

{44648,31481,21930,43807,23543,42718,30625,34998,30427,32695,4944,35675,42768,26820,49489,15294,46776,3374,35151,25345,43499,25303,49007,29184,39640,32746,40179,5858,24943,18755,41266,11659,13727,16332,17846,19532,1661,23554,45126,37327,41637,40039,49151,29532,42085,29773,37356,47290}

48367

Returns: 1.727720826353862E12
{24069,10480,38859,22188,15908,8485,22660,23023,8632,25274,28551,44349,40690,19899,11905,43329,40650,41178,18436,15679,37772,24407,46440,9022,48898,17556,29785,35995,4794,2473,35324,47425,10327,16490,33207,28022,25961,13887,32182,16456,4985,19657,28272,46586,15297,32097,46736,38045}

{29234,7273,15879,20520,12212,40161,48022,41996,8338,27040,36346,8462,31270,39054,27390,21529,22215,35476,5629,4600,37819,39879,33020,28633,41233,46235,21726,30449,29432,42573,25659,32404,14723,35437,37466,42476,13424,14661,23566,17781,37838,40850,8833,20897,20072,25545,32961,23449,18369}

48501

Returns: 2.260473378688828E12
{46884,9739,20393,33136,49964,2601,30253,33186,21375,25152,12952,9900,265,28509,28299,38077,31132,15497,3244,18721,4938,11957,31638,40833,10191,36258,12551,22046,38581,48101,26898,3480,26743,42150,6643,44479,46228,13052,48293,17061,33799,11216,24507,8806,49762,15812,47207,13550,7055,46533}

{17529,6850,48990,48330,25201,43970,35612,36246,23364,40544,7026,9754,28285,35454,41532,24235,13588,39442,40488,39437,45495,399,42227,30567,45031,37522,11887,39122,29921,12669,26437,41091,9158,47282,37533,31234,45814,33807,2558,31310,18051,5479,13494,17214,26663,46457,22702,1278}

41577

Returns: 6.324363488758231E12
{24569,17992,28423,41028,42881,19990,17090,22249,7335,40163,38879,12073,24740,14775,30343,11617,37148,15419,46688,4382,25445,39782,16671,11730,5184,5360,1482,3314,12092,8861,18871,21547,5198,18199,38192,21263,35824,43456,13774,27826,32653,19835,10862,18134,41863,34981,41162,38776,41166}

{15211,23964,45610,22756,36509,31920,32383,14649,39756,20111,22491,33036,42408,30595,44921,36891,18849,23237,701,1841,34298,26909,9753,11634,30964,44400,6352,44628,21958,4525,23905,46368,23493,9651,44693,46163,20136,21478,33866,30501,31914,9666,25637,34191,42849,20867,42831,18742}

43275

Returns: -6.08629539480537E11
{30099,14881,27233,15005,48390,40546,3699,11972,27418,10768,1087,12832,35519,1259,10637,12328,23173,30748,47620,27901,26496,21249,34838,23997,45113,17856,38473,27132,48452,27834,13180,23455,11543,19609,12389,4291,542,2747,12216,37775,45373,30191,10108,8947,35293,31285,5403,46758,18842,16408}

{5693,37160,27968,9821,12315,36374,29712,37745,10193,22543,44039,20685,360,34968,25972,9786,42468,33951,25400,4990,49882,14116,5442,38693,29474,31290,37821,5831,8699,22718,43445,12311,28401,32508,2693,23203,17850,22321,6482,31897,33308,44308,3207,34481,13122,2700,40736,30878}

45195

Returns: -7.371200971496965E12
{10947,27040,20975,5237,49059,17223,29993,18514,13027,2743,23616,15098,19517,28375,18075,14242,20124,22294,3936,21736,18151,4134,30319,39781,4425,29877,42148,43158,1779,38022,24157,14900,6240,30262,42305,158,30309,1804,9496,9597,4835,37774,32566,46956,38504,39178,15772,26708}

