TopCoder Statistics - Problem Statement

Problem Statement

We want to find the location of a local maximum in an unknown function. y = f(x) is a continuous real-valued function defined on the real numbers. We already have a number of data pairs, (xi, yi), and we need to find a small interval on the x axis that is guaranteed to contain at least one local (or global) maximum. But taking a sample from this function is quite expensive so we are only allowed to take N samples. Our problem is to choose them in such a way as to minimize the size of the interval that we determine.

The sampling will be done sequentially: we choose a value of x and find the corresponding y value, f(x). We repeat this process N times, choosing the x value based on all the data collected so far. We are willing to assume that no two y values will be exactly equal to each other.

Create a class LocalMax that contains a method length that is given N, the number of samples we can take, and double[]s xData and yData (the existing data pairs). It will return the worst case length for our interval around a local maximum using optimal sampling. If it is not possible to make such a guarantee, it returns -1.0.

Definition

Class:: LocalMax
Method:: length
Parameters:: int, double[], double[]
Returns:: double
Method signature:: double length(int N, double[] xData, double[] yData)
(be sure your method is public)

Notes

The returned value must be accurate to within a relative or absolute value of 1E-9

Constraints

N will be between 0 and 25 inclusive.
xData will contain between 1 and 50 elements inclulsive.
yData will contain the same number of elements as xData.
The elements of yData will be distinct.
The elements of xData will be distinct.
Each element of xData and yData will be greater than 0.0 and less than 10000.0.

Examples

1

{3,4,5}

{3,4,5}

Returns: -1.0

From the data we already have we cannot guarantee that this function even has a local maximum -- it might be monotonically increasing.
0

{3,4,5}

{3,5,4}

Returns: 2.0

We know that there is a local maximum between x=3 and x=5.
2

{3,5,8}

{35,923.2,17}

Returns: 2.0

Here is one way (there are others) get an interval of length 2 or less with just two additional samples. Take the first sample at x=6.5. The worst case is that the corresponding y value is less than 923.2. In that case we know that the interval (3,6.5) contains a local maximum, and that the y value at x=5 is greater than either endpoint y value. Take the second sample at x=4.7. In the worst case the corresponding value of y will be bigger than 923.2, in which case we could conclude that there is a local max somewhere in the interval (3,5).
1

{3,4,6,5}

{32,53,68,47}

Returns: 1.0

If we take a sample at x=4.0+epsilon, for some tiny epsilon, then the worst case would be that the corresponding y value would be smaller than 53. In that case the interval between 3.0 and 4.0+epsilon would contain a local maximum. So by choosing epsilon arbitrarily small, we get an interval whose length is (arbitrarily close to) 1.0.
3

{1,4.3,7.2,95.4,534.0}

{72, 83, 19, 25.3, 624.0}

Returns: 1.4500000000000002
25

{0.1,.85025,2.06418,2.09258,3.79}

{67,72,20,25,19}

Returns: 9.999999999999999E-6
25

{0.1,.85025,2.06428,2.09258,3.79}

{67,72,20,25,19}

Returns: 1.0000823770728132E-5
25

{0.1,.85025,1.96418,2.09258,3.79}

{67,72,20,25,19}

Returns: 9.999999999999999E-6
10

{9,4,7,2,3,6,1,17,41,11,19,21}

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

Returns: 0.01818181818181818
3

{9,4,7,2,3,6,1,17,41,11,19,21}

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

Returns: 0.5
15

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

{.34,.23,.56,.12,.66,.77,.32,.54,.44,.22,.68,.61,.99,92,.01}

Returns: 0.001639344262295082
8

{9493.624410234632,4158.603909872154,3096.923773014052,9207.459486760645,9171.484991356174,6493.171104542499,1961.4359466082753,4684.974785387779,4143.750728291343,5731.056382755446,6579.292401170634,899.9398372882739,1235.1360706033365,3807.3956527630494,8239.17477993585,8250.220637777767,5264.330163062839,9185.819595073905,3738.52656636237,9776.589185728153,1737.9089135428105,6060.696134435641,7844.615799416957,3515.905759809067,3736.7494354212317,6550.705558169429}

{8869.823493874512,9865.200535119096,1662.0194024387047,2649.1660883344325,6872.41340145846,1318.901028305164,5790.125753886262,9988.379755369191,4157.144685372137,1778.9353840625045,3071.389672706286,3492.2594968524777,1355.8132199395557,6697.7125490980525,454.6315468867901,9131.951598794381,7732.238465207269,9654.590727949857,427.3035850783913,5911.810546292458,454.00793435215303,6330.535016071685,9744.329019159728,7099.0003833143355,6889.7361738722475,385.2403250774528}

Returns: 0.6826001770347959
11

{8467.608405122619,2203.2175311121628,2627.14842883627,7057.032761966604,8261.507534515826,1776.8479476932187,407.30158690615804,2805.860873265079,1389.64031384624,9605.872293081995,7670.255628146322,1819.6919275597556,4358.257622403486,9361.829375094865,2907.508397851344,2704.62233768103}

{2787.040368440894,7877.762973948886,8891.559407737788,7194.252178519801,3667.3449660018687,6733.758439978579,7135.681162214019,4267.6366082358945,1417.4908963053613,7594.246625542595,366.6529114946049,1724.7456501332792,112.48293237250073,9950.000726447686,1936.2490926609278,5745.714166637237}

Returns: 2.6889419017151304
3

{2236.6619148246346,6584.1834698917855,1731.8627539303566,3894.9409768654696,7500.510114635588,5652.854609626613,6982.141917830172,9371.09032979434,2637.0703539927563,3637.6706512922906,9608.644413760812,5758.192446949682,6435.7912973734465,1553.588856814584,631.3280810296595,910.6562452205313,6771.613448358391,9294.3899981941,4635.684489004435,1105.0032153219458}

{5285.153701031013,3516.5040236794043,1179.0180665636728,5504.2087990565515,8970.194951309135,352.5309980728053,7091.993745511587,2156.466556684615,6822.236467052307,6673.318086584516,6586.547168460476,3537.079251268207,5256.822579307281,1671.6456477140318,2727.6582634930855,5819.412519436424,3211.7088171625564,1291.2801523424212,415.6671935442502,4796.037159273567}

Returns: 97.17348505070726
11

{4041.744747945686,1521.546582643455,3905.2426992071796,2517.1117905565943,1367.0062434789809,1865.8525335309505,7750.254367002743,137.87477632805079,5944.485807987,9179.472661548949,4494.85956349414,3420.5510891052836,3133.655153931754,4571.910806037731,4931.1201342190525,9835.995488498966,3026.2132062231904,8569.147607918441,9243.459533315834,8710.375830896572,7810.3305173312365,2231.0901313654495,9860.27213005458,8362.213929176098}

