TopCoder Statistics - Problem Statement

Problem Statement

You are given the int C and the int[]s x and t. You have a water tank with capacity C liters. The tank is initially empty.

At time 0 water will start flowing into the tank through an input pipe. This process will consist of n consecutive intervals, numbered 0 to n-1 in order. Interval i lasts for t[i] seconds. During each second of interval i exactly x[i] liters of water will enter the tank.

The tank also has an output pipe. The water will always leave the tank through the output pipe as quickly as it can. The output pipe has a valve. You can use the valve to set the output pipe to any maximum output rate R (in liters per second). This maximum output rate must remain constant during the entire process. The rate must be nonnegative but it doesn't have to be an integer.

Determine and return the smallest output rate limit R such that the amount of water in the tank will never exceed C liters.

Definition

Class:: WaterTank
Method:: minOutputRate
Parameters:: int[], int[], int
Returns:: double
Method signature:: double minOutputRate(int[] t, int[] x, int C)
(be sure your method is public)

Notes

Your return value must have an absolute or relative error smaller than 1e-6.

Constraints

n will be between 1 and 50, inclusive.
t,x will have exactly n elements.
Each element of t will be between 1 and 1,000,000, inclusive.
Each element of x will be between 1 and 1,000,000, inclusive.
C will be between 1 and 10^9, inclusive.

Examples

{3,3}

{1,2}

3

Returns: 0.9999999999999999

In this case, we have two time intervals, the first one lasts 3 seconds and water flows at 1 liter per second. The second one lasts 3 seconds and water flows in at 2 liters per second. The answer in this case is 1. During the first interval, water flows in and out at the same rate, while in the second interval, water flows in at a net rate of 1 liter per second. Any lower output rate would cause the tank to overflow 3 liters.
{1,2,3,4,5}

{5,4,3,2,1}

10

Returns: 1.9999999999999996
{5949,3198,376,3592,4019,3481,5609,3840,6092,4059}

{29,38,96,84,10,2,39,27,76,94}

1000000000

Returns: 0.0
{9,3,4,8,1,2,5,7,6}

{123,456,789,1011,1213,1415,1617,1819,2021}

11

Returns: 2019.1666666666665
{100}

{1000}

12345

Returns: 876.55
{294152,659431,773807,984996,178320,433743,190533,214507,596274,783487,525293,525524,188188,216499,40428,189387,366211,299892,520361,51754,860151,343536,683132,688463,32295,839749,884813,132499,181982,589029,140667,690285,893552,407497,398005,534456,720529,933780,813081}

{563428,849126,205858,523741,536602,385138,677872,795730,480743,819747,750918,641588,331302,125843,212319,491912,23823,696418,250965,343599,494835,657525,954974,958256,885669,973114,115254,298353,314581,97971,757488,205893,985898,783666,431505,505169,464455,397279,49682}

804472

Returns: 985897.0996920157
{77305,226094,890516,551652,874827,80845,757573,851438,488181,858963,746742,746672,561833,594903,584922,15854,482401,648528,511596,448358,133476,748764,549467,512874,228300,21121,784901,185944,288571,932826,92184,525208,295642,180144,771703,865948,404651,289510,514564,969678,882634}

{85480,144452,331382,508033,675931,798470,617164,913705,628914,403867,937383,340378,676083,731922,359788,860764,590900,174019,653619,938304,19219,179680,88900,488635,751970,905209,502263,223292,103678,904874,748575,192022,635740,592094,186006,413783,194817,499815,26706,366338,124414}

300138

Returns: 938303.3305840421
{413764,825115,443650,54976}

{107444,954791,60003,608397}

168259

Returns: 954790.7960781223
{664737,794601,425052}

{608455,393515,333520}

93513

Returns: 608454.8593233112
{688045,838307,124368,190002,844041,1736,88099,979419,13921,581451,256016,741524,954162,22083,219882,459089,122506}

{565813,922698,608132,387154,134716,235387,829685,996424,855838,930599,154708,491133,13535,307619,495016,205989,547445}

483303

Returns: 996423.5065411228
{52005,742822,126071,850895,474966}

{8474,909910,928686,138528,316533}

629276

Returns: 928681.0085586692
{406090,91418,857701,570635,331023,670298,575017,282426,619058,685515,950863,596399,383229,374439,124701,649435,753123,623411,317988,579793,828631,140212,409943,411491,492720,938336,447635}

{429068,406218,844158,8293,528043,279956,95770,59843,498613,316461,688226,217498,601328,645932,834049,380127,330071,245174,379084,990478,537094,99612,15990,916338,128064,427201,446346}

