TopCoder Statistics - Problem Statement

Problem Statement

Mr. Green owns a beautiful park full of trees. Recently, he arranged a new lane in the park and planted N trees along the lane. The trees are numbered from 0 to N-1 in the order that they occur along the lane. It is known that once the i-th tree grows up, its height in meters will be a random integer uniformly distributed between low[i] and high[i], inclusive.

Mr. Green has quite a strange conception about beauty. In particular, he is very fond of so called alternating sequences of integers, which are defined by the following rules:

Every sequence of 1 integer is alternating.
A sequence of 2 integers (A, B) is alternating if and only if A is not equal to B.
A sequence of 3 integers (A, B, C) is alternating if and only if (A < B and B > C) or (A > B and B < C).
A sequence of L, L > 3, integers (A[0], A[1], ..., A[L-1]) is alternating if and only if each triple of consecutive integers in the sequence form an alternating sequence. In other words, each of the sequences (A[0], A[1], A[2]), (A[1], A[2], A[3]), ..., (A[L-3], A[L-2], A[L-1]) must be alternating.

Mr. Green measures the beauty of an alternating sequence as the sum of absolute differences between all pairs of its consecutive elements. In other words, for a sequence (A[0], A[1], ..., A[L-1]), its beauty is equal to |A[0] - A[1]| + |A[1] - A[2]| + ... + |A[L-2] - A[L-1]|. Note that the beauty of a sequence consisting of 1 element is equal to 0.

Once all the trees grow up, Mr. Green will write down their heights in the order that they occur along the lane. If the resulted sequence of integers is alternating, then he will be satisfied with the resulting lane. Otherwise, he will cut some trees down so that the sequence formed by the remaining trees is alternating. If there are several ways to obtain an alternating sequence, he will choose a way among them that results in a sequence with maximum possible beauty.

Return the expected value of the beauty of the resulting sequence.

Definition

Class:: AlternatingLane
Method:: expectedBeauty
Parameters:: int[], int[]
Returns:: double
Method signature:: double expectedBeauty(int[] low, int[] high)
(be sure your method is public)

Notes

The returned value must have an absolute or relative error less than 1e-9.

Constraints

low will contain between 1 and 50 elements, inclusive.
high will contain the same number of elements as low.
Each element of low and high will be between 1 and 100,000, inclusive.
For each valid index i, low[i] will be less than or equal to high[i].

Examples

{1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000}

{1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000}

Returns: 4899951.0

max answer
{100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1}

{100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1,100000,1}

Returns: 4899951.0

another max answer
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

{100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000}

Returns: 1633333.3331700016
{1}

{100}

Returns: 0.0

Here we have only 1 tree, so the beauty of the resulting sequence will be 0.
{1, 1, 1}

{2, 2, 2}

Returns: 1.0

Once all the trees grow up, 8 different lanes are possible with equal probability. In cases (1, 1, 1) and (2, 2, 2), Mr. Green will cut 2 trees and the beauty will be 0. In cases (1, 1, 2), (2, 2, 1), (1, 2, 2), (2, 1, 1), he will cut the middle tree and the beauty will be 1. Finally, in cases (1, 2, 1) and (2, 1, 2), he won't cut any trees and the beauty will be 2. Therefore, the answer is (4/8) * 1 + (2/8) * 2 = 1.
{1, 3, 5, 7, 9}

{2, 4, 6, 8, 10}

Returns: 8.0

Here, Mr. Green will always leave only the first and the last trees.
{4, 3, 3, 7}

{10, 7, 7, 7}

Returns: 6.171428571428572
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

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

Returns: 0.0
{1}

{100000}

Returns: 0.0
{55555}

{55555}

Returns: 0.0
{153,340}

{880,499}

Returns: 197.8543956043956
{5,4,9}

{6,5,10}

Returns: 6.0
{514,464,178,654}

{637,532,667,770}

Returns: 502.2245295500154
{16,6,6,14,42}

{38,17,86,83,58}

Returns: 93.8313498453595
{48,25,52,21,11,54}

{80,64,79,52,14,74}

Returns: 146.88636363636363
{9,1,4,45,11,1,17}

{91,54,82,91,36,31,65}

Returns: 167.07797416061658
{146,18,536,383,74,367,10,394}

{153,216,965,928,597,912,800,415}

Returns: 2015.0929997217636
{1,2,2,8,2,2,1,6,4}

{3,5,8,8,3,5,9,10,5}

Returns: 23.186507936507937
{8833,14149,58287,64867,22357,2792,57966,26618,13276,30841}