{5498.829450886463,9809.331212822255,9091.139664324555,6685.465701791211,2820.2316186434564,1555.8759522040489,2175.976670306057,1292.199900240536,982.339291670884,193.8611988168748,8972.2113067578,3643.2882224451932,2504.22987523511,5748.606390518317,5945.081092504885,357.6550083697505,8477.111357172735,5344.757822547453,7389.905597301963,4651.751098471092,4275.811665068901,1207.3575170494844,4973.225445229586,6554.063965001873}

Returns: 2.3910135478298304
14

{7587.7721208903,9779.247504980436,5470.353912652039,9177.367100844534,3642.358122297765,4962.617667040956,7832.149947251179,306.52159952294977,5023.300217116078,992.512321086938}

{4419.532580307917,9332.999753992199,6675.09664929662,5177.724896086807,7911.943795465829,9062.986405398418,4051.3662425748685,9087.10830633796,9556.390996391017,7196.422094852569}

Returns: 0.7328749107146905
9

{192.10684732536842,4035.231325268891,2162.9146346545326,6507.692922639945,8648.735637132691,1285.560401727771,8326.66568529605,5591.443966005032,5591.513686788203,1245.4378773458097,8878.118380031545,9183.673202477516,1740.2886839443488}

{1059.639768047812,5947.077284575579,2950.1073534504794,4098.625988950696,5880.428996155101,3390.0552133206543,5423.570473915686,1149.1071028607037,619.5214767627722,9947.19107616609,2324.3166153002635,8918.971873872977,7962.608522745622}

Returns: 6.746551261730982
17

{5805.120289415754,3366.471280904809,4058.12967793162,1963.186937498691,9712.432807916846,5217.354978367863,2143.878350713866,5937.732980639432,1329.9571102628981}

{1155.669336805858,5932.163707880587,8902.780459699547,6286.433987101261,4795.939739970887,4436.570792615539,5065.724669916367,7727.184336677015,5237.086682798657}

Returns: 0.2450579826763904
10

{878.475412651516,4484.182992782872,6311.930697400805,7630.442189255134,4061.7135897744283,1714.337335088164,4779.136541686967,6355.789230493686,6183.299659529044,1035.0767852510357,6719.192516127368,7835.587665058644,155.24972864697563,5203.689813683801,1385.559006295507,6843.4630690423155,6797.623830946825,9990.978430651401,2224.7828959425174,9002.271161668503,7723.094579109558}

{1770.9949960081183,481.1162291964266,9843.859142905832,8943.11454975851,7033.5486296065565,860.0644797923374,6224.373114945127,2323.49957260898,2031.249631955785,5542.492960744312,9012.973025987936,7646.74438371371,3533.1487848877796,120.51011717666759,6020.800850272722,2635.9975890457144,431.4963208204736,3384.913163563229,6821.159886921228,399.43857734772047,1118.5739832676477}

Returns: 1.4452925603568627
9

{4808.985145253527,3418.8907641332657,7496.654043069475,2419.315369924836,5199.406926917634}

{1195.6972306842672,4667.048929900752,2233.3568525076043,1301.4587150725808,3448.119984112258}

Returns: 29.399276300247934
5

{1888.1668711818845,9047.691757414612,2567.9432744155674,9431.360114886875,8649.993979443698,6183.995003931815,1590.8470191837298,4002.84748527472,7080.386689743734,4812.585245637912,5686.758340177686,4607.196096287282,4826.317355475716,5403.101259699697,9701.750674890913,3096.0156452607466,1290.9511638305526,6984.8047800490785,1471.1772873341688,8258.781531586465,8927.487137960336,2840.5968927882286,4621.385178791191,8635.077049833159,2285.0738451557686,8455.064284887849,7658.660108547092,7678.521546754909,2.1112126584776902,36.86556502030314,790.7165290231566,5842.693140525361,7442.256446493487,4435.771190877763,4426.043147760757,6659.363429476693,168.43837689170417,3774.669233473885,5796.417846182264,6379.353310224448,950.1991942631738,616.8495442036937,2647.903040100722}

{738.5365316899761,6212.52271429355,4772.093688795485,7000.416043075716,3228.5157990297953,2373.496792720827,5410.773744528003,5808.51175331112,2652.935005504432,9170.888336333832,6366.117100787499,5764.48941962268,7328.385889685126,4750.5866661710415,5153.228815769876,9059.15948210149,8013.813526507757,5839.458177820677,7905.319121620216,4483.093066898002,5995.205038013684,2301.7436138395688,5941.36290916273,2052.9058903270325,450.67234042250436,8680.930401047615,7805.560614512451,4876.921506063833,603.7448600425066,6359.910555592959,8536.413776491876,8143.0273971850565,672.6813332433335,2472.2382722146276,423.2276769589838,7611.53551491043,8123.615058374695,4197.297030045556,2007.8514272434145,2495.8611383279895,8235.344173547235,9572.191299958193,4589.472755674604}

Returns: 23.9000083558401
21

{113.83009233674635,483.58155167682384,8453.17439942914,7990.2743576257835,2192.4294646883823,4752.4722359238995,9759.425121233442,9839.768392505403,5208.813423983732,7881.197998818086,3631.9844584275584,5135.619639904344,9650.375330697936,3553.472850380428}

{5499.673934261259,1988.87803361953,5445.6369255396985,2973.8084411439536,4631.520044881753,3079.3754903429062,2037.7289381202502,1495.821058001765,3042.107915677721,3934.0110844482047,1223.5765832099476,4561.314191320468,7403.289693923093,4967.0249092322265}

Returns: 0.02163330156289562
6

{4171.910847503825,6242.837718573708,8966.053318998074,9609.590674281035,5133.888317807678,6929.68887251151,8369.377684219087,4915.3329782539,5396.538037257416,5875.872360542381,2849.6002532288667,3443.3088586854665,6921.877424948816,3873.182566733393,8545.610432466205,2238.768419754976,4617.011175170031,8119.721165887381,3095.179654301946,7232.006545003678,8680.521129217717,3854.160089142283,6217.742887971042,3875.617292199579,970.466623924574,9826.065480231748,8478.94156431178,7340.464839975811,1839.2992120598085,7172.594295485573,932.2425569361903,8090.681465854705,6381.01341939872,3771.872555692356,832.944323429855,1158.0087349638147,1535.8372101054952,8643.374726012573,1119.8843276644589,9935.788877283094,7997.782409615089,3465.608687210281,3860.157431210992,7812.924544386248,3370.361662384701}