766533

Returns: 990476.6779195333
{98141,571874,325553,724379,926825,918563,925656,466489,266813,709485,971201,638508,321502,926552,821895,364103,508965,169240,934922,504287,788053,142922,226130,670696,972017,896220,530399,531274,332289,350471,579538,352386,253092,255268,452223,515285,561764,951079,892846}

{849318,43597,486227,314872,324456,736499,12375,742443,721556,361477,751079,206488,965135,925949,363900,32280,46497,359384,378254,197480,131984,912416,247324,911915,109119,583768,554359,40198,299335,475792,959698,829002,94270,453040,720221,202585,957182,858157,998694}

909380

Returns: 998692.9814816888
{81543,647856,891949,183890,194739,483469,341851,166732,874272,738373,518000,454691,304901,483423,159877,782414,911785,725531,933652,762643,284122,358909,421039,614120,981873,515628,295009,881783,799200,63204,332671,196282,813140,759626,498619,835667,207171,495174,321317}

{695087,430230,223282,244804,496833,419784,91507,998602,605923,324375,594026,116323,929147,956824,498968,361366,777737,917928,402481,835990,875304,690150,858519,809112,861231,105622,25770,702896,4012,352408,814280,799103,39267,203528,667691,824745,403556,79974,926536}

79491

Returns: 998601.5232408895
{607373,869022,922501,548549,173582,197070,313957,893560,241943,868198,939433,298087,165404,127385,158328,366940,694885,133301,558021,316273,529343,832240,436125,119737,251980,884648}

{224148,426706,125567,180587,531197,697192,632447,926038,218763,315353,734873,454269,725268,410279,619472,486945,472045,63414,157057,812344,31274,775161,830010,679745,603977,270672}

928606

Returns: 926036.9607793544
{372658,515070,347720}

{425915,203634,353423}

780920

Returns: 425912.9044593166
{954833,473616,940785,930864,485614,717947,845502,304741,663689,772809,258070,452557,148922,956601,671740,30590,843590,459337,831473,322713,287993,80178,181017,115711,336204,540396,848486}

{305401,100066,923724,609430,67415,785442,179841,156702,984045,344570,258310,868172,762042,760172,834656,439446,103993,744880,545161,520233,619327,517679,642188,99552,833627,534549,586868}

46009

Returns: 984044.9306768682
{586678,453710,136190,27441,340609,237938,114086,643668,320039,988416,350521,829998,83942,962977,41956,582777,133475,614043,291825,226247,866125,828546,434332,770691,955411,277614,892277,465499,214162,483120,453599,203566,254260,470856,934290,649242,416879,299079,684654,834138,514637}

{724951,493216,419284,800258,564096,143377,366993,969732,712148,654879,10929,750494,646914,6215,891322,232716,686065,147877,836771,957109,705278,786233,421997,762508,387519,656370,537739,511173,598340,636846,646692,90166,479153,251675,999554,107638,503738,203482,941698,129659,52829}

289472

Returns: 999553.6901690053
{307603,430577,5453,17435,376824,645967,608055,864684,883705,598264,473047,152635,569174,409190,372021,1931,431991,488231,166724,916302,328434,116958,959934,313391,538856,763045,904704,586247,603272,365853,207023}

{326344,291325,493378,900699,813979,129282,599508,259767,346289,126041,392043,302011,595473,214522,697749,233386,158474,471557,490028,474417,549404,865777,445400,604401,943887,871622,720841,919132,940612,945478,297854}

560322

Returns: 945476.4684504431
{729396,533985,43332,674957,949010,240781,975958,27642,70248,145797,629042,904321,104840,684694,323580,429982}

{642931,295521,910607,252483,899952,79169,839669,589265,389860,768197,237099,707798,984108,401676,266618,171679}

123630

Returns: 984106.8207745135
{429962,181263,104824,590092,281253,475983,566039,816092,215114,859453,518901,284237,14659,13767,757010,310006,31147,331381,971151,26431,139221,572093,24372,419632}

{331354,639566,19647,322715,6869,701315,506089,364649,869808,447043,560029,430551,786607,655670,532893,167735,141992,327447,769828,691442,475936,121600,375860,336631}

866177

Returns: 869803.9734047992
{272633,781441}

{878382,824717}

248993

Returns: 878381.0867099727
{556949,648960,322334,877384,791809,480000,102713,64146,225509,38523}

{135338,901805,920906,659102,531441,800604,917327,715042,145251,274603}

689212

Returns: 920903.8618079383
{485163,606071,452520,499687,478105,365023,6689,775817,311293,189056,760370,875598,231692,547542,840739,319027,210046,84281,194430,993648,667136,22274,739116,52767,656071,905942,827033,154619,668734,724174,589458,428123,825334,993682,525081,415152}