{55226,28210,80542,91900,84621,98447,67481,95934,26675,60894}

Returns: 237813.4050397304
{336,199,353,826,476,606,163,716,527,145,138}

{891,285,754,961,507,812,190,934,1000,730,524}

Returns: 3481.7510674110827
{544,522,180,128,360,646,136,315,651,577,599,256}

{902,638,510,677,840,920,593,689,699,794,904,792}

Returns: 2158.6979228729465
{22,35,11,88,30,2,23,31,38,54,15,39,56}

{74,58,97,95,58,3,25,63,42,80,52,81,99}

Returns: 326.54429321754753
{6,3,4,1,2,5,2,3,6,1,5,2,1,2}

{8,10,5,6,10,9,5,8,6,3,8,3,9,8}

Returns: 37.49074074074074
{287,17,496,357,257,393,557,193,11,594,142,362,367,882,380}

{937,354,904,438,891,885,776,343,905,844,488,610,531,931,770}

Returns: 4202.126853416785
{3,2,4,3,4,2,6,1,4,7,5,4,2,3,5,7}

{3,4,5,5,10,6,10,5,6,10,7,10,8,3,6,8}

Returns: 38.01156462585034
{5,3,1,6,2,5,3,9,5,6,6,9,1,6,1,5,5}

{5,5,5,6,8,7,3,10,5,8,9,10,9,10,4,9,8}

Returns: 47.953968253968256
{15870,19735,18287,38917,12277,37806,43377,22610,54427,1403,35418,21692,80577,43807,68202,43695,1595,34307}

{39272,84085,78239,46358,57008,76892,49750,65346,70177,50967,40692,37693,83915,45462,78006,80473,43221,37344}

Returns: 387608.2745328143
{19410,61541,72027,57165,17403,6744,52120,45840,13655,64183,83889,16134,32633,7269,78818,3657,6355,8122,19221}

{32296,85530,77206,68497,34821,90205,85269,82251,92156,91010,83994,37870,59041,28309,85338,71045,17466,64697,28228}

Returns: 509094.38042878546
{41793,8007,81400,31913,44090,14530,25780,59397,64236,31682,19578,12310,87220,14623,13972,36860,2559,34016,21455,68018}

{69282,64182,87233,62620,71580,83847,67796,61675,89513,32245,33218,56854,91937,33895,80439,37545,9810,38541,45177,86223}

Returns: 528736.3921211346
{8993,6912,64649,41103,6040,4910,40805,57713,49227,57785,14292,33260,15558,29480,57560,11613,30362,6007,86237,63458,32859}

{11908,27613,97365,78432,79695,45254,58560,85831,92762,71381,91913,87907,71259,64234,58898,27989,86732,16896,87331,74119,75986}

Returns: 542456.0935149934
{540,230,172,305,200,278,857,657,22,689,444,887,654,648,621,24,594,482,182,166,199,189}

{985,915,778,673,786,537,866,957,119,774,759,943,744,733,622,379,760,693,871,341,424,587}

Returns: 5352.947891503087
{561,544,101,136,265,99,159,109,366,118,33,32,454,320,197,358,147,89,27,645,438,49,826}

{886,901,336,188,709,987,507,189,565,747,760,453,987,769,711,810,933,810,71,737,696,212,922}

Returns: 6573.831051362502
{300,119,41,53,227,566,369,29,516,397,137,146,210,148,255,695,677,313,430,751,789,222,175,101}

{643,651,539,664,589,852,570,507,645,760,518,381,800,180,489,695,887,809,707,950,864,403,491,719}

Returns: 4954.725916451024
{33,32,60,40,69,12,37,20,61,36,68,90,44,91,63,7,6,40,8,3,5,58,13,47,63}

{84,44,97,53,84,57,94,100,61,78,72,99,54,93,65,66,94,43,84,61,19,67,32,64,100}

Returns: 703.9465736524523
{71245,37471,26497,12681,23885,96874,6458,13863,62779,77192,57912,63563,3297,91656,22639,44034,50793,19756,43038,4150,69984,45793,57440,37891,807,18400}

{77943,83045,46114,97435,78990,97079,12635,15142,91715,98806,60439,75605,27164,91732,88079,49483,59640,67440,65742,40043,89782,62391,92928,48258,53332,32040}

Returns: 766614.0958003382
{1,1,2,7,3,5,2,4,5,1,1,4,4,4,6,6,1,6,3,7,9,7,2,5,3,4,4}