{5338.771291627312,5576.700499804875,1037.750345132158,4671.759286307959,8760.684115334174,4366.211179603758,785.9489719939161,6629.312540952728,6500.502295967351,9030.316540696575,7398.511932110196,2582.853608947313,689.9597454291339,7977.879761259926,2963.6119844454756,2494.312953493781,4303.8362378772745,9612.815077065734,6278.313566367492,2156.9919804342376,4293.780215840755,7647.627552946613,5959.506966883426,1479.3790403467876,2303.3054638557583,9515.707326573309,7952.424003029651,6746.624898287429,9721.780208457254,2765.1911557457975,444.55020059823715,7992.494246296223,6335.215021662336,6817.204733698971,1692.7438982763153,5114.600334295828,4331.667565240129,9971.295846909705,8771.378542980212,8865.741306157477,1919.0716704914646,4040.8738515629907,7749.313007525025,5354.145391068307,3313.307673246042}

Returns: 1.0019335017231452
8

{1501.4660647045464,8303.513276463085,5185.44137630676,4354.323659468683,2534.6033424879633,8277.127574517177,879.1636722283058,5508.120741386261,1850.1495393631108,6189.834334634244,8692.606830946306,6512.415223276577,7669.884065875817,2208.273052206681,3484.8412882018597,9423.790851336582,7755.153058489427,584.3687053076518}

{352.1612375821115,3468.115935172218,5515.788075881427,961.2649658785743,3082.277108716085,8144.6881916375805,7542.968375007507,2494.6407891331733,7230.503806006289,5726.323195086462,8379.602663591719,2680.196170808069,1920.3521027596782,8934.006354148749,5373.703032758648,8284.623762867832,3908.3147126849726,7464.502589508981}

Returns: 15.352191647874994
12

{7869.843591263735,8240.771830955751,8908.225171206208,6390.671436164486,3205.454232111661,2955.2493383166734,8245.815022313394,5643.938224829964,9072.472126156246,7295.838488340223,1038.785108414304,3899.227761534161,8689.659159180123,6829.030700139749,4597.701731509454,2682.679031647803,7730.905189111037,9377.9965154055,8243.030875451072,9022.449806080029,4454.821093042072,6471.302803244103,8233.62088507911,7462.9236409121695,6980.940810160399,1752.6887298183713,4001.950442779568,4762.63477922288,4157.840895106044,5922.21572214467,8391.449332531767,3096.2184544844795,8968.492988069127,279.09983812378414,7091.209353530467,80.70575506895273,5918.15898274579,3436.542889749644,4963.392500920457,6446.467941540298,6350.142882850974,8278.871700147305,9458.654446281751,4673.129301765862,8134.712183046252,8731.300425774234,3814.891851013319}

{9324.151101044768,9861.400539766591,9069.367163562318,8478.568426638985,4444.287900184797,6502.390835490997,3311.3889127401553,7901.727770492328,9962.37532533487,6406.936979828628,6744.316506033468,6881.171495579397,2235.202956356367,7550.946151590842,8975.827464949849,1947.5982300945004,2719.9619715404324,9147.594115984079,8182.385284068867,9698.459490147081,3344.3938250686365,2478.4439617393637,5519.00093314298,4661.8536463500495,7583.117793196058,2948.317904256814,2051.577138263917,9263.08063396598,3997.945666190981,8246.737668175705,1219.6480590919657,7026.669660392765,1499.9993508989107,9998.743784627233,2337.327910468111,2646.6939891625752,8091.442715703164,8787.907751958612,3140.2791337496674,5058.184085660217,7344.639493941993,4934.349704865617,1886.5134426719687,2142.4516391128345,9376.551930315785,9910.572038949356,2018.839254803174}

Returns: 0.03069075483537058
10

{8199.137161667364,5576.189080617873,5777.92439234916,4896.76682173799,7817.79464768314,8842.921162956005,2526.510058938375,8605.68315348707,2281.822641294825,3593.470137396749,5701.347074066571,3351.111253957534,7137.560038250415,2295.3882183340734,9197.598145154276,6445.863006266535,2061.351574236975,7784.841127531118,607.6791663508674,2397.9026834749575,6657.4024432859205,3126.5023532125792,9003.059520986235,6106.728113803147,8319.229755185328,3273.376191732176,7533.56934995072,9676.087146468013,787.5258796485584,5284.359338965513,5727.023040926206,5850.838011825363,4537.2459310207905,6357.354412110258,8871.971806922873,3585.768912276781,2626.7301944418655,1435.7479257587647,4366.399451921902,3754.187151258481,8141.675013845708,4646.064389291522,7415.173968561197,5504.092019184346,1866.767785592115,1324.6100180320452,959.0648188334972,6269.742563224431,1317.790562908664}

{8676.499710242877,8412.627634116285,5234.627596445818,3006.6430642733476,2685.700623783408,5741.179268416311,5736.346710662131,1957.987104729616,8658.374839909775,2564.311946481623,5875.094170129788,2610.7984414494854,511.1689084689286,5881.789140718523,4027.648175687931,6925.32271641392,3315.7691718858628,4733.340141586001,6437.581943638044,1628.3135145749438,4578.398967756423,6820.7169593200215,5715.524407731457,6572.452834520882,5009.672375641969,1934.5619718468977,7989.934735447982,623.2407721694722,5230.116151831215,1756.3952897553036,1403.700681829687,893.6626619267607,7356.674513319669,8106.038595053146,1151.8763548163868,3646.9453842696653,2915.506254103649,4204.785095131078,8755.868893806244,7687.719801369421,1026.3899726263614,6024.629740955678,5769.388517800946,3561.896633871229,3304.0469679788307,3293.870319489567,4611.472860469184,4385.571771871872,4421.695572036435}

Returns: 0.9254791167809923
19

{2229.394984971774,1721.900421016911,6623.272133006693,9782.15057295311,4565.964678387273,734.303228634261,1635.855154961282,4241.778293444375,9952.807266357693,5862.291984785661,1318.374003894739,8332.619861694107,1287.831774276308,8193.907431897516,3648.220468502781,927.9982302052492,5059.778725355473,89.70785994874775,6463.859185829477,9796.915743482316,1268.616674043117,5379.809256233348,294.4655410848929,3992.5622057084033,9994.499082831326,5555.185253085455,3560.7787269090973,4520.237939624635,4185.591258384599,4648.544347411562,5967.483719950083,2230.011266234049,735.085891853362,8000.094154523568,8407.433734701885,4379.41810028756,4417.710586306802}