{230979,66136,908179,475005,804865,289363,341640,957843,365185,931342,554782,502358,633337,358276,715630,50053,162139,539928,509236,500171,881621,500597,429515,384878,893410,311988,208314,274883,895725,627389,836457,804088,305520,136458,19206,409850}

661295

Returns: 957842.147614708
{541646,203421,258785,788572,630316,539850,622553,284174,107067,549065,601489,688454,497681,843304,794399,825327,87833,214694,569772,253939,122586,716098,443846,244356,970544,575277,270819,143185,425435,347807,705583,982284,869635,148748,529201,321456,982164,893869,463515,609935,37930,228334,43630,801682,615519,224036,965674,565959,707580,986380}

{1,1,26,6,933293,8,124362,1385,42,10251,267,11,2,2482,21,742,442,288325,905457,5,18,3,2886,518,81,184306,109415,16073,5875,121,58244,14304,282917,274,453028,52923,48058,22,98219,71,7387,143206,64,521,10503,6064,75603,24,186445,8564}

43478260

Returns: 933224.0214876347
{243321,612554,209420,271660,527312,854018,19476,180893,319523,300620,158217,143274,865025,239264,708333,735027,964227,726967,578232,75615,588877,173042,441433,263349,213136,582209,78981,838712,4397,41082,295431,825103,859376,816579,622919,10994,768022,127206,228018,657947,141160,246785,792525,745765,547325,105098,652036,198979,770076,961019}

{15,73302,1,185126,30,2360,6168,93779,781380,196511,746,1224,736811,221,518,29652,4049,2,382280,25,4344,22292,91457,2351,92987,559434,87,28,50123,1114,1575,35077,1,984043,57,45,8,4,439485,7631,4,206046,8,406207,1,10,316687,411,8145,6}

200000000

Returns: 983798.0757489477
{256231,791892,439998,911602,585859,476194,684793,581693,110920,82099,541112,127668,9791,391242,856004,236390,294085,164640,988396,130427,810672,962943,706983,868434,680181,192357,510998,638978,282731,520436,655026,335076,344027,756135,429536,600034,23582,394960,925543,94725,161709,292752,594842,952298,3063,350566,406492,258342,781906,668337}

{46,20,1,506903,620,1102,36,11,22013,422,42,2,668712,28720,5,8071,647527,8420,39990,7448,4123,55978,460,134,16424,339654,123566,4,6,123919,914,738,240861,2,160,1,74,99512,289,18,44,1,18748,518,8154,2033,6613,49,3005,5185}

50000000

Returns: 663605.2693289756
{240788,345653,917099,490744,281598,649710,244907,10868,29070,216236,983896,897356,701190,303916,410946,69340,886896,647247,150344,882093,278579,504595,688241,103606,668736,685449,433204,231502,984866,475712,68141,294269,993118,806659,248421,285619,313923,846166,666857,291958,561766,430090,128296,190307,746463,397197,554839,517662,554737,942760}

{344587,1469,137,263620,935,96,3,74,75,3,664,3790,176995,613,12679,1653,744,108,131194,30930,729117,6115,2076,120063,634789,9444,12,637174,133689,8589,368297,7,1,4,824919,2711,10898,1,103928,30914,105,14796,10320,150120,5,275,1271,2107,1,10}

2178649

Returns: 824910.2300127605
{86455,538805,810159,990343,653019,462931,183478,114507,887880,750774,569129,351481,521405,727071,854833,317012,631256,501112,802658,480080,431837,288697,12787,34272,416626,158035,666260,754077,316182,559089,187725,659003,917638,711746,630347,227380,780747,300194,152405,976887,281044,949277,428763,460298,212474,643120,220249,112637,389792,587151}

{28572,40897,2421,2278,17346,168424,1,1963,453,108953,5,31217,398748,25,238,11089,4908,519497,16044,2060,4482,399,2,91422,18989,12816,7,22412,12,19,2,132207,10,184986,41196,5002,1757,4504,102712,33284,269,124,857168,467,127,11162,3,27,154610,41}

100

Returns: 857167.9997667709
{761,468997,407699,680971,979830,200969,88650,637302,910787,695043,269291,302542,796440,270123,833635,532258,255704,650500,685293,110245,251358,378642,250549,380349,351017,247338,597610,991496,651362,295562,843579,408156,617714,229769,345870,984026,869404,355984,156268,948426,375911,237923,353480,612951,619604,332522,164025,470157,27961,796627}

{379505,67,1,4531,9053,311095,2,382599,1,2,50,25921,6594,103715,807107,2,976537,1796,40907,1937,10,115,81,482,3,953133,113664,41,1,85,812780,1,3,1,71,8,666,73173,132,526,165566,2,94703,6,229719,7,23373,2,684,2}