{2,4,8,7,9,7,7,10,6,9,3,4,10,8,10,7,4,7,9,10,10,10,9,6,10,7,6}

Returns: 59.58018518518519
{43290,64362,13642,36180,45947,24530,37027,18861,27577,40861,39456,72233,11581,33120,15020,81356,56796,6318,16502,24648,4791,29539,38060,34802,35736,10388,38400,68190}

{45021,88802,48145,49710,79763,67403,49153,64993,53298,98461,54891,94157,99015,93633,93658,96473,57397,53086,18166,87257,61933,31754,56831,74268,98580,50339,86350,76460}

Returns: 659814.1878091833
{50,42,12,1,5,50,16,49,6,39,2,65,21,19,9,71,60,14,25,8,50,25,42,18,19,72,6,4,3}

{94,56,72,28,71,55,66,58,53,75,41,66,70,31,11,77,90,92,95,82,84,31,52,26,45,88,41,57,32}

Returns: 744.4643616956045
{28855,63044,29271,25176,97041,84165,46253,18927,4657,76072,51436,37863,57299,29349,16867,44836,30467,10105,135,7992,67326,24982,51462,73784,39896,9935,3612,30899,16531,22538}

{55118,70688,66772,47189,98726,99261,87604,53579,74137,81889,79630,76027,92744,36742,54642,98113,94053,68735,17861,90822,74155,69634,52655,82386,65945,72006,50757,99367,81373,39269}

Returns: 733114.4605093416
{130,599,146,75,598,692,443,624,244,461,369,526,956,64,195,767,289,327,369,116,289,551,76,217,663,201,436,140,494,174,574}

{639,959,708,893,708,925,729,965,284,778,647,926,996,796,529,848,329,631,566,329,306,834,623,734,970,822,459,557,846,497,685}

Returns: 8430.35201034263
{1,4,3,1,4,2,10,4,3,8,4,10,1,3,1,2,6,7,6,4,1,3,2,3,5,8,3,6,5,2,6,2}

{6,5,9,10,10,3,10,7,9,9,5,10,9,10,8,8,7,8,10,5,10,9,6,10,6,10,9,7,8,8,6,6}

Returns: 90.47906746031747
{3,9,5,8,4,4,3,5,4,2,2,3,5,1,4,3,4,8,3,4,8,2,1,8,1,5,4,4,4,4,3,5,3}

{8,10,5,10,8,10,3,10,6,4,7,6,6,7,9,7,5,9,4,6,10,5,6,10,9,5,6,6,7,6,6,8,10}

Returns: 86.89788359788362
{308,450,493,37,517,626,812,550,540,389,110,538,153,221,34,382,606,323,250,552,2,768,691,75,153,864,219,541,39,615,499,127,23,52}

{317,641,896,430,688,764,837,645,600,992,607,838,718,847,389,879,643,533,663,749,16,892,950,887,646,920,541,691,207,856,634,914,574,867}

Returns: 9821.302390034618
{15,32,3,13,8,61,21,17,71,67,6,57,16,35,27,11,36,54,65,65,29,25,17,24,20,12,41,39,28,13,13,89,24,8,50}

{67,53,31,48,71,86,80,93,80,89,95,71,79,44,60,50,64,62,93,67,72,47,27,73,40,41,64,70,96,76,73,94,90,25,63}

Returns: 739.9808973018561
{3,1,3,10,5,1,1,6,2,8,9,2,3,7,5,7,4,8,5,1,5,3,3,2,6,4,6,1,7,1,6,4,2,3,1,9}

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

Returns: 105.25568783068783
{7,6,2,4,4,2,5,2,3,4,3,3,10,9,1,3,2,2,5,8,7,6,5,4,3,2,2,7,3,6,1,2,5,3,6,3,10}

{7,7,7,6,8,6,6,3,10,6,5,9,10,10,4,9,3,7,8,10,8,7,8,10,4,10,10,8,4,10,5,5,6,4,9,6,10}

Returns: 97.17502645502645
{66420,41379,48002,62258,27725,78544,14151,40318,79326,31924,71983,16557,28421,35037,52623,30896,25705,42171,5714,27274,22061,12117,164,55813,63076,44738,32341,48329,38700,79765,45985,27187,40625,13106,15729,49878,15419,88734}

{87729,72592,75505,90358,41738,84940,65122,49016,95850,90308,82796,63733,77508,98414,72393,81548,88124,95671,58581,36264,87895,48437,2411,94631,79172,56903,46718,92230,75592,94509,60687,93929,87057,97682,46798,81466,97072,89212}

Returns: 969885.2215425364
{7869,5939,1198,1384,5653,7173,429,152,1571,2244,5813,6550,6664,2734,3625,2104,8218,8886,3701,1180,7396,5453,5962,1576,4763,7706,4201,7529,6921,4635,796,2214,3578,3808,3200,502,198,1815,854}