{14040,39096,10750,33184,20906,38530,28168,15318,6278,12218,12218,36219,27575,32564,35485,13326,18786,27509,15014,14402,9890,35538,3378,25384,12141,7811,17985,34108,39490,44788,15638,49061,13053,45624,24206,41882,41518,1837,13611,49773,49933,4663,49506,32337,4419,40050,40453,26781}

15

Returns: -1.3023242433333333E9
{33942,42936,17651,2030,7650,3447,37892,29152,19242,23266,17994,29039,18734,43466,12798,8390,6605,46671,22281,35805,35414,16943,37437,44831,46814,25724,17133,19842,28063,14560,32594,9806,49528,46621,34529,27635,28046,33105,14234,4400,34097,24782,36554,6393,6036,47843,36329,39424,25174,35707}

{24592,42328,49268,43830,44463,48485,45059,47771,7821,13908,35000,22935,3983,43915,17752,32251,13689,43796,18791,35154,16575,8959,43486,36775,32627,36943,12659,16747,49703,21836,34465,19139,7201,22969,10615,4476,1492,32361,39591,42270,48338,3433,4852,12895,33959,23663,5962,39118,49382}

19

Returns: -5.550734630684211E9
{26238,31160,30841,41413,27800,30665,21255,34650,4805,673,33996,33966,40359,19135,41589,43072,31383,32494,31562,34012,26524,19307,2248,28991,34679,26074,34592,36395,44030,39154,2321,45660,48059,14114,21621,43772,44864,18938,8419,17020,14687,19400,9140,17081,12940,20617,44240,6904,27119}

{46094,8394,13439,36274,23386,43815,128,15210,26783,30552,24020,32519,33707,669,15911,38266,38477,8627,13266,3716,19411,44654,47051,45493,24760,23256,33582,43692,18819,7937,49531,47525,6003,26130,867,6252,9315,9724,45950,4936,12184,47043,47761,24941,32903,2196,873,47219,41000}

12

Returns: 2.0795209966666666E8
{21327,17202,1050,49219,42988,38315,39286,48088,1840,17493,8870,5789,48366,28364,773,25687,48316,18293,12594,38020,20250,43742,29684,3400,49142,37919,23825,43485,27435,459,29762,21610,1893,32530,48174,32637,39560,28740,2268,37013,36179,32708,49542,4566,41991,33479,41145,10487,33622}

{34153,35243,29815,23531,34914,4494,13731,23231,15154,9249,35097,25163,14177,40607,6108,34623,46805,24097,14975,21977,20536,48577,16570,3765,25832,32866,10239,40257,49325,20291,26670,44733,5008,3862,28326,22566,26845,17656,12941,17380,30453,27224,11243,33768,40623,2444,13285,18434,20974}

2

Returns: -4.85487707E8
{14722,30945,47644,19404,33261,4539,37804,10468,19383,47465,30586,13819,48872,27035,41230,25647,19958,46011,23465,42597,17920,30526,45491,19569,24182,17566,2089,12995,5030,376,31717,29344,12209,14362,44205,43315,34919,46303,20877,30906,44917,2049,39949,45285,21125,11959,33766,16081,1806}

{25660,38468,12790,39456,3078,1935,16422,44896,1999,40719,49990,9920,38332,40429,44503,10821,18596,3103,8817,9531,36820,26148,4841,35360,15418,22169,22997,49340,49988,29149,39818,46020,46198,5287,35994,27661,33808,2640,25301,2043,45695,13028,21862,10736,21112,3259,42962,6989}

19

Returns: 3.1660449349473686E9
{21920,20145,17809,39888,15978,22818,11241,17512,40409,4177,30078,1277,18230,42097,27375,1026,34577,40360,43086,21668,34294,5075,38672,9271,8498,24908,20290,9314,27492,44362,37058,924,49378,48776,46648,18157,21485,43354,39963,26182,44541,2921,27450,30513,49127,17616,8292,41539}

{2175,47574,29520,12726,49437,37176,11899,10142,28889,35970,42002,41298,1519,8528,30556,47062,10741,33244,49443,13598,47289,44395,46026,17255,37175,43769,23866,4007,32002,34032,44300,24436,39041,20655,34466,1483,21212,6787,3399,16330,46784,28860,44986,29454,23230,40923,10949,17987,25292}