3225

Returns: 976536.9873877608
{933260,295065,755561,666668,754209,247917,991802,954502,97972,746374,877606,471504,150429,769392,65430,372872,574635,569268,806396,814874,753394,552668,818108,128034,249585,499903,599313,827296,838173,298888,356357,44292,437434,101635,8128,151393,146827,698858,444216,188055,385082,952196,325248,197019,814437,323744,234889,731278,335602,899060}

{5746,194,1105,1,13,600340,3,465295,69224,382579,392,52,2267,39123,8300,404801,47429,12292,5,3238,15,2223,55,115,1,66,6528,28282,1,2393,343421,26471,124,73,176,7,40931,19,6,578882,804732,3421,436,10,165943,253,4904,1,353,2}

8264462

Returns: 804710.5384359694
{718408,959757,703523,164883,293977,805936,761782,115244,808208,105028,314476,824053,669395,414395,350483,395667,177557,316564,423544,599010,675168,47848,358411,676309,255283,599835,167908,251970,364627,877653,255285,541226,276883,956897,567052,594287,205385,345386,608559,754144,774600,426406,137905,854775,676244,936883,913321,941399,598553,416891}

{4107,454461,74964,13117,271,6945,8223,38268,783,412238,31,3297,33313,8762,26,1011,61,557553,199951,151,6612,349,2,134955,373,6,2398,4,16102,117,9207,405,43214,98,2498,821,39819,183,71,23,680555,17290,12438,496,107,570,4,119,3,33}

5

Returns: 680554.999993545
{546802,795896,548207,903203,278954,9235,895763,990916,419091,159600,5978,683268,425262,270652,305003,283354,173361,353838,404496,372909,55922,148138,466669,106114,928466,551113,874721,338214,812458,461125,686574,287829,878253,747676,542256,132020,251860,720156,793856,789659,616144,774812,631908,161298,410092,865625,893157,262715,669007,66799}

{541,414153,2,14682,235364,151,35,43,400856,3,2003,19019,146844,621,8,415,965361,51335,12896,144,337,2,414791,109,524161,38,5540,2455,109193,10776,121,104695,942940,622818,17946,73786,750266,31,18804,1,3,180,3,2,8,511291,24,2,671,49015}

200000000

Returns: 964207.3379883595
{155396,780150,313036,61738,88682,549409,415540,202490,914619,143264,969513,690760,949934,573393,562786,243837,605804,734282,313002,924263,197986,326457,708204,236099,941307,123327,187898,588815,650169,744153,543349,39837,70011,944281,822342,403562,824267,188657,186292,397627,677156,935782,86569,486519,184737,626641,202083,478091,834955,846783}

{1,14,43416,5394,387975,55794,1,85612,3635,46290,770659,256764,2729,81873,1,546076,461,369,129,328,4533,6,411,10028,386481,419,5003,98,3444,2,96,1,8,3,1,357933,2573,9902,210,43,22394,77642,949,22,9,311579,897,276255,178582,1}

500000000

Returns: 770143.2771577069
{14,37,523,3,110,7,2,3,1,13,21,29386,5,282197,3,17,3,104996,131845,37,89,2353,14,17,1,441815,1,15,339,53,41913,769602,1829,30,8800,17608,115372,111120,11,6151,5,218468,324,692289,6908,2676,2,17,71784,349}

{56,3,14,253176,29,1,1485,95,26,238,115452,9,264,936586,303484,8,8642,1624,121023,79,290044,1,150,1257,384532,4771,135025,837620,139194,3099,67,77073,155,28247,290,61,306,5,37,3,17049,37,1339,27944,66,255685,113,24,131,4}

2

Returns: 936585.9999929128
{87105,27580,120,1,71,1576,4,17033,251567,169547,65386,91073,37,13,10694,119010,460,44,6531,31,27906,113382,9973,3,25394,8,2074,39,17,31,3744,16400,12,982780,6258,158306,27240,25,2,224206,8747,31,67,21,9,60,175671,117911,16,2}

{97,39653,857,646254,386,20554,4386,103,917209,9,4,836935,674368,66,77,289,2483,3,4,59509,2,21,14,36143,41140,509,310572,1246,712,38,245262,6164,2,387291,194145,330,53,357167,3,3,1,363,9631,3,34908,185,276,7,134964,332093}

92747

Returns: 917208.6313228682
{5406,10,294,2814,575680,146,104,1,838592,272,1220,5727,275337,241691,827928,18034,327,231,221739,3782,407391,128206,130923,337482,83,6216,24918,25394,201,6,575987,7666,962549,2,79,52,4381,55547,126,74,276852,47,2630,16,4420,36024,11,63175,2375,27982}