{8456,9210,5441,2590,5917,9898,2703,4943,2743,3232,6154,7146,8010,9001,8413,4202,9824,9755,8065,8447,9612,8823,9974,9178,9487,9623,7036,8551,9668,6422,1393,7486,3825,5438,7152,2965,3911,9986,3450}

Returns: 93842.56027272709
{47,32,44,14,75,45,26,23,29,2,30,12,75,90,63,7,59,68,31,70,10,7,68,16,58,4,61,71,75,15,9,14,31,29,18,7,48,13,67,49}

{68,73,79,100,76,92,56,81,86,35,31,19,77,100,67,43,78,100,44,90,35,35,79,31,59,30,83,80,79,53,77,28,94,94,53,81,72,68,93,90}

Returns: 1129.1177743523267
{297,61,120,666,624,10,328,49,130,90,85,298,166,413,234,38,130,391,296,583,595,43,20,422,661,397,52,191,43,101,672,8,37,8,497,69,206,639,102,507,493}

{650,958,588,694,806,201,494,750,752,344,459,472,976,893,251,659,943,942,329,779,807,401,837,736,769,836,286,988,992,399,709,153,821,935,738,954,384,854,455,636,843}

Returns: 11659.453496623028
{52,81414,6799,12548,61246,1580,81732,20342,24527,33745,49409,4196,19363,4442,7476,46580,14020,5089,4676,47206,37804,542,58696,40185,27237,4089,21918,10063,18901,2195,12231,17390,6901,15234,28390,90087,22028,13001,51002,434,18231,3462}

{61245,86612,62612,17785,89541,2056,92334,83644,25135,41555,80663,7539,45457,63379,22095,66634,73068,44846,5687,85549,44941,43398,63969,65830,47440,43690,82734,66552,66316,25227,84924,82718,61062,40708,47203,92612,59951,98107,61944,33131,35069,66105}

Returns: 1283141.7992976215
{7551,4659,2742,5862,1166,7736,1534,8198,3452,5658,2884,3129,4119,91,4448,4212,2351,1507,471,1718,2487,1564,1639,2853,491,1254,6188,7550,1775,798,4859,2840,5298,3077,5584,5259,6399,2439,1923,131,4359,3111,919}

{8162,8495,9703,5880,6571,9369,1957,8282,8674,8443,4855,7578,8636,9371,7178,9758,3653,8821,8366,9617,5074,4510,1648,6245,3275,8752,8977,8332,8557,7544,6353,8285,7413,9319,9367,7000,7137,3729,3481,441,5491,5757,6559}

Returns: 101672.97716886493
{7,7,17,5,51,13,15,3,43,38,8,78,12,65,8,66,14,23,36,24,17,4,4,25,6,39,74,74,18,32,56,18,46,22,9,32,79,10,88,25,65,24,3,21}

{91,18,55,81,60,47,54,57,71,76,53,90,57,91,66,73,28,83,85,95,28,86,63,45,29,77,91,75,18,34,76,55,60,65,22,63,89,44,93,95,77,26,78,93}

Returns: 1290.8918084424154
{2785,2387,2260,951,4069,4887,1946,6967,7340,1386,5368,5424,8151,2890,3004,9743,5221,786,263,3533,172,501,63,3410,1673,3489,4947,2277,2366,629,2249,4367,18,613,396,3212,2311,6732,7129,6015,1778,2974,2680,882,2301}

{7098,2844,2564,2832,7354,6414,6887,9204,7939,9373,6068,7752,9979,7242,3690,9783,5560,3319,3956,5079,6900,4838,275,7648,3423,7759,8904,5090,5295,8864,4733,9898,977,1681,498,3438,4036,7216,8575,8439,5647,3049,7150,6582,2528}

Returns: 103974.49556304861
{22478,3574,30718,27183,2176,5247,47409,46090,1182,66699,53289,10761,53373,8170,20581,48309,3899,6839,11365,2611,13734,4737,1765,21928,81342,17637,29278,22453,43742,18941,47358,33798,71118,25936,66184,755,11014,53921,47548,30975,2124,67416,3670,59525,20,25158}

{98124,60763,48750,95654,7432,75804,84454,59522,7666,89030,88968,55560,57849,60830,79927,74674,55002,15510,61385,26965,65213,75340,15482,75273,97753,71656,71812,77086,81952,93938,88357,96859,90294,46533,88484,70547,88077,72310,65767,94926,95330,68086,55317,81846,72768,43878}