{7218.14085241391,946.4342362737576,4767.014992990098,5325.811804567418,732.3608742546284,8236.294583417177,6394.6921233574585,8511.883779549838,5282.168612314192,4672.913525867052,1199.455105458541,8194.228897882469,9571.905363657757,9332.618028150533,800.4446651054675,4819.218579691235,9058.85229331318,4740.206037970885,3763.972462004506,8009.143173268136,3810.7154406019195,1976.9491119906302,6587.53019631717,1930.529756478242,4774.365332823773,498.67913850163313,3973.9620431993326,5313.951381977028,3338.644186508678,5671.771326944653,9528.610731948984,5383.135931513473,1574.0525216087365,9534.833436319705,512.2486667274562,7451.189040335065,3032.1286903843593}

Returns: 0.004595814454243225
25

{2793.9169142226197,2782.6073112111994,4441.746633044964,6487.333518886731,8559.060291078156}

{198.02519883690306,3811.519440389497,1756.0491199002727,9227.389149579481,6970.040907798041}

Returns: 0.027265403343442414
8

{7193.6257152790395,4386.982882449388,9007.600169416659,5029.268261984062,1262.0054787586032,3998.566559928035,9705.675122707633,511.2117460666388,8517.885403168732,3407.6518806371846,9328.724356533607,4149.205287173821,6320.058095305065,848.5710388701817,7306.08379982122,4976.244024007399,5819.408186449829,7043.190853106549,5918.043912503518,8780.840751099884,9680.671357768273,7122.653074356074,7171.964630557074,9637.226048737928,36.73444306248608,1971.1106350865537,2821.0919181147733,5330.200715519154,620.795218940765,6061.773540723379,7721.386508711818}

{3092.862814748144,7504.25125311048,829.9786386599484,131.08679380651745,6101.453054679333,5212.921615421991,3238.7104060430693,7179.873701884145,1966.098927690202,4175.11304575013,6057.035069550495,3784.964705089694,6786.030998027356,3724.352305673859,1976.4744744611785,3809.6719459424435,4774.1015497024155,9662.51984934127,3668.6882503029474,1761.5197343056986,6741.5569678574075,5695.8265118835225,8634.078487177943,772.7153162498446,8312.426020280898,4492.981142775648,9346.413980438008,9831.718917330945,2125.335259088418,748.3646603018879,9201.288411593849}

Returns: 1.2778032067748535
6

{8898.723190650995,780.5620547755399,1133.0202290833502,7276.223890362502,3037.858346794956,9790.140580476498,8516.274366273385,7410.23072396404,9198.931084353935,2288.831631165734,340.7990509074865,9610.64087354232,1781.5144176934805,9763.769583978494,3533.9300145421803,4295.0221640245945,5614.197042217006,5560.59805494013,838.052405256765,2375.987205521959,7481.807173114968}

{9521.68890680787,1355.5781429620938,9221.677243114778,9792.156252878929,1507.6969419962904,9332.788952027928,7782.45308756413,9938.655651139821,1364.149579298004,5727.8494838382485,6518.605122293033,3914.058799762805,2190.134835478843,5037.790926672921,9861.430125461175,8163.542213325216,5099.627498703313,4374.514154733028,4035.2114382089967,8117.186618591399,9272.346458621003}

Returns: 10.308217969349103
22

{8731.25588484972,4543.685383209856,3846.152264576963,3799.660420035984,2233.551896020408,8361.70914594285,6176.007210455287,5270.846305102606,2445.00967265603,1027.4411477786982,6577.523056979015,7545.0182463006995,7298.2033167107675,1330.3461693168872,6655.247706958934,2654.0384041735697,6721.002717048923,8790.33900978132,5554.169247943954,4281.720732053433,3528.650491772608,1623.377227279129,6104.782405289705,7764.641231437669,651.8978723010505,5388.817565293752,3026.8730743697856,3059.8684279437603,4271.512672396171,5013.847131757579,9012.328431309495,9624.923364675335,4929.472522581992,5390.302222441736,7007.289844629582,4655.285748653616,1187.1539054493007,8239.187419630243,9513.957651801782,8624.753684501577,2900.831587903471,5438.20733627544,8232.363309470158,4573.97594071505,3684.8008484920015,1507.6243071542006,9862.418353869005,92.46232006294264,4632.432551015506}

{5942.865054344658,6696.714448892437,9833.422701599415,1829.7880647255604,7302.338486575939,2824.983636157128,2803.9782087720223,1368.3064121872746,3019.177083793969,9713.550593477688,3182.286269060669,6933.725861078042,1679.598829094142,3234.662509798424,1458.2788895068766,8980.274692936977,6521.244903992798,8096.533805983881,582.2877834378947,2601.281070092618,2817.0315972588623,6149.592603746153,2569.172230532162,9689.482321639682,857.7579154033643,1590.3084369554144,1580.1071868416682,7936.327140059168,9416.278596784545,6070.417398609783,4614.8470277966535,5928.075128467018,7076.05927208498,9219.354099459348,3447.2742349949135,6096.514119971888,1306.9226535545897,2587.7046199036813,3937.0453550631023,9782.102763865298,7670.79988807272,7519.4919918260475,1350.1519605483747,1167.352467131184,4040.299607207669,9961.108466489444,2821.200521971686,9338.260879863921,7212.90620162365}

Returns: 0.0016716723255645594
16

{7714.7037954777,590.23227376236,231.61049154118098,1803.6214176354727,8143.845792463516,2146.8889948619953,2725.94296211877,3798.8598346854565,6839.262626304092,5914.742731979291,5634.0237234693095,3654.412247037062,252.4824426940009,3608.595311778049,4854.607102602832,6320.28952011651,7805.177902230759,2897.5684266947487,2441.316874720234,8075.256995989157}

{6386.5551586507245,3439.390259886993,3865.476666308383,4637.401021591697,653.2709383111957,7748.516288581195,8981.924665921908,5946.586305558858,581.8866316647386,9762.507558294927,1972.744675962471,1828.8102632023983,7808.835913352349,2042.0046878431374,8677.800038335094,1518.232568184299,9095.792466062388,94.72778310631647,7351.2662852320445,69.04134245591109}