{4,69441,7459,10,1335,387524,3549,1,306,35,46883,14,13528,1,62306,243,382515,11897,2,19128,309557,2,349,541396,1227,5091,126063,838438,526,258,41291,1839,676,174,31,9,28,153906,3567,153,78004,69,120,33,641,32,447679,495229,2186,15130}

144927

Returns: 838432.2928644561
{1,215,3157,24450,4817,142,669,4485,22777,42849,52807,1,4007,17,680,17126,41085,123,78101,59,128,34956,36,9660,1,77409,54,14161,7,28,307788,50194,558,13335,1,1,67671,3507,852,259614,42214,187078,6442,214,401385,4,143535,60185,2,114}

{114,1,120,262,112,28,33217,49,13,2,59,6,117996,251820,2,12337,42,462818,541,777516,2147,313988,466,889,94946,7,145,1,7,3426,446,689,363,1,45,12,3367,1134,9,48,1127,1,1161,885857,764,17,111615,29264,7,46}

216450

Returns: 884845.551401869
{1,11388,844208,50,764,60,43545,49,16935,269,12441,9072,171683,692,13697,212,610269,8839,1,2302,4204,115,125146,147,270622,232,25,4,6,141,6976,460,616,71,6776,103,6,63,1148,1,42,7827,112,3,168305,201,114,1185,10363,28}

{25520,52327,150,475,269,1,189640,671,1,9,759098,1,273152,360231,346,988,35,1,88,1,300590,6590,257,740478,48451,40172,30,349,69,6,944585,280,110,32,186,1374,757,876,199,146005,376218,9,8225,7634,1,15,60,8,10445,22}

4

Returns: 944584.9994266054
{187,229,313,49,10638,3,66666,388,1000000,1,3030,76923,579,1000000,38,1282,7142,1000000,100000,321,47619,3205,23809,500000,306,31,27,11111,9708,71428,66666,6172,8,42,23255,39,10,1000000,30,5,41,166666,1718,12500,575,2,111111,1000000,1086,1000000}

{145,760,20842,2068,65,568276,99,35,11128,13,7172,72,7,166,704,166,7846,105149,21,1254,2,38542,128,40394,9,8,25807,266,5595,23,548046,317143,9513,104849,613,9,1,39296,189,119,4,68993,3734,6504,1648,88,33966,1,296,4711}

46

Returns: 568260.6666666666
{65,7692,1,3,3,5,1845,333333,10204,7751,328,834,17241,3533,7042,10,10,4329,382,6666,39,1,1,21739,77,2,1000000,3412,130,23255,5780,1000000,100000,342,16393,69,2341,2061,71,2,29,125000,8928,1628,1000000,2242,62500,111111,142857,1001}

{3,15,976002,715,190,46,4987,120421,5,1,260102,771,4871,334824,1602,530527,22988,480,1537,305,7,2,6,18596,3,125071,1,260,1,5984,70,5745,104,1126,4,102882,168,29681,381,224023,3,2,44091,3,3249,327326,273,59,36,7}

5205

Returns: 970796.9999999999
{609,62,60,1,19,28,2,3802,626,7,1113,7,21276,13,333333,57,4,4,500000,3,9900,1000000,246,125000,40000,1,9,5,6,76,45454,32258,74,45454,17241,37037,1,2,127,5376,4807,138,3906,20,500000,1000000,24390,1133,90909,37}

{479080,51223,59,151291,1846,10129,417140,33,10,279846,212511,8448,32,1,398,4360,16559,10,547908,2421,3697,61194,42,4297,16,10978,596,3,657823,1,395,401,7,11,5112,1608,320,2,9,285,6,154408,6,2255,269,981061,132,9,4696,59491}

223613

Returns: 981060.776387
{5952,6,3,714,1400,659,12,102,102,34482,7936,33,1000000,22727,1066,4291,90909,89,12820,290,4,200000,62500,1727,6756,322,142857,208,250000,32,58823,1000000,166666,5,4,47619,76923,142857,29,10,27,4950,10,8196,3,268,219,1375,151,1124}

{3564,969,94710,11595,2117,2,2,851,57,75505,11,1178,379863,83,6794,6,266158,5,361494,34563,3,1,220585,6801,94196,3,156578,13300,101,59446,70586,174729,43431,436792,25322,987970,284,665395,96,93271,4811,310584,1,133968,16,1,570383,30,1231,2525}