115

Returns: -4.679376352217391E9
{44178,19767,47505,38497,19328,47044,40611,36684,4040,26052,16480,38167,10477,33367,26671,33286,8753,39490,3860,46517,49847,23110,37587,8535,46254,19293,22554,28146,4755,22087,23510,44797,17716,38091,18953,126,12528,45748,32041,31213,845,11450,44957,17010,16352,45746,36054,23612,45127}

{37576,37042,27551,16679,32195,2749,34894,44533,40193,25343,18477,32450,32273,33778,41074,6345,30631,26751,23116,5229,5729,33699,12077,234,4313,16978,18340,17680,34753,42009,45493,38193,48750,49803,26420,41110,746,41143,40088,27864,15416,35342,25550,45197,28458,36625,38321,12434}

72

Returns: 5.234532541027778E9
{3230,28496,32708,25582,45676,37953,18399,19850,3271,33825,13394,14598,22295,37643,33134,4245,15587,15637,35716,13239,35724,886,14216,5839,4418,41785,29691,13559,46134,20625,22734,39651,20079,40769,44184,31956,7128,29846,3507,13380,33944,27789,45552,987,6986,9635,12185,37568,48391,34062}

{29275,26535,48340,13284,23513,41023,35870,32887,48160,5177,47473,25826,28451,25451,33284,14680,45884,46427,21883,44377,23694,29818,48705,7752,17990,18631,37670,49973,47960,32622,30271,31837,34336,590,20920,22569,2777,44162,26071,48445,2015,4232,34467,8018,30679,33685,44054,15884}

47

Returns: -9.559456774595745E9
{8390,44500,26732,9876,27467,10515,9493,22207,20209,43902,19148,27184,6789,14134,23128,41361,1595,44631,45243,41411,13126,37500,47417,4817,39208,47608,38830,20529,5451,5846,13034,19118,40937,40530,9916,29860,10812,13692,6277,15369,13265,40588,37837,1777,45791,40746,34966,21041,21820,4571}

{40092,4374,48513,31829,36853,45462,1748,13043,32065,4358,27330,24210,15530,49481,23752,17955,21209,13309,11538,22866,16481,40743,15784,46352,1203,24896,20075,39555,15967,32321,23331,6487,7194,21792,49703,29554,19880,43043,5306,49649,17437,24933,34728,1535,13006,31703,25699,29670,28936}

100

Returns: -4.66400182808E9
{24505,28007,45595,34537,23335,34094,14822,10931,33545,838,13745,981,46,18032,4010,26811,37969,40672,10526,11662,42710,4981,10533,37396,1653,48490,33176,45692,3229,2711,44995,10488,5080,31821,17636,14758,26115,3193,6149,27059,19257,8095,4854,33875,36487,13772,11005,16460,29094,28183}

{14321,4706,16410,20504,15813,34458,1179,15021,16742,44011,29452,42759,45989,34213,31541,10347,13768,35677,40866,49537,41580,16601,46686,28033,35349,43208,21297,33379,37794,27405,48571,384,13493,40686,42469,16541,21118,1663,22226,6140,4931,38474,1141,30190,10066,15329,37989,19749}

101

Returns: -1.0746233774158416E9
{16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781}

{13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141,13,141}

90

Returns: 1.2960156330666667E11
{16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781,16397,32781}

{13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13}

50000

Returns: 3.9142184452096E13
{13,13}

{16397,32781}

50000

Returns: -6.2633776513024E13
{31530,27056,22838,20753,49856,11935,34766,47574,44063,47178,48367,39238,27826,44267,25429,22363,40949,43694,15783,49975,49911,47815,40813,20522,5338,46171,42411,45968,18384,45641,23859,7226,43330,29008,48388,49908,17380,31754,48681,12521,32614,26742}

{12892,2904,26398,32945,19788,27573,5535,5639,28700,5194,20138,32821,690,30206,1648,23740,18957,568,1552,26608,8422,13179,33135,12477,20481,6975,30343,1448}