Returns: 0.16911652708728736
20

{1319.9532201390218,8369.939476606842,3406.856354552832,418.3364577474624,3366.7863638098315,1563.5772260734548,9913.169424624408,6169.838192668502,745.5563917840668,179.36640400045388,5909.472674367225,293.73309407556667,1247.9422225161386,1791.2273865888606,7112.231570793415,7437.971163790416,2470.056703078101,1952.289589686448,6082.698660534951,46.32390964512623,4518.183457429922,1195.8243935151813,1425.8746046429383,978.5199896406193,3718.5409616532093,7073.408488192653,8091.154637105557,7827.766274561357,5651.3880883036645,2675.6327855857153,3344.9709825761174,6630.970834315377,8329.782419058232,5580.666566857759,5485.745531345862,5166.9769399410925,8843.305195283196,3675.991042672332,4871.464275628457}

{6506.788129011206,1846.4533171014896,2553.8764142444493,3414.9503271834246,6390.483549303212,6097.538468129917,848.8625170497943,4466.380493307661,4109.30881479129,8164.4147602737485,3071.5712301413632,9319.641685314511,1044.6982234538982,5274.706868681117,1253.4303883082644,6083.985689944316,4583.074452771051,1435.4608266226444,5971.123862167827,922.2560927304269,8902.714718058081,4918.771516036437,1578.3443016193633,708.9409214718368,1496.091604519506,9969.213105950304,7426.925576291585,9226.433228260308,9060.499522952956,4490.883174507015,4960.167371656194,4907.311854530344,8889.781650588,7971.873075710579,3061.164436733159,630.4555549229395,4399.965103240191,6403.97923542715,6538.953761624064}

Returns: 0.0036606971261648356
11

{8578.802202890869,5921.621807968325,3455.4636909275914,5135.291659258373,5666.566626365441,391.7654301184881,9654.681017196819,2934.8721669438837,7543.7281258602425,6078.095788972601,3842.3815189189945,561.8020948674574,1685.6023409188804,968.4049156811059,3650.5025414514134,5045.141678445705,2575.306356613869,5957.957901331063,4265.263218619964,4736.326385189143,4486.935068764972,6467.657547928708,7232.372200969072,9161.280397601427,9877.254346822823}

{9287.063237123715,6798.614305094556,9330.186389580467,2230.4459469379567,296.2835633861871,5639.079836496274,8523.800425700267,347.8168490688771,3006.8094781920095,1854.582417151527,4335.34043552386,9215.36465219428,2761.8134841451247,5836.50158517153,6850.173369672948,9047.454838329408,385.0388427299167,1077.6688001457323,8001.3712357260365,8875.56541102816,9340.880596827708,6584.67511137688,7449.581380624611,2431.360018790254,9601.621526852934}

Returns: 1.771216538908915
2

{1280.5386858262946,7767.704576289096,5180.274333965983,1542.132588798495,6843.039518197946,8500.697031871481,5200.928541643174,5682.3524861275455,7924.035537376914,1170.8053407670104,3105.6758500217084,6597.857935457957,1195.0736156327323,9798.549368224778,8697.60233545184,1818.8366702734959,7164.605745995453,4009.765142417656,4559.290045298378,9037.777499322807,1212.1257568600963,4299.018358968847,9268.653232883184,7446.187005248611,2784.535711640268,1519.703914556746,5437.163596475739,1520.6487647301637,4200.057288020735,5171.141856077999,265.7773023106691,8078.53460117555}

{3562.1634587815574,6190.0356091436115,3893.7301306732606,8646.300323816851,7892.468883937465,1406.6668783024973,8006.70220405787,6535.991244908569,2967.0461376885537,7062.358495380089,8273.514404791335,7764.158968681365,6187.367264667853,494.41238352580183,6242.418433627186,9026.777821726262,2495.5865947167977,4394.011274994912,3004.0572850055146,6738.465122477747,346.49755066862855,3805.548799765188,9398.347473190963,9384.89969836324,26.288762537776122,7240.340398047476,7884.56570450554,7368.52760053778,6075.918270468018,1787.5255782118393,4082.4595416936118,6480.365109317168}

Returns: 98.96107094811214
4

{8076.9116720349575,4604.976400240518,8492.188977722319,3630.714376082117,6557.400090529206,5673.021588642208,1400.9134731657534,5971.600975202731,3276.2114939138087,9193.802123514412,6483.838601539347,7043.749084284928,7642.8232689610695,3519.0683842406056,1107.5315668205621,6080.904087828774,3530.9945721513113,1989.2320868057866,3843.319961039765,9104.317801059664,3243.8861383213157,9566.486441978383,2198.587273008311,2940.205438470108,7888.482417860468,2644.804571592444,6073.774971213558,5792.990194385281,5917.128268296536,1919.6332609626165}

{7552.983000322072,8813.871095434308,9923.682037613335,4328.697748865599,3357.2360262475077,2676.5061643178333,1902.3508135814316,2181.9255589648333,6768.230710423533,9265.329968765529,7689.769280901417,1144.1130908704156,640.826500023951,9388.42597987636,8127.584063676795,2384.662707206383,4827.181317454425,3324.428917662244,4432.526405106652,463.6863912756495,3222.39329277295,8086.212529354758,2096.6061277616386,9857.474847246158,1599.3254751072416,1069.4671214746254,3799.146704419475,2654.0105415113158,802.9285289088195,7781.4763473873445}

Returns: 20.434799202165415
12

{2150.9730366591884,1363.8365897603687,2374.373775927505,3845.4066636231764}

{507.1462737236454,4093.9909732497704,700.08709277677,9335.439007386176}

Returns: -1.0
3

{9150.452440469699,7644.264210439814,3546.4648833762126,9417.274662618092,51.468784675303695,8843.920494893151,2615.892349181248,6528.710410735044,924.0519792563118,5807.830730692359,1598.9091243759046,5337.172811637083,4211.715841442253,5734.058813025223,9629.809645545065,7322.530855260409,3284.6559719187053,9362.14626309043,53.552075570064694,8532.804045090425,622.2464041071951,5903.198041367629,1432.0463470979628,7128.079630948581,1613.8218957216254}

{3291.5946236401296,6175.305553775816,3975.4224584577323,3255.9973814276964,5413.545255177217,2082.5323300185537,3117.9379563514067,7142.446734516026,1206.3807710693752,323.46069977968625,7454.320913400668,2383.1344840419033,3372.645835683401,7522.591929319208,5460.35674870782,8956.461371939798,8908.076058385628,8029.38852633339,1717.790287490648,650.1792292944853,5456.167894362562,2597.8278917278685,8673.253686332748,9599.403276227042,395.2939813885192}