Returns: 1291023.7288117912
{5855,3229,5460,1762,5292,2280,5219,5947,8991,5332,4274,2733,6129,5872,839,2397,4169,2187,5305,5484,7845,2420,4066,2397,6128,6246,4791,1279,8149,2551,2583,2332,6167,411,6505,7752,109,7966,3037,1867,8336,2830,109,368,1866,662,6663}

{8082,8764,9882,4565,9476,6370,6390,9120,9000,8834,9035,5379,8912,6303,8435,4932,9904,4761,7865,6647,8299,2475,9467,8026,7066,8293,7018,7738,8908,6995,8540,3385,9751,6015,7062,9879,3672,8026,9522,2413,8839,5485,6319,2110,5014,2959,8526}

Returns: 138140.5542072493
{4,436,531,733,417,126,819,565,321,188,179,260,204,23,70,53,870,59,495,139,174,390,724,79,432,119,12,470,191,52,877,228,576,32,375,700,208,293,600,472,161,462,59,200,69,973,149,13}

{965,756,878,898,622,914,897,975,329,996,391,815,223,909,402,249,882,714,558,827,469,970,945,853,874,525,12,689,271,230,951,959,702,767,813,819,539,948,842,516,171,707,229,835,852,991,657,16}

Returns: 14823.201735091003
{758,124,118,186,26,187,19,597,16,11,251,118,463,60,53,74,617,77,513,590,182,468,264,416,441,147,426,469,382,215,224,503,380,340,744,592,599,44,415,674,311,733,11,65,584,594,764,660,566}

{837,647,969,368,801,687,712,617,59,375,982,591,465,268,765,830,691,616,773,680,547,958,575,559,503,300,993,947,680,369,923,874,598,999,983,779,988,577,555,788,584,839,421,444,939,683,905,913,930}

Returns: 12369.94985622414
{5,8,4,4,9,6,4,4,6,4,3,4,2,3,3,1,6,4,3,3,2,9,7,1,8,3,3,5,4,9,2,3,1,6,6,3,5,1,5,5,6,1,3,6,3,1,2,5,10,7}

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

Returns: 134.0248677248677
{13,42,57,94,25,33,16,34,81,11,13,45,49,18,61,71,71,17,7,33,37,17,50,20,15,52,51,49,7,39,40,16,19,61,68,34,16,1,74,32,53,23,17,10,44,65,48,68,60,9}

{19,52,75,99,36,71,62,93,92,32,33,76,74,45,80,82,73,43,17,68,44,78,87,30,65,78,90,69,66,95,74,71,39,93,88,35,93,74,90,58,97,65,96,96,65,84,100,82,74,66}

Returns: 1271.1905027440855
{351,527,152,413,263,726,4,305,121,490,453,585,148,450,138,338,130,661,6,177,238,737,90,631,463,244,279,216,160,523,156,308,712,429,8,354,88,481,752,437,652,30,545,919,31,437,35,748,345,66}

{990,987,693,576,390,731,890,640,513,509,530,882,872,739,861,678,962,748,888,898,339,740,286,856,649,355,407,397,278,741,875,667,734,923,209,518,680,877,827,946,811,52,748,963,304,599,297,851,526,354}

Returns: 14034.667558394029
{6642,229,3210,905,6493,8452,4832,2253,504,2378,5041,652,1664,7893,2380,3079,2499,7697,7621,2068,3649,9010,3163,2980,1620,5273,3902,5557,6668,4056,2229,2458,2945,1422,1979,4911,1320,7351,4880,5639,1665,7682,2411,7276,722,2468,7838,1721,5763,8939}

{6759,6189,9072,9554,8699,9759,6446,2418,1460,3486,7471,9268,5223,8408,5128,9609,3546,9168,9475,4832,7111,9337,5083,9874,5070,9573,7866,6656,6997,5412,4905,8247,6483,2816,9852,8515,2801,9447,9136,6088,9720,8029,9011,7839,4246,7901,9367,1848,9573,9078}

Returns: 146769.92397472553
{19230,42115,42981,64151,51280,46584,1715,6949,6245,20475,17389,38701,50539,40715,46691,27258,29199,56556,31710,32151,9798,74052,10954,91899,29937,3245,52055,87640,33798,31385,787,54961,28211,13246,26612,87378,30512,9750,37587,5783,33949,18741,48506,37365,77691,29990,67182,34581,6925,11139}

{70948,98410,89359,89518,94402,56507,37700,80284,98135,82077,42344,78010,91334,43181,58124,30102,94417,85823,82948,93184,89104,96358,96540,99122,39431,86233,92281,91786,93891,92115,85311,95732,68342,37001,31077,99114,84578,32293,61017,89810,73055,33080,98839,76154,96828,40465,99036,64755,34664,16115}