1007

Returns: 1.0606078389741211E11
{42559,13912,42910,19704,47255,19204,26190,37998,48175,44048,48786,29475,38547,42929,35884,44316,39249,34080,46991,46838,40589,32967,33689,30559,49369,41005,20986,23448,32837,44806,46141,23779,45942,30229,38978,30402,39121,42417,21814,42234,47708,21233,36312,35867,35037,32219}

{48589,2043,24403,12550,28197,12494,10308,26514,743,15169,14342,2321,40025,215,28724,10838,18304,3051,6484}

35301

Returns: -1.7108584746309438E12
{40373,44727,25217,38012,38965,49539,46289,42500,49490,27161,46069,39001,31434,47229,43688,28853,24947,45253,44350,45972,49389,44021,42010,27184}

{13662,28294,1607,18612,974,2427,15885,24086,286,4519,2399,3790,3011,3497,909,26511,9721,25332,1734,34593,3356,8309,24157,44441,4929,11746}

47064

Returns: -1.839567936377838E12
{4746,48474,48553,39156,47467,27280,49669,39505,30174,20385,29572,35170,48914,41013,47647,47585,31927,47832,48003,25736,27187,28862,19104,33630,37326,30457,34564,41794,43734,32686,47235,31230,47895,44368,45297,32166,49148,49972,17757,42245}

{2367,4151,35780,4914,30245,12129,64,1757,21608,18605,31921,24601,24359,4566,14329,37496,5176,22516}

19655

Returns: 2.53281874883785E12
{48855,47348,41698,18896,43217,40261,43949,33768,47953,36732,42910,36141,46376,45603,48342}

{13837,344,2929,6566,3232,873,2980,29908,13796,27664,2639,3966,36928,26757,11139,13555,47610}

43371

Returns: 2.5406979900901626E12
{7874,38580,11486,31739,3152,12883,14776,409,6692,17481,8012,13183,9768,9839,13537,19552,23961,4788,7941,859,7422,15947,14638,12562,3650,1431,1613,25360,2824,7088,11808,7116,1054,25621,9954,16799,2409,22263,1283,8378,3226,6568,15724,26416,43403,3823,520}

{17177,20194,35953,39607,42804,45438,37512,49952,42348,44816,15994,24844,46544,49028,37579,40103,49589,48734,35646,36470,49407,19778,42791,41663,49656,34821,30190,40276,32173,48849,48890,49712,27522,27538,40908,42447,23017,40212,44631,48211,48846,39212,49706,27903,25709,29819}

21665

Returns: -8.889615639892883E11
{585,24822,3650,9068,40726}

{11935,45154,38142,30923,42804,45826,48225,33198,41467,49309,49092,46267,39868,38434,34183,48193,12934,27108,25971,42793,28893,42190,23991,33501,49378,28922,45147,23357,34976,49783,3783,11458,39654,34839,21691,34886,49711,22311,44315,48172}

45948

Returns: 2.9476079377038936E12
{20437,43088,35754,41560,105,2268,1297,990,11237,12161,5872,13310,42219,4550,7888,8397,18633,19770}

{45330,44062,12130,45910,32278,45315,32509,27148,38679,45486,45436,44057,40290,30031,45324,15522,27944,48213,26888,39126,49953,22910,47141,45382}

27328

Returns: 1.1819353107363042E11
{7729,1511,21619,4427,234,8898,4934,4173,33983,29089,12667,33601,15191,3258,23095,22630,1532,2806,20082,20788,19018,22306,3754,322,26083,17309,10927,32333,31119,18776}

{49864,47657,17325,23574,40649,26189,12549,45704,46508,30158,45964,34318,29745,18218}

22355

Returns: -2.97203710476598E12
{22828,4140,11975,20878,1137,19736,22526,22054,10487,6475,5757,3513,19061,16432,28931,20794,8780,11190,16254,6636,4991,15546,2012,32420,9222,1208,8873,22570,22635,650,32505,4158,3895,12504,8720,3682,13179,23176,3715,1987,2895,25470,15027,765,10166,1840,480,14449,25322,9973}