Returns: 70.56460754024374
16

{8987.949118006669,4039.8948106695198,7219.276314632312,6603.6737309133805,1559.7140868459526,4037.0181366835136,4852.600322521829,1347.5120093286341,9429.486770327216,5163.052075175053,9952.74414144495,7237.621762755055,5259.449131683884,9697.15173484381,6122.144479375729,6699.837982286404,9250.263117971497,2624.7545243201266,7826.708697020872,3904.5396825963376,5407.293340719331,182.39619477142145,3106.4330981633816,600.5910906390133,9650.701054560715,2717.1034558238216,102.55167400238906,4799.012086333876}

{672.6357214079449,8720.449298370511,110.56161815571785,6372.0612357136115,661.5822724377896,17.77983147080331,4361.28020174244,4712.1507976446865,7285.370021241648,3779.1288761757755,4464.9447981663525,1077.5447382178604,3222.637844275583,589.6177130164504,4972.728811935622,548.394913595539,8389.555508253072,5462.577158252015,8772.41194699208,9602.270023409752,9421.453241333405,9776.773212603797,887.9432553364109,3565.6049601664186,3073.520205041953,1556.5310350616157,3326.976759240996,8599.450186830582}

Returns: 0.1815842475741829
4

{923.3811590981067,9602.56438258318,4609.19447128237,9977.337093724784,5258.367503113759,9481.328720619375,108.22660728324607,913.0683195799827,8530.291167774272,1880.7035806641725,1839.9838909018363,8696.248615342183,1260.537315947362,6339.8237853723185,8830.212564522313}

{7055.673821362365,5721.522987133516,3751.6955739701916,6281.4423497883645,6079.155167165418,7256.171560740515,5170.478920495404,7794.385481744046,5697.839158709565,284.2965995431979,3131.8855748009623,2897.2171012342196,1922.0790194438364,8665.055541881467,7612.847952977393}

Returns: 115.88931499089486
24

{8192.888556824786,3224.2445312708232,4953.44219852042,9102.723605832945,518.5256914170144}

{5778.286785023439,5860.8663840422505,1694.0872287015673,8872.244462914441,5674.679984101915}

Returns: 0.0372929103530365
10

{410.60926822289235,7560.650113169325,6407.654283897413,3355.736530088277,9819.572855095934,3974.913615270318,7625.937265571642,576.8419637873978,9086.55581650327,2910.434187304942}

{2053.1648168879647,2236.9189573972335,5931.3768031571435,2534.1171682661557,9428.243453800887,4897.431066082292,7101.133622614842,6536.428450836121,9693.632367919856,1725.6207286469817}

Returns: 16.411444392490218
5

{1178.9371455735675,7492.749326914756,3905.1853993789555,3492.530880410041,2713.378707912628,5476.564193358226,6369.273698614749,6272.059663050008,8683.812835789815,4246.5002969245525,2292.3696740211476,6862.3036780592365,5221.290394959263,6114.996878274006,4090.90912815827,3400.382212800526,8087.427901881104,3670.612297891066,4681.744185542868,2616.0554985420235}

{9341.614563459194,1596.381084148575,8525.175228220955,2977.418650697945,3047.9644164859633,8258.660948174313,4793.465198467503,4024.7435922371455,264.1565000188073,3075.394573916741,1646.8704761091612,6970.344709287656,6017.693880060194,8145.212789010471,756.7883534474452,279.082140407243,7979.826744879782,3612.079367825841,4591.57931971841,3991.3318198414636}

Returns: 37.144745755862914
2

{7428.50703300504,566.2643359628971,4881.045444724129,7259.273762063782,7372.597277410243,7405.397553209756,9121.071550275079,9284.667077633761,2720.145156000885,2663.4215994620545,6251.239039039245,2915.9294223919896,9873.540938184797,9815.249018261582,5138.226608983389,2662.3293805433455,5634.364027714791,2064.943016956601,1997.8089896010088,1383.1055348395605,7800.736313134731,7625.2291368335555,5388.267108548538,2409.3249712436127,2339.993517902884,8496.15319242659,9908.02164444819,6356.2943007346685,4519.484140391586,8250.697389197096,2230.3032999732154,4384.333486944505,3878.312614760915,6835.166417016841,5607.671229433293,2165.7274249292677,5422.8374004924835,2892.1577383268914,1479.1922844235971,1315.6672734010556,1928.7347456224002,6613.925707737513,9313.094672423631,7544.991940868997,4732.444270383318,8633.954561505096}

{6049.281625883566,8573.499205265942,7669.449352040823,2246.226226412441,9949.836618821118,4079.14384608703,3018.1987385102693,9042.096220677784,8089.101385132288,2470.0922735011477,5259.322682047217,8561.3226455199,291.8746936471406,2392.145433142667,1391.1443279529478,3350.960139913465,4911.113791426573,363.58500749309684,8440.564634216278,8315.965100367363,773.6298659011487,675.7338195886841,901.0083394699398,5472.357076762929,2346.6094959202424,516.2948024676573,4926.349120066862,9020.812236821295,3320.272748274835,8635.780541338234,726.1296778609849,5311.007630329906,6301.9830838586395,8377.345730724617,7107.3873221237245,4767.020716396495,8817.118314420592,8390.335969182424,4608.400265640103,5344.104598494141,8312.017699567548,6847.865159334952,6169.663186758865,9587.14574024566,1354.316138603816,7488.733073176597}

Returns: 56.66175767323057
13

{6787.408544039333,9861.119614821944,4725.979727302434}

{7292.544931763994,2894.8058496959316,2964.5522233313072}

Returns: 8.847333977411582
7

{7153.497857063511,7094.958070583868,3119.7019295630835,4488.276761170854,279.0216113712862,2451.6739573718114,5310.516618451977}

{6094.983312856387,8823.855605756697,8604.352516607778,6188.503152098184,317.39502290311304,4711.4237063257315,4526.5292649050525}

Returns: 65.1702300765605
3

{3377.7152754646654,2544.3390756325125,3506.456644973237,3332.3658835013557,3990.1062846910086,2767.020102990697,2559.7185683229227,781.4397592507161,1495.4756244258626,1624.0801660468596,2735.2323446344717,1039.2735166128996,429.47210685342463,4301.944990250486,8649.281313109002,728.1326894448737,8174.647902824229,3534.9024515314386,9073.59329507305,8737.712280425027,5128.353224450323,3150.2242864559526,2073.022319915707,9491.023050938067,4077.783147352395,6103.645911206415,1948.0410227090717,9860.79065667554,2102.4923793360704,3450.5122678599396,7552.353876474388,2431.678993320535,824.6857729004597}