Returns: 1374676.9579633186
{772,3489,4509,7022,8886,11311,12369,14224,16520,18938,20599,23389,24475,27592,29064,30630,32421,34001,36289,39350,41405,42203,44319,46106,48454,50290,52700,55464,56579,58539,61268,62513,64009,67209,68779,70540,72022,74201,76217,79390,80849,82307,84038,86208,88855,90944,92206,94529,97174,98262}

{1512,3600,5719,7789,9851,11755,13599,15977,17577,19151,21149,23752,25832,27800,29241,31213,32953,34120,36542,39569,41444,42273,45767,47298,49168,50506,53260,55780,56966,58589,61358,63981,64371,67460,69206,70757,73163,74567,77104,79397,81010,82899,84520,86302,89045,91261,93550,94567,97593,98877}

Returns: 97427.5
{98809,96632,94776,92279,90852,88409,86163,85150,82341,80575,79040,76297,75056,72969,70817,68114,66019,65392,62668,61315,58217,56544,54281,52442,50936,48208,46612,45399,42626,40066,39171,37642,35412,32025,31145,28265,27226,24174,22706,20775,18170,16908,14761,12077,10445,8339,6201,4646,2800,673}

{99958,97664,95176,93445,91453,89855,86922,85783,82825,80578,79144,77872,75241,73266,71161,68663,66508,65677,63933,61708,59202,56630,54569,53176,51355,48678,47776,45664,43768,41379,39539,37905,35611,33648,31157,29172,27233,24980,23016,21401,19899,17635,15887,13230,11842,9046,6471,5158,3303,949}

Returns: 98572.5
{842,10156,12065,6343,9117,11914,14786,13785,22150,25228,19327,28752,24715,28745,30616,31634,33509,33903,41472,36721,37518,40129,43388,51382,48721,47163,51861,51576,52524,61347,61956,57624,63145,61941,66050,70791,68737,68479,70796,74394,76754,82993,84016,81817,84774,85152,84607,91956,92645,96393}

{6474,10263,13456,7448,9507,12310,20465,17384,22451,25914,20850,28984,28550,32625,33551,33729,38908,41003,42384,44304,40518,46273,49061,51460,52380,53004,53414,53802,55456,61435,64554,63588,65555,66511,66113,73101,69908,76982,74644,74439,79449,83318,85830,84802,88793,91902,88101,94029,93814,96543}

Returns: 161933.94585673412
{842,10156,12065,6343,9117,11914,14786,13785,22150,25228,19327,28752,24715,28745,30616,31634,33509,33903,41472,36721,37518,40129,43388,51382,48721,47163,51861,51576,52524,61347,61956,57624,63145,61941,66050,70791,68737,68479,70796,74394,76754,82993,84016,81817,84774,85152,84607,91956,92645,96393}

{6474,10263,13456,7448,9507,12310,20465,17384,22451,25914,20850,28984,28550,32625,33551,33729,38908,41003,42384,44304,40518,46273,49061,51460,52380,53004,53414,53802,55456,61435,64554,63588,65555,66511,66113,73101,69908,76982,74644,74439,79449,83318,85830,84802,88793,91902,88101,94029,93814,96543}

Returns: 161933.94585673412
{8861,8067,19922,4910,6759,9049,16900,14839,23996,30824,27485,18445,19991,20631,27927,32455,32518,31118,39625,29884,50069,32704,37975,43796,57031,52813,42027,47044,44579,50900,56973,57116,49968,54949,58879,59567,62947,57515,64701,83845,73718,78696,80906,73852,73089,70440,85613,87188,82233,78970}

{14988,16041,20555,29530,25917,18346,30494,27299,31418,33053,33623,41456,23092,27555,34694,38244,34107,34167,51538,48165,52186,49837,44442,47844,60572,55648,44975,54368,65854,51624,66629,57924,72457,66878,63536,63710,70316,59369,81214,84355,80285,86039,87784,88415,86472,72996,88059,90470,92439,99197}

Returns: 318655.57667842554
{90375,81091,78794,74271,71342,71999,70576,64756,73886,70418,65737,65577,71212,74541,61159,53852,67563,54733,57702,48567,48712,48240,48007,46447,40459,38451,46074,52354,36782,47751,31192,27760,34690,29371,35684,25897,40048,24264,17219,18466,22880,20602,26848,23091,15557,18956,6658,19517,1845,19681}