{31028,30219,44816,33261,38293,40681,49035,28117,26527,32633,47347}

15830

Returns: -1.4736047475908604E12
{11,0,9,1,0,3,0,14,1,15,14,14,4,13,7,3,6,10,0,6,8,8,5,1,12,11,2,4,12,12,10,1}

{4,9,3,1,3,3,7,13,14,15,5,4,13,6,14,12,12,5,9,9,11,13,15,8,14,4,15,7,14,2,11,9,6,5,10,7,7,14,4,10,4,2,9,3}

42164

Returns: -7.812741777043989E11
{3,10,2,14,3,15,14,14,13,9,0,10}

{1,0,4,2,1,1,4,13,5,11,4,6,7,4,8,10,8,2,9,11,10,2,3,0,4,4,10,3,2}

17444

Returns: 2.7081227509666104E12
{2,4,0}

{14,7,6,7,15}

28704

Returns: 2.9517434587091486E11
{13,4,13,1,9}

{5,14,3,2,0,3,8,0,13}

4101

Returns: -4.477074592962019E11
{6,10,3,7,10,9,8,15,13,3,13,13,6,9,2,10,15,15,14,4}

{9,12,8,14,6,14,15,13,12,3,3,12,9,1,9,9,10,15,11,6,2,10,6,9,9,2,10,12,10,10,14,13}

24989

Returns: 3.059365464850833E12
{14,4,5,4,3,9,6,0,15,2,0,8,8,14,2,8,10,3,2,13,5,7,10,9,10,7,5,3,2,4,6,5}

{25400,788,10692,48210,25374,20235,39743,43147,22926,34438,41515,8094,5335,35132,2919,30770,3215,42178,35690}

42030

Returns: -3.9644369015213477E12
{0,0,5,1,6,4,15,3,9,0,15,6,0,2,5,3,4,14,4,5,1,9,2,13,9}

{47691,16390,5529,34463,5007,6108,12037,47697,24571,7945,44933,8355,5258,37719,22173}

48443

Returns: 2.8170033882356177E12
{25522,49715,3962,5345,16887,38827,39155,48697,2279,38737,4120,44847,38327,38839,40232,29663,22691,20216,16663,32464,29059,14771,22979,19892,27872,26619,28710,46054,19184,40137,13084,34733,45137,19302,38437,31747,33781,17956,20211,9733,12633,34047}

{4,4,2,0,6,6,5,7,2,5,4,8,7,14,2,2,9,1,3,9,15,3,2,2,4,12,13,9,10,10,4}

43580

Returns: 2.7062613530048677E12
{19064,19440,37032,12004,26842,47790,33662,31838,9203,40389,10888,41127,4796,19131,3835,11741,23762,23046,17007,11609,17145,12238}

{13,7,1,15,1,12,10,15,6,10,2,3,2,7,4,1,2,11,12,4,5,2,13,10,15,14,11,6,7,2,2,15,9,8,13,15,4,12,0,5,13,15,14,4,11,5,4}

40747

Returns: 5.223787602257056E12
{39086,10872,27431,35797,3142,39701,48946,28603,28942,28602,4059,23896,48151,42458,7063,13814,9509,4448,13029,13422,10634,43181,28516,14186,31111,30815,10048,42600,19034,26240,40177,21820,16683,7480,42177,20958,25849,7915,5127,10620,32940,13430,49881,44151,4563,23358,18309,14712,25003,11924}

{26724,47462,8698,32449,17954,16880,46707,29290,30999,29393,34958,35269,32508,26765,37372,14276,41820,5569,6100,2638,39495,15492,40850,38970,11802,13380,33206,1148,46498,25582,13944,14289,48045,28478,28391,9476,24700,27674,39133,9470,26752,465,23178,7449,37305,41083,14027,10273,47158}

50000

Returns: 1.4468368706658726E12
{12024,31182,27041,47010,39151,15190,31480,30715,1845,9727,22877,48906,6142,32646,5623,29392,21965,10114,19207,31277,27112,8835,2613,30925,29718,27285,38,38406,21011,30534,47867,9041,38738,12774,12188,49879,38824,10956,25566,49191,7205,33534,27802,14509,49199,35845,11737}