{2063.5947217078465,5443.020237186833,1147.2248691538057,6384.477729113176,2299.502657115691,2859.1485054545496,5566.924805839826,9706.070481627432,9246.55868198656,9097.649814269924,3530.623457065142,6103.706619152988,8841.821213170086,587.6590799996873,6959.091706154038,7113.6213344251155,1207.2874945868639,998.2616238547115,9220.597155096219,9158.852045901467,8088.37111200889,8989.014071274289,7053.331383940043,7136.245644476171,7355.979550596648,2760.3914261822683,2305.3394822482396,6619.798731135269,3205.002372593828,8161.974408602133,8374.770495270559,7688.144505632232,3182.0230140193107}

Returns: 21.623006824871823
14

{9616.187158057466,8733.254202707265,5883.995831189975,5675.066491390929,5615.400657843561}

{4055.9445885530977,303.6534752747566,3327.6019529780774,483.07964811764134,2723.8728159341586}

Returns: 4.670915363143098
23

{1131.7918120003624}

{8313.36059399966}

Returns: -1.0
11

{3998.1969858961397,3050.211759079221,3855.9859422467835,5392.3386590053005,5703.77454130604,7126.712340060636,6961.374552685644,1249.3155721690152,8255.186854704643,6130.559001367011,5791.762476335267,8290.362534223324,4692.867109963393,2795.6595458734023,6743.283417424211,3935.6596587504755,5426.409884225089,6535.282248277845,9609.049211489364,34.74898485720579,4785.598088983981,3293.4082611175786,7403.189279406166,7968.435225860341,3463.1548386713685,2274.1339814453277,7330.516679436581}

{3023.466253189483,5781.12779204979,597.8600165915582,6563.154094047451,8283.645817367302,5933.85558451294,8008.96098763094,292.3993027499161,1304.517073906617,2617.270631046679,9218.573324439712,2433.9863128541283,4640.021118544776,9540.564175259464,4565.288834363914,7957.113442917266,4346.723454038759,599.1224101848691,2024.5628904328948,5769.716209632977,8471.561768635158,3724.3668767339386,8268.790493874681,5282.234636325387,6983.077387978249,4741.5285093684015,2831.01959212132}

Returns: 0.7026665971422946
15

{6201.972563744045,4591.4389894834285,5805.670036811304,3067.614730306244,2378.360709370546,402.57420900193574,5486.267310539439,115.18310842735468,3019.4345136424995,851.7189954028171,70.6624062289618,8537.076941741778,7099.841574043669,4861.699374322602,8156.702274648239,4854.782035897585,9280.687991832378,2671.2564452841125,3104.872732431271,2659.506846897476}

{482.0294085373134,1306.9367961004596,2784.638133350614,9499.55122080899,820.0336334294411,5105.62019396014,8757.319777488749,6701.291927402188,7324.63857981169,3178.7453301117907,5541.917893688211,6081.5707216702685,8050.745234920738,6649.365998907439,8113.691362829491,7785.474979490169,2654.2403120017143,5741.877453602539,1069.8065115362965,4957.811254203264}

Returns: 0.06107869200824083
21

{3974.152629154429,2193.792676778602,1511.8455068499316,2870.2736347597224,3436.218404016923,3350.2558686999196,4753.633663277073,7797.757646609067,1410.6718903930482,7199.1099615534185,237.19569944482544}

{2278.7278578245573,420.2447729753878,4499.285737195825,184.8899525668024,9946.399198537549,9634.539039088857,3236.9055571234594,5013.402433675923,3710.8354799311483,2758.6298334746416,8073.970231517067}

Returns: 0.030372888325758345
18

{700.2489604623574,1344.507578616897,3875.7908578914526,2936.4174726365886,9472.847005946845,6714.024186260951,6946.005323677048,7416.7950721843235,7450.315956045697,980.2838972948668,1391.6440400852293,2968.6146933051937,4114.959309363191,7585.857773299761,7534.831664429887,9548.0929250619,9858.088998028526,2474.9160394858736,6456.807477202375,398.591634305725,2420.502979741638,3491.0117118728813,1349.5964703129991,5173.072518337344,5547.928331526439,5398.032947947837,9930.302997581606,4089.875136563569,5681.742858000952,9469.63565280738,9988.33897583189,8317.133846085011,5005.287072133855,9092.472678415244,2635.8979171389974,4281.1449310774005,1666.0799338259458,5328.5264541159595,331.9898353230466,2093.9951040705505,494.2513218731326,8881.862950657674,9250.348530755562,795.7673628535111}

{6157.071412684415,104.32770320450201,7539.654148093658,6877.786453547034,7488.973871472141,1495.6182755404989,4853.88420347305,2627.2461303158757,3791.270830846796,2272.0254730397282,4825.733665016285,7707.204259090538,3522.9978452216583,6177.324861783629,5130.624869062422,3320.2454473140365,4838.430955791542,5905.0381052183275,3672.3474910192954,3099.5971019073754,9459.279555680712,8190.871504354069,786.85724709046,4448.211381997073,9430.792757691805,4650.39582112179,3333.8913896166446,3689.493779379678,7894.588389193466,7619.776146208801,8059.214311521109,537.4897888806829,7511.017948262518,2757.3674644825487,4110.305569519816,9894.340422960086,2663.8807434377063,2663.98520086505,7088.302225975452,1482.8237696690571,4080.2983905324395,8279.668411423747,9519.010277747819,321.7882074093603}

Returns: 0.049269944651811726
11

{6998.563410404238,7314.73991065236,5125.792825088711,3552.2975303380354,6516.7749637734505,1472.9847995036205,6787.154293787951,1622.293672374774,6255.070475099946,6724.753845815789,561.8272460315865,4337.593185835188,8964.271620534175,3387.8064016665235,664.176548324793,4787.030687733809,213.751867329397,5273.704748219868,2772.7348080152638,6649.558500740038,8791.340537958577,9657.57373303599,5554.679003892228,2891.1169684296055,9948.076025246575,2329.0364728224113,2789.061998879483,6359.08906765732,120.61962998827002,4482.138719997631,971.6126600936759,5282.149699874304,4264.143317915478,702.0758697955354,9783.914623501716,9183.322166628448,9428.503538035578,9806.534684740885,5309.777204931169,3214.0570539486403,710.5132816176074,2799.460360462964,8381.612890510023,1417.1425290786199,8215.12593945903,4695.063170346068}