31095

Returns: 987969.3470043469
{1432,125000,13513,5,981,125000,142857,3703,4,374,23,36,500000,5555,369,15873,500000,20833,9900,55555,18181,1,27777,200000,7042,2288,27027,1317,903,372,567,1,17,500000,52631,2020,8000,23,1000000,104,832,47619,500000,2,200000,15873,13513,24,58,892}

{17,4,265373,135329,101,10874,23174,1522,249238,1145,125203,18,24,1,89,103347,566094,349,303961,293,4190,25,824757,122,9,1979,17510,321,169,368,164,37589,9,257,17477,1439,40,6058,1,3,23393,1,13,5622,2080,3531,475936,3036,26491,5}

333333333

Returns: 812756.664002592
{316,3,3508,529,3,1000000,34482,21,1434,317,1000000,4424,18867,1000000,1000000,9345,1,31250,470,3125,218,29,76923,9259,1795,18,3,14492,9708,4329,1000000,5000,11,124,10,125000,1000000,1000000,1,61,10,52631,189,2487,2,200,20,83333,1582,1000000}

{44906,69490,54991,25,4,276258,2,1,53,1627,56,25407,251,8220,46,612,768,43,1,56766,1,7,1148,79564,4604,1369,6366,52,12,2138,499931,433257,2515,154,1,603,599847,718991,1359,140,3,2,12,957,4,21,49,192,3968,644941}

519182065

Returns: 718471.8179349999
{19,37037,6,40,38461,190,1228,30303,1349,321,108,24,33333,628,40,145,1033,139,2,500000,280,83333,96,2,22727,250000,10,1000000,124,2840,13,1000000,3,15,119,9259,82,166666,730,368,69,134,1,12,2,22222,333333,26,147,831}

{65210,174519,217,38060,4696,7661,380650,14293,68,805,147126,908,31,160,5,5,17092,80,6,43457,11,11681,288737,41575,690425,21,2,1278,1,14,1,50,20,7757,73385,32794,389677,2,35,151188,2576,98,4406,3,2,2393,45693,103517,36495,8}

33694048

Returns: 688942.4440973292
{4504,4,1000000,2,16666,2336,4,15384,9803,25,2,500000,948,40,231,250000,314,24,1000000,15,333333,11904,333,111111,1000000,2092,455,39,250000,3,239,341,2,20000,4761,2624,1000000,326,820,76923,22,6,3,7,126,27027,152,1114,12820,4}

{1006,272812,1,355663,1,333980,2360,138803,1574,183004,99976,4312,3,25,950,613,3510,474367,416999,147886,163713,566,15986,54,425,1,226,13752,27,10,100,1881,1782,50,38905,10,28,160751,31436,2,364016,416,23,24272,12786,690456,142799,12,14977,1722}

917407231

Returns: 656511.8985088984
{50,1101,13,1494,3906,127,250000,1000000,2,62500,505,12,10,500000,5,5524,250000,111111,219,213,10989,18867,12820,8,22,15,4,1000000,102,333333,500000,5128,200000,3,4310,5347,333333,431,11,29411,450,2,136,15,2,1000000,12658,8333,142857,244}

{4,36,15,176277,1,3,41295,234421,12827,1430,1045,179262,141614,3707,114053,66,93,17,4998,426729,1870,785,2586,192,425,9933,1274,3620,964456,15652,2,9127,1334,1497,93753,1,1144,232,66405,142599,558329,14,19,70199,11,402779,14909,229849,145,680060}

163

Returns: 964454.4019607842
{1,250000,30303,525,11363,83333,1000000,1398,19,545,1000000,200000,16393,250000,2652,3,1,8,151,100000,274,3484,3,12500,250000,4901,13,661,6,308,427,203,21739,333333,500000,6451,55555,71,344,280,500000,30303,5376,471,781,203,547,1000000,14285,5}

{25,5259,10241,2,3,3222,873352,30320,26700,333027,172177,658,723333,16,24,62,4,964980,2,38347,158085,1,83,52384,40093,843,281094,2301,8,253104,356,297,67540,2102,114,15,29392,21,4,397266,969,170937,198015,8,819,30702,1,1,21395,100263}

260620

Returns: 932402.4999999999
{55,476,2036,500000,6,88,500000,166666,1582,7407,15,21276,16129,1310,1529,4405,9803,1703,500000,47,500000,952,27777,35714,415,57,1197,44,6849,111111,8,500000,16129,12,10309,43478,10,333333,5319,250000,166666,111111,62500,26,6578,2475,2564,59,142857,28}

{5617,200000,12345,2,1335,1512,20000,1000000,76923,115,4016,1631,1,333,213,3,1000000,40000,6,6,1000000,500000,250000,7,1000000,10,6,273,7,62500,10000,3389,63,31,3,1,8695,1000000,98,216,500000,83333,1,84,265,40,1000000,1,12987,8}