{29991,22205,25076,7007,3052,30511,26150,49742,23718,36479,2661,20616,2783,21419,2628,18029,38435,21936,15460,39393,36390,25692,17055,20727,27004,4056,30734,43774,11213,1699,31486,43286,45974,42046,40581,1013,44082,41660,13296,31985,30143,12535,43756,24487,10597,557,17222,33639,1894}

49999

Returns: 4.684943330552193E12
{42274,6648,38692,4017,38942,45051,25578,42318,32858,11827,34382,18836,32364,12869,8141,21301,12711,24528,24685,25820,5881,15693,44459,46420,6590,7099,20025,35872,13203,16243,48162,45694,1455,21657,4585,40252,27331,29534,48408,4027,21700,41501,6681,44304,8138,46823,17898,21020,26531,22763}

{22708,34629,34186,32163,3025,22387,19660,24293,48762,26660,34155,29948,13360,38569,43491,49736,24827,17769,26328,33558,36233,25330,32637,31042,21060,33364,3411,43610,49240,48348,28346,36491,25811,3819,33079,7415,7171,48216,3918,27412,1924,47177,26844,46149,5946,4223,30599,31940,34307}

49997

Returns: -7.367088155727168E11
{14502,38511,15790,45565,6897,35765,21623,28135,11047,6434,37445,42131,15309,36356,1767,44890,24074,44341,13358,13740,18929,7220,36244,10671,1431,2686,21911,39612,2489,45417,27735,25621,14054,36806,47765,39426,36871,18377,6733,7961,31199,15352,33876,49175,37750,5939,1684,11763,34870,45532}

{395,30669,28255,46266,11695,14746,32887,18971,40512,24867,22122,3593,33226,48424,46494,46328,24207,38800,5896,9019,38970,15668,3043,21890,41820,1273,27424,12562,10331,17647,22689,16050,6685,29961,29777,11774,46667,27599,44749,45877,20631,24585,12670,18944,44427,5406,14179,43081}

50000

Returns: -3.6302567941463706E12
{2661,19968,26049,49790,22915,5359,14086,38742,17360,23605,34607,24834,31107,15907,47948,45991,33855,37529,24928,32431,45017,7250,36406,47959,19045,40906,28898,14870,29776,15141,27190,31916,33291,4859,2952,33297,11825,31440,4667,35788,29692,25176,22257,5511,13022,18023,17881,3373,6769,40091}

{49359,48041,1517,12699,7857,16377,40534,42979,38563,30494,30723,191,37369,44163,49270,6529,33734,28472,37179,17345,1241,46376,26232,37540,15003,521,21275,6080,40124,28894,44898,24121,12556,45269,12954,6867,19344,44947,39089,8317,11845,19878,47131,3588,27968,11915,42259,34586}

50000

Returns: -5.047051637996085E12
{7266,28725,32896,8667,8212,25653,11728,20322,4503,10270,2418,44197,7996,39911,36872,48501,23981,17116,6106,9211,30634,21600,47712,40970,11306,26745,22107,40188,20651,41776,5151,35538,42502,12148,31027,3478,45842,40310,17069,911,14202,17848,41357,20745,9978,7124,48247,10629,44990}

{36247,47495,37842,6734,39102,21132,693,7929,14351,41361,13012,22829,20241,17248,502,26616,29622,29756,28079,4116,26258,19689,29188,7908,33541,25576,7738,31214,650,25334,20204,46259,36830,19653,38220,25662,27840,17584,24425,13891,32801,28515,29102,14877,14136,14348,10732,14750,12347}

49997

Returns: 7.652577588311531E12
{36828,21340,20809,39728,49855,30353,47852,14873,17893,21409,24804,38309,39904,32561,28362,49759,1418,31446,16159,10389,44013,188,35204,15961,37306,41677,33221,46622,47803,45652,12238,1587,31635,40703,34054,46428,17270,29380,49382,46562,48506,40274,31262,27299,38520,38451,6158,32109,21436}