{7415.1156785101475,8061.521304682474,5606.6326243950725,4232.895304953341,9661.014120957983,7699.45849308931,4884.142150932691,9535.831584084142,274.26895353960145,9182.910412620666,6981.033436449926,826.4469784844963,1869.1249485391813,9061.947692969248,9698.860172852914,1913.8218380487149,3187.897417874934,4559.915344961419,7532.760379676297,8958.267619920161,4845.800336376118,2981.1343780861253,4402.675477297468,7632.0193951185165,6597.382818356014,2454.6634773625633,2066.3296936238216,7338.643081548417,2569.882462002321,3584.4306044857153,6909.288172167275,8311.473098407972,3408.8132030676575,4076.052323057322,307.39996772112255,9911.387978629906,6781.093435666805,910.6481051382531,256.9418388618816,944.2419440538141,181.03345727369157,7135.963470122096,4467.775952531141,5318.26124656102,2484.490305404745,2845.1183773800703}

Returns: 0.191857674006005
19

{7614.830778903354,8861.718436993086,3196.505690320348,2413.287049579075,7943.222240602284,5621.1973138931935,837.7347187019745,2562.6260206519937,922.3223828152993,4460.762831478571,4414.985061444478,8325.762024245914,144.09210682758467,9282.344919087025}

{1926.2606037087892,6158.342764179957,9469.878367721987,1786.65861773574,9610.001868944682,7744.655334509614,9900.688442202521,9621.412680544887,4168.149903399161,1951.8387771195567,6546.123420513942,5733.015077946616,4188.049722292199,855.903194160732}

Returns: 0.07854376027240602
10

{2629.7492770069243,1239.5833423884405,168.87050036983874,8629.021957785284,4082.4591756283958,8253.69881430817,2021.5774580668267,5843.243649257981,6501.978875127527,857.5678555402477,9052.423814276755,5212.8035472233405,3287.2979645442324,270.68573525324655,2937.7750874510166,7407.84703066874,1705.8411664788719,9092.820638980156,6698.080150163287,8072.374319144511,6151.191449697335,2005.1263478591297,5178.799158192453,9679.224801739967,349.1765808669578,2812.1970898386094,5046.10298277813,4354.906279557014,2770.1337627039,207.87750580706143}

{6478.15167375,8160.989778379615,8687.651758104497,2310.0057545743234,8509.625220280897,2458.765920376458,3401.923182250226,9890.724440829883,7705.429245453896,4259.459005101922,2279.838182604499,2588.180305872538,7407.076179475138,349.9044181112443,213.88725776139262,3013.597823254961,23.317364028235808,631.0672131127926,3765.5241120321316,3791.3114644575608,8861.551648309964,6583.513784750524,2839.4072185640416,1086.798338474113,7349.979308648393,8344.33374914992,9221.0455267833,2781.316660809171,2720.8157387497345,590.8229123082109}

Returns: 1.4109887372180585
24

{5298.159948613557,7738.463930826757,3724.878947838216,9926.244055115432,8786.07125209415,5107.965157364015,4447.858980741749,8962.97306232586,1777.4327768783005,5112.006725182872,8798.587245995408,4798.346304702526,4936.611820206694,5259.426018655972,2739.612897440008,2078.5204524388137,159.04056652843224,8433.069191510273,3830.4025417542975,3345.6586174230883,7515.843166079556,1795.6317438787296,153.47511126378,1863.7515437587904,4804.054098644088,7959.291985803476,3193.7821394944167,4618.391841925243,522.7410588245251,2364.4515269002886,1741.6486315755142,5685.809762474191,3595.3416130880423}

{6307.088043732584,2005.1616786474658,7147.640412837361,7848.787417855886,4987.566913547591,1364.1769010219507,1210.3435938725415,4044.389382811765,2623.5176315873077,4453.581673121532,5832.179860664844,7866.809924633929,2249.845457670129,5991.360245696207,4795.631544789002,3585.0989950220655,4875.446621562543,4617.4141310355435,4856.241949908139,510.89090422747006,6916.1933586102405,6956.949357308935,3890.0181238628993,3816.247269642664,1527.4562663546842,4694.7269059229975,4444.273981989272,8928.769572322191,9968.973926236777,8917.990979176706,5074.7300028809,11.796136353228182,1634.8840930788622}

Returns: 9.079613446192707E-4
24

{8485.88650449233,4351.679645588433,5537.492273771524,3881.72825909183,1683.1776167763546,4918.035654733646,6460.650570609709,5287.243373557932,2916.080983880016,7482.0684141876545,5001.0116213953725,8472.750811302534,8708.026238254293}

{6389.586629605167,2666.483214735109,5658.53006866501,3600.6779435255244,6693.291822205184,1378.6365613945718,4237.9234320370515,5196.067449014224,5567.1382041053075,6506.940670905309,7630.942524562218,907.8269915009618,7984.482401582343}

Returns: 0.003815151644952471
5

{8401.72272361995,4817.13765451513,9489.179659510004,3553.089167821142,8724.003990552148,6216.29245439809,3122.749173581805,5035.992569749469,131.67370813104816,3614.6196786435635}

{4541.914811611196,1121.9571906693027,9753.154027007713,6824.815683996887,3653.099662729936,6328.978996757162,8285.368637327587,5523.453035388461,9745.460410296593,5908.40300293033}

Returns: 273.1787836527326
2

{2520.7517606653287,712.9368560121563,365.5733610950929,2800.195116912033,2431.155321221932,7830.5171152179255,2637.808119027876,1202.271060083503,3606.782539837472,1401.2732015374118,3861.8314224038686,5563.5397926653295,8465.570762978175,5292.451419607064,8773.322058338013,2070.234210989854,6567.188878709387,1964.9906287571496,1475.7043303591388,8758.339209977825,8289.461433737682,3105.0562677959547,2550.715639202904,2884.931711533785,8625.031453846588,6518.389934749514,4355.617962566593,6691.24401857214,356.0766895123557,6670.289625185527}

{7388.104146896297,7702.1140641021475,79.35966483757606,7063.054082352814,4378.878913041065,2286.5874726785464,3182.0938379741424,5986.502801677043,2371.3556221040444,8491.698099357582,7351.088505724422,6957.347667239153,3327.8810514582656,2483.2435073726524,3672.976928388171,6085.562466408887,1612.830030247372,7307.764437387478,7964.097221191153,3758.2809171085273,1662.637000860151,5927.106878769077,431.79459413675403,9260.357519628327,6093.448084431263,4661.311969133115,2746.0016872793326,9338.411821109732,6316.708469943462,2235.141100469542}

Returns: 44.79821972169839
5

{841.4110945629949}

{5190.263828789656}

Returns: -1.0

Statistics

Problem Statement for "LocalMax"

Problem Statement

Definition

Notes

Constraints

Examples