201548680

Returns: 999596.90264
{29,1692,4,200000,6,10,120,200000,2,625,13157,1165,1,2,1000000,62500,12,130,113,3,38,1,650,1592,13888,11904,2,1937,7633,5,76923,121,25000,14492,968,41666,200000,32,803,1000000,27027,1,52631,1,200000,250000,4098,4587,34,9345}

{31250,12345,250000,564,26,10638,45,21,500000,1096,4,4,6134,240,54,1000000,250000,19,29411,32,250000,6,2,166666,500000,839,189,109,64,73,31,49,17,30,76923,27027,30,130,90909,71,9,71428,809,12345,1,2923,1254,4,11235,9345}

923294253

Returns: 985227.2919519999
{6993,2967,6,13333,1000000,58,500000,25,5,254,1000000,200000,17241,116,38461,99,500000,132,125000,50000,200000,1000000,4608,3,1782,324,1000000,1,250000,500000,780,37,34482,8,11904,74,27,1,181,55,6,100000,6,6944,12500,10526,154,509,39,66666}

{594,1631,145,1000000,37037,967,83333,16,291,1047,36,529,3875,1298,43,205,1,359,4,38,83,24390,3,9,3236,2881,1347,2450,1010,4,76923,111111,90909,18867,12,14,38461,130,3344,1000000,1117,14084,71428,5,1,35714,35714,1,495,7}

984398984

Returns: 926168.2304057601
{2493,2,142,1,12345,7812,16393,1,184,16,2481,1996,16393,500000,347,3584,9,3,500000,401,5917,136,173,33,250000,217,14,209,16,22727,501,4424,424,57,4,494,33,333333,219,16,30,333333,38,2,3389,34482,2,38461,25,10}

{1879,240,5050,142857,4,1000000,193,1000000,6535,22727,23255,8000,133,152,9,10,250000,1277,83333,2,4,333333,1529,121,31,1,500000,23,454,36,250000,1000000,1597,66666,55555,513,9345,186,16949,3300,62500,1305,1,1,904,1,2150,989,3571,1000000}

58941261

Returns: 992455.0357142857
{2,1626,4,142857,1000000,19,35,15,1650,18867,35714,415,1,1248,2,1000000,6024,76,307,28571,200,1,1,500000,1785,219,777,18,1000000,1000000,47619,24,34482,8,8,3521,454,2531,4,2506,2,571,63,1000000,51,125000,333333,200000,3144,563}

{71428,4975,19,1335,1000000,14,1000000,3,88,20000,45,12,31,31,166666,27027,105,2,16666,2,30303,402,1000000,24,7874,111,142857,14492,12,13,16393,339,122,40000,100000,1,1000000,519,91,255,333333,2,500000,16949,125,11627,3906,1086,18181,1197}

123843540

Returns: 999876.15646
{1, 1, 10, 1, 1 }

{3, 2, 1, 2, 3 }

1

Returns: 1.9999999999999998
{1000000 }

{1000000 }

500000000

Returns: 999499.9999999999
{1000000 }

{1000000 }

1

Returns: 999999.999999
{1, 1, 1 }

{30, 20, 30 }

5

Returns: 24.999999999999996
{65536 }

{65536 }

1

Returns: 65535.999984741204
{999993, 999991, 999997, 999992, 1000000, 999998, 999996, 999992, 999997, 999991, 1000000, 999995, 999998, 999998, 999993, 999997, 999993, 999991, 1000000, 999998, 999997, 999991, 999991, 999993, 1000000, 999997, 999991, 999992, 999994, 999995, 999993, 999994, 999998, 999993, 1000000, 999997, 999991, 999991, 999991, 999999, 999993, 999998, 999997, 999994, 999995, 999995, 999992, 999999, 999996, 999993 }

{999993, 999991, 999997, 999992, 1000000, 999998, 999996, 999992, 999997, 999991, 1000000, 999995, 999998, 999998, 999993, 999997, 999993, 999991, 1000000, 999998, 999997, 999991, 999991, 999993, 1000000, 999997, 999991, 999992, 999994, 999995, 999993, 999994, 999998, 999993, 1000000, 999997, 999991, 999991, 999991, 999999, 999993, 999998, 999997, 999994, 999995, 999995, 999992, 999999, 999996, 999993 }

500000

Returns: 999999.4999999999
{5, 100, 5 }

{100, 1, 100 }

400

Returns: 19.99999999999999
{1, 1, 1, 1 }

{1, 1000, 1, 1000 }

500

Returns: 500.3333333333333
{1000, 1000, 1000 }

{100, 1, 100 }

1200

Returns: 98.8
{10, 10, 10 }

{4, 2, 4 }

10

Returns: 2.9999999999999996
{1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000 }