{24628,31693,13382,30445,1183,5860,29408,23915,17371,19534,27376,7823,26425,7827,10794,24879,10607,33076,14886,26594,19643,48835,44546,957,41600,21619,22246,39685,22211,47295,39938,40628,43202,36270,19794,7403,30890,4853,39923,25466,8364,44527,2899,12654,24360,24199,28071,38513,9290}

49997

Returns: 4.540388713606496E12
{42065,35578,33370,25734,19408,2709,44847,47095,34569,18404,48039,8258,47385,5704,3257,29050,15376,31822,21263,38461,37680,48705,14300,6251,33000,47201,10188,22897,46179,36815,48499,29142,15757,10152,9403,6208,32280,18910,46257,14975,13610,28129,6410,34728,27079,35032,35599,18367,2338}

{552,42593,29944,6718,25659,19806,21204,22409,33189,29941,9350,19528,6102,31126,48118,25055,8952,37820,5434,14678,16413,46668,39156,25598,24173,24302,19495,37607,6429,32782,40768,49331,12373,41704,49611,24243,8219,12222,23174,41019,15228,36237,37168,17054,26459,7256}

49998

Returns: 3.418483608777647E12
{30719,28681,37525,3439,434,1742,39884,47952,18947,30636,29934,22607,7264,3507,8721,46607,12668,36406,25926,11681,14034,49641,49526,40115,45704,45537,32535,8953,10679,7396,29987,12545,22012,32832,1238,8944,16683,36224,47639,42691,24501,15912,3215,1705,9278,34338}

{44042,46723,10506,32163,6690,37614,2091,31805,841,26658,46377,8027,22199,24318,17211,42375,40128,49383,22099,48062,20150,16249,26367,23202,44811,38746,42656,29556,16275,33870,10842,9439,43814,15445,12057,13481,46032,45334,6745,15011,47984,3143,2999,9343,21960,18084,48080,25071}

49999

Returns: -3.080051008888924E12
{21888,30836,44941,29250,11705,8727,44879,21605,42731,16578,42133,16664,47008,4344,36871,28514,28366,33988,23654,45702,47687,33030,46240,6992,49430,25707,43753,7395,24585,8045,19140,36084,34483,33598,40905,40746,16604,45981,4202,5175,115,11255,44521,44095,26610,25211,1386,8841,48527,9421}

{41257,19519,17316,36877,38714,30964,42794,27215,12392,2347,7127,3730,12395,19392,6765,24151,36070,2755,30949,4329,47181,926,43486,1156,9587,5901,31980,38461,14797,3165,28555,29596,49710,11440,5095,11157,27665,6781,6607,24851,906,24289,3946,28919,47169,19047,45506,15363,2918,19627}

49998

Returns: 3.3918275665697407E12
{0,1,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,1,1,1,1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1}

{0,0,0,0,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0,0,0}

49999

Returns: 5.493709153093309E12
{0,0,1,0,0,0,1,0,0,1,1,1,1,0,1,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,1,0,1,0,0}

{0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,1,0,0,0,1,0,0,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,1,0}

49999

Returns: 2.0642101684387495E12
{1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0,1,0,1,1}

{1,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,1,1,0}

49999

Returns: -1.413009211412639E12
{199,67,199,12,220,31,107,32,83,17,198,199,87,154,83,97,85,158,21,245,129,227,15,172,81,149,202,84,0,197,210,222,12,229,57,224,184,78,18,20,139,186,247,215,207,202,132}

{171,19,130,218,182,170,200,29,64,42,232,246,57,237,19,18,177,147,219,161,93,126,185,216,25,85,135,111,96,130,6,35,214,180,90,53,191,93,137,234,133,53,255,9,54,181,13,96,3}

48

Returns: 42388.375
{195,111,160,252,109,242,185,109,162,175,143,113,33,119,102,103,80,219,102,181,186,179,27,67,139,152,244,253,22,105,196,84,80,202,68,190,82,160,142,50,219,151,163,172,204,156,231,175}