{97552,91552,87772,77159,74320,82693,80622,64865,83239,80667,84607,76477,74193,79553,63254,65314,72562,72816,63860,63558,65807,66821,50116,53507,60352,59947,57108,53372,50198,51849,40762,37293,38055,48997,39614,31406,42149,29353,33358,21099,26150,30057,35144,30795,19107,19559,18104,21156,5074,20830}

Returns: 339142.0514240494
{16022,7306,29674,22926,24115,12911,37617,8222,17523,24427,24013,30381,44079,37027,23539,48724,32577,29749,22386,29059,33515,29110,23306,35482,57449,37137,45776,53529,32563,39500,65872,69493,41511,55494,57806,37184,42388,74500,60965,40621,58700,45684,53681,48562,72030,54036,75880,70608,55156,60415}

{49291,12842,50426,52604,49614,37212,43728,45463,56735,31214,50597,42393,60430,45763,25059,59382,60997,41313,43269,32201,64902,39236,50422,67961,58176,60797,51392,65048,52325,58687,80297,76782,61485,74527,76537,76694,67225,76391,73786,60545,81383,46071,55925,78860,86143,85929,94274,95717,96157,64823}

Returns: 662625.0949962189
{89915,61959,53536,59120,70135,76785,69162,88010,66404,55547,65854,57340,41972,48112,46122,35769,58869,32740,32231,37654,64123,70800,35073,34205,32220,35753,29272,40223,24289,26908,50655,22016,30227,29311,50104,19626,20785,19029,22525,10401,16736,26413,48109,6425,6846,10412,27522,19478,30635,26779}

{94176,89132,85875,89134,74158,89944,92580,89070,73134,89300,75693,63823,81435,67025,57612,52025,61268,42335,57857,39401,78362,72840,51799,70308,56329,70275,39836,43607,26522,48320,65580,67236,39261,63502,60302,41830,27961,61529,42906,51289,26702,44804,55526,12244,32636,27825,50498,25339,39485,37150}

Returns: 669375.0023438723
{8,99996,3,99994,2,99994,6,99993,6,99994,2,99997,4,99991,3,99997,3,99991,6,99993,3,99996,1,99998,1,99991,5,99991,7,99995,5,99997,2,99997,2,99997,1,99996,3,99992,1,99992,5,99992,4,99995,1,99998,10,99993}

{9,99999,5,99998,3,99996,9,100000,8,99995,5,99999,5,99992,4,99998,8,99998,6,100000,4,99999,10,99999,7,99998,5,99998,10,99996,7,99999,8,99998,3,99998,10,99997,8,99996,6,99995,6,99997,10,99995,10,100000,10,99999}

Returns: 4899541.5
{65,99927,10,99920,68,99970,22,99922,31,99922,12,99965,65,99991,2,99948,68,99957,2,99954,43,99912,61,99933,89,99969,42,99909,4,99932,63,99936,31,99916,63,99937,74,99928,27,99942,51,99932,31,99967,4,99926,15,99916,73,99911}

{76,99957,22,99923,72,99972,57,99932,67,99960,80,99965,76,99992,94,99979,70,99957,24,99985,58,99973,76,99993,96,99987,43,99930,23,99938,94,99957,94,99950,82,99951,97,99965,33,99952,57,99966,89,99975,31,99943,97,99917,75,99967}

Returns: 4894860.5
{99093,142,99187,659,99027,159,99615,304,99382,352,99065,300,99153,81,99250,51,99773,50,99277,583,99663,73,99521,311,99365,59,99605,80,99576,507,99577,379,99596,70,99251,87,99465,101,99695,533,99592,161,99173,176,99307,661,99003,53,99032,568}

{99481,167,99418,669,99188,407,99616,718,99485,961,99953,636,99232,220,99461,949,99778,763,99410,940,99859,378,99816,323,99701,571,99753,115,99892,680,99967,675,99701,592,99257,739,99987,625,99856,626,99630,673,99871,660,99705,861,99428,69,99444,690}

Returns: 4855267.0
{95035,3512,90933,6446,91588,4051,91458,721,94344,6180,95844,4082,90335,2197,90806,2913,91737,3948,99410,3095,95133,285,91287,5255,91681,3409,92355,278,92608,1827,93492,5176,90510,2022,99328,2300,97997,1001,90059,2375,91675,2748,91234,8,93809,2148,90457,6606,93934,9378}

{98467,8769,91142,7375,94965,5828,97848,4177,96482,8039,95887,8235,93022,5735,91665,5528,98957,5572,99549,8347,95321,9786,95901,7176,94905,9916,93142,9484,94030,7799,96026,5905,94855,5470,99597,2562,98019,1872,94436,7698,93107,6219,96084,4162,94760,6514,92441,9828,95766,9416}