{19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19 }

994382195

Returns: 0.0
{1000000 }

{1000000 }

100

Returns: 999999.9998999999
{1000000 }

{1000000 }

1000000000

Returns: 998999.9999999999
{469280, 843409, 956220, 435726, 379004, 178003, 643990, 212646, 812720, 478079, 195180, 281467, 477324, 205492, 80889, 666505, 66145, 911828, 485002, 630687, 52008, 516789, 370184, 819076, 661125, 892316, 55715, 96337, 720742, 494546, 764886, 528772, 587237, 203565, 986147, 179628, 956494, 539191, 665350, 976684, 751869, 288356, 79223, 674334, 736566, 649045, 217470 }

{46349, 59789, 21343, 1117, 79436, 21995, 86802, 40692, 7141, 46475, 10444, 84263, 58024, 16668, 37002, 82615, 80014, 93244, 406, 86477, 99063, 49342, 53645, 27867, 93535, 15162, 76056, 72935, 41830, 73218, 4691, 32951, 21538, 24850, 33832, 98531, 2132, 94400, 26191, 3551, 8237, 30550, 40292, 99440, 56939, 34894, 52529 }

526912275

Returns: 98658.61825890433
{1000000 }

{1000000 }

994382195

Returns: 999005.6178049999
{9000, 3 }

{1000000, 1000000 }

1000000000

Returns: 888925.9135843607
{1, 1, 1 }

{3, 1, 3 }

1

Returns: 1.9999999999999998
{1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000 }

{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 }

1000000000

Returns: 0.0
{10, 10, 10, 10 }

{10, 1, 10, 11 }

12

Returns: 9.899999999999999
{1000000 }

{1000000 }

10000

Returns: 999999.99
{1, 1000000, 1 }

{1000000, 1, 1000000 }

1000000

Returns: 1.999996000008
{1000000 }

{1000000 }

213

Returns: 999999.9997869999
{1, 10, 1 }

{120, 1, 500 }

500

Returns: 10.833333333333332
{1, 1, 3 }

{3, 1, 3 }

3

Returns: 1.9999999999999998
{1, 1, 1, 1 }

{200, 250, 150, 250 }

50

Returns: 199.99999999999997
{1, 98, 1 }

{100, 1, 100 }

100

Returns: 1.9799999999999998
{65536 }

{65536 }

123456

Returns: 65534.11621093749
{1, 1, 1, 1, 1, 1 }

{1, 1, 10, 10, 100, 100 }

50

Returns: 74.99999999999999
{1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000 }

{1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000 }

1000000000

Returns: 999979.9999999999
{3, 100, 3 }

{3, 1, 3 }

2

Returns: 2.333333333333333
{1, 1, 1 }

{10, 5, 10 }

4

Returns: 6.999999999999999
{1, 10, 1 }

{10, 1, 10 }

10

Returns: 1.6666666666666665
{502, 4196, 405, 4299, 1124, 6883, 1567, 338, 3145, 4898 }

{6518, 106, 9452, 2189, 9506, 6753, 6717, 4439, 1502, 3872 }

55829

Returns: 9456.330071174376
{10, 10, 10 }

{1, 1, 5 }

10

Returns: 3.9999999999999996
{123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456 }

{123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456, 123456 }

1000000000

Returns: 123293.99896319336
{945030, 811436, 201804, 413003, 538715, 546272, 963339, 29115, 598776, 420774, 193549, 314789, 122999, 587351, 756820, 988063, 234901, 755181, 352143, 355790, 973130, 664091, 768758, 640505, 795299, 211430, 15519, 321703, 54294, 90811, 268248, 607219, 392414, 693642, 51006, 558117, 216401, 993753, 275157, 742540, 360119, 210084, 279008, 809490, 479205, 24683, 153914, 910680, 200849, 420628 }

{693741, 128331, 5038, 337596, 484170, 195262, 978242, 550096, 240643, 90177, 128447, 244328, 437054, 538361, 852504, 684702, 557874, 179192, 559454, 488676, 474430, 664408, 312786, 85468, 529535, 619788, 443524, 120372, 222250, 262014, 167139, 883513, 295970, 458663, 893598, 798514, 617684, 869732, 143412, 471353, 487753, 232333, 170959, 950863, 401219, 852051, 828319, 70005, 902035, 778385 }

426661337

Returns: 977799.1015634163

Statistics

Problem Statement for "WaterTank"

Problem Statement

Definition

Notes

Constraints

Examples