{170,99,160,190,31,226,123,226,121,212,6,40,41,56,55,31,70,207,227,94,8,161,72,252,77,120,132,22,23,100,28,77,12,53,118,70,244,4,95,40,63,171,133,33,125,72,254}

50

Returns: 287295.68
{191,29,205,52,38,13,55,148,113,239,66,13,69,130,182,146,40,139,122,89,7,84,29,92,177,40,80,219,89,216,106,216,24,58,227,154,104,164,217,42,171,117,142,217,162}

{140,232,185,247,207,240,31,179,166,83,39,200,126,228,48,137,70,24,92,44,245,137,17,79,2,116,123,112,234,58,7,116,173,226,234,33,82,150,152,164,95,34,77,12,97,120,135}

50

Returns: -12056.28
{138,61,142,255,219,26,101,70,197,2,141,135,216,250,37,229,101,232,82,172,3,25,189,201,13,188,19,77,33,100,133,238,162,138,70,133,55,9,15,145,74,160,158,179,139}

{116,50,48,106,139,17,115,160,82,2,136,167,24,212,161,61,145,213,149,229,84,91,92,101,92,63,149,74,139,93,0,95,34,22,4,58,75,206,42,176,144,110,159,91,97,226}

45

Returns: 127403.4
{156,100,146,217,16,195,166,84,54,144,3,1,11,173,151,69,16,159,20,102,201,17,113,17,63,79,105,213,127,203,251,166,25,156,233,91,162,250,57,48,50,196,183,68,231,250,112,28,96,67}

{56,30,66,104,37,23,183,215,18,182,234,33,30,15,140,124,42,25,83,66,94,48,117,112,164,147,49,40,44,231,70,47,231,179,122,112,12,226,21,119,149,68,99,246,194,12,54,68}

47

Returns: 137916.06382978722
{34, 3245, 2534, 53, 53, 46, 346, 246, 346, 2, 624, 624, 6, 245, 6324, 6542, 624, 6 }

{345, 234, 523, 4624, 6, 2456, 345, 634, 634, 7, 3457, 376, 34, 6234, 62, 523, 52, 35, 32 }

7

Returns: -9713701.714285715
{34, 3245, 2534, 53, 53, 46, 346, 246, 346, 2, 624, 624, 6, 245, 6324, 6542, 624, 6 }

{345, 234, 523, 4624, 6, 2456, 345, 634, 634, 7, 3457, 376, 34, 6234, 62, 523, 52, 35, 32 }

50000

Returns: 3.554157166328439E12
{49998, 49997, 49996, 49995 }

{49997, 49990, 49996, 49995 }

50000

Returns: -6.233876919701828E10
{1 }

{49998, 49998 }

50000

Returns: -2.5395092429469086E13
{0 }

{49998 }

1

Returns: -2.499800004E9
{1, 5, 4, 4, 4, 4, 8, 6, 111, 551, 12, 51, 512, 512, 66, 7, 2, 34, 5, 3, 346 }

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

77

Returns: 3986245.922077922
{1, 2, 3, 4 }

{1, 2, 3, 4 }

50000

Returns: 0.0
{511 }

{213 }

50000

Returns: 208001.616
{1, 2, 3, 4, 5 }

{1, 2, 3, 4 }

50000

Returns: 2.1873353775805095E12
{1, 2, 3, 4 }

{13, 27, 84, 46 }

50000

Returns: -8.913384772085927E11
{1, 3, 4, 100, 1000, 200, 4, 6, 7 }

{12, 23, 45, 67 }

50000

Returns: -2.1027388486532253E12
{1, 2, 3, 4, 5, 3424, 43, 345 }

{343, 23, 2134, 23, 43532 }

50000

Returns: -6.152359735381179E11
{1, 3, 7, 11, 13 }

{17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 }

49876

Returns: -2.216667787181693E12
{1 }

{2 }

50000

Returns: -22.99956
{45, 35, 236, 2342, 5543, 21, 32, 2, 6, 23, 24, 23, 41, 1 }

{2345, 45, 2345, 345 }

50

Returns: 1.2721986164E8

Statistics

Problem Statement for "RandomFights"

Problem Statement

Definition

Notes

Constraints

Examples