Returns: 4372696.0
{74230,22249,74644,24375,60126,15542,59912,15748,61610,16993,67262,551,76881,27741,63138,32754,76947,29376,79229,26545,55600,9982,62281,29070,55759,26057,57801,12489,64773,5456,62745,3745,61827,16882,50098,21723,59373,29127,50423,1359,67820,35032,96329,5064,58633,29921,66825,3361,53059,2390}

{90580,23537,86539,32195,91705,19080,85796,31620,97543,22841,79135,40088,89142,47979,70094,45878,77617,39823,86675,47478,61680,46306,63862,46717,66589,40272,59861,45352,72500,45492,75682,35760,97644,21300,97374,22242,73962,42059,54073,38695,97209,42287,98370,49121,85036,36458,96247,39611,60096,45586}

Returns: 2182610.0
{24503,91385,70416,51376,4006,36253,48482,39516,11223,77383,13641,72844,2,32444,28405,62713,39131,63503,71981,40777,14718,60067,14363,41259,8722,44365,2242,33519,7910,41711,4139,33147,64043,46627,28151,65971,2652,46161,51522,59282,19758,67352,4704,78278,19760,28507,12562,41034,4516,66037}

{30808,97479,70520,55341,47380,36315,63268,90023,71781,77864,62822,73521,23836,89164,35279,98980,66600,78483,73151,83264,53935,70717,60542,68641,48303,68272,53082,94115,49241,53868,12834,88706,65154,55471,36639,80770,24671,73621,65941,84335,20353,75286,5961,99579,39432,76733,56363,61357,58801,78493}

Returns: 1596697.2173674693
{4, 3, 3, 7 }

{10, 7, 7, 7 }

Returns: 6.171428571428572
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16263, 69701, 49753, 17257, 58120, 68352, 54109, 18331, 32170, 26918, 37973, 6981, 6224, 67593, 26552, 16191, 40636, 4921, 19311, 37364, 14711, 51877, 50432, 676, 24191, 58135, 41630, 44031, 29127, 34105, 29750, 30257, 35573, 2491, 27120, 37406, 30328, 33498, 66825 }

{100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 65934, 77744, 91530, 75509, 87257, 99712, 72844, 78706, 46394, 37367, 57933, 69848, 32869, 38550, 88165, 76170, 50428, 42625, 27945, 69863, 98485, 43302, 67237, 79930, 60398, 70492, 59345, 68426, 52728, 41744, 87335, 74761, 65621, 70933, 31614, 54510, 75696, 54050, 56720, 92597 }

Returns: 1164267.6540346846
{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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

{100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000 }

Returns: 1633333.3331700016
{1, 1, 1, 1, 1 }

{100000, 100000, 100000, 100000, 100000 }

Returns: 133333.33332
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

{100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990, 100000, 99990 }

Returns: 1633178.1827006664
{94324, 87583, 46186, 45388, 98948 }

{99999, 99783, 99432, 100000, 99723 }

Returns: 70620.01055922412
{1, 1000, 34, 54, 43211, 1, 1000, 34, 54, 43211, 1000, 34, 54, 43211, 1, 1000, 34, 54, 1, 1000, 34, 54, 43211, 1, 1000, 34, 54, 43211, 1000, 34, 54, 43211, 1, 1000, 34, 43211, 1, 1000, 34, 54, 43211, 1000, 34, 54, 43211, 1, 1000, 34, 5, 1 }

{100000, 99563, 54214, 54, 98723, 100000, 99563, 54214, 54, 98723, 99563, 54214, 54, 98723, 100000, 99563, 54214, 54, 100000, 99563, 54214, 54, 98723, 100000, 99563, 54214, 54, 98723, 99563, 54214, 54, 98723, 100000, 99563, 54214, 100000, 99563, 54214, 54, 98723, 99563, 54214, 54, 98723, 100000, 99563, 54214, 54, 10002, 99563 }

Returns: 1828835.0458379681
{1, 1 }

{100000, 100000 }

Returns: 33333.33333
{7, 4, 6, 3 }

{8, 6, 7, 10 }

Returns: 6.0
{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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 15, 1, 1, 16, 1, 1, 1, 1, 1, 1, 13 }

{100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 23440, 12999, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 99999 }

Returns: 1625109.4989430858
{1, 1, 1 }

{100000, 100000, 100000 }

Returns: 66666.66666

Statistics

Problem Statement for "AlternatingLane"

Problem Statement

Definition

Notes

Constraints

Examples