Statistics

Problem Statement for "SpaceProbes"

Problem Statement

In this problem we find ourselves in the standard three-dimensional space. We have two space probes. Each of them is capable of flying back and forth arbitrarily, but only along a single straight line. The line for the first probe is determined by the points [x[0],y[0],z[0]] and [x[1],y[1],z[1]]. The line for the second probe is determined by the points [x[2],y[2],z[2]] and [x[3],y[3],z[3]]. The two probes can move independently of each other.

The probes are equipped with powerful scanners to observe planets. Your goal is to scan a mysterious planet Theta, located at [x[4],y[4],z[4]].

The midpoint of the line segment connecting the two probes is called the focus point of their scanners. The precision of scanning decreases with the distance of the scanned object from the focus point. Hence it is crucial to position the probes in such a way that the distance between the focus point of the scanners and the planet Theta is minimized. Compute and return this minimal distance.

Definition

Class:
SpaceProbes
Method:
focusDistance
Parameters:
long[], long[], long[]
Returns:
double
Method signature:
double focusDistance(long[] x, long[] y, long[] z)
(be sure your method is public)

Notes

  • For the purpose of this problem, the two probes and the planet are points. All three objects may share the same location.
  • Your answer will be considered correct if its relative or absolute error is at most 10-6.

Constraints

  • x, y and z will have 5 elements each.
  • Each element of each of the arrays will be between -1012 and 1012, inclusive.
  • The five points [x[i], y[i], z[i]] will be distinct.

Examples

  1. {0,1,2,3,4}

    {5,6,7,8,9}

    {12,6,4,2,5}

    Returns: 0.0

    The first probe moves along the line going through points [0,5,12] and [1,6,6], while the second one is on the line through [2,7,4] and [3,8,2]. In an optimal solution, we move the first probe to [-1.5, 3.5, 21] and the second one to [9.5, 14.5, -11]. The focus point will be located at [4,9,5], which coincides with the planet Theta's location. Hence the answer is 0.0.

  2. {2,6,4,5,5}

    {-1,7,7,4,7}

    {8,8,2,4,2}

    Returns: 2.23606797749979

    In the optimal solution, the first probe should be located at [14/3, 13/3, 8] and the second probe at [8/3, 11, -2/3]. The focus point is then at [11/3, 23/3, 11/3]. The distance between the focus point and the planet Theta located at [5,7,2] is sqrt( (4/3)^2 + (2/3)^2 + (5/3)^2 ) = sqrt(45/9) = sqrt(5).

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

    {-1,-999999999998,1,999999999997,0}

    {-1,1000000000000,1,-999999999998,-2}

    Returns: 0.8660254037861707

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

    {1,2,3,4,5}

    {1,4,9,16,25}

    Returns: 0.0

  5. {3,-4,-5,-6,3}

    {2,1,2,1,2}

    {4,3,1,5,6}

    Returns: 0.03329635791060134

  6. {2,2,2,2,2}

    {3,3,3,4,5}

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

    Returns: 0.0

  7. {5,2,2,2,35}

    {7,2,1,0,-9}

    {2,2,5,6,4}

    Returns: 29.73722121485791

  8. {4,6,9,12,-6}

    {-3,2,5,8,-11}

    {0,0,3,3,1}

    Returns: 0.5

  9. {1,5,4,-4,2}

    {3,2,0,2,5}

    {4,2,7,11,6}

    Returns: 3.2769033000830583

  10. {0,2,2,4,2}

    {0,2,0,2,1}

    {1,1,1,1,3}

    Returns: 2.0

  11. {0,2,2,4,1}

    {0,2,0,2,2}

    {1,1,1,1,1}

    Returns: 1.4142135623730951

  12. {0,2,2,4,0}

    {0,2,0,2,0}

    {1,1,1,1,2}

    Returns: 1.224744871391589

  13. {0,2,2,4,2}

    {0,2,0,2,1}

    {1,1,1,1,2}

    Returns: 1.0

  14. {0,2,2,4,1}

    {0,2,0,2,1}

    {1,1,1,1,1}

    Returns: 0.7071067811865476

  15. {0,1,0,-1,4}

    {0,0,9,9,4}

    {0,0,0,0,4}

    Returns: 4.031128874149275

    Test against people who, in the 1D case, incorrectly construct the line as passing through (A+C)/2 and (B+D)/2, as that is the same point here.

  16. {0,-2,1,4,0}

    {-1,-1000000000000,1,1000000000000,0}

    {-1,1000000000000,1,-999999999999,0}

    Returns: 0.288675134594428

  17. {6, -8, -9, 3, 1}

    {-4, -10, -1, -7, 3}

    {1, 5, -5, 7, 7}

    Returns: 9.130789467865487

  18. {-6, 10, 8, 7, -8}

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

    {4, -10, -7, 3, 0}

    Returns: 8.503492463540868

  19. {0, 10, -2, -7, 1}

    {-6, 6, 9, 8, -8}

    {3, -7, 10, 9, 5}

    Returns: 8.491302461752397

  20. {-94, 19, -11, -58, 66}

    {82, -18, -93, 47, -10}

    {-78, -60, 67, -80, -34}

    Returns: 46.26120771088258

  21. {34, 89, -85, 95, -80}

    {-10, 8, 90, 0, 42}

    {-47, 72, 35, 72, -69}

    Returns: 2.727684966309196

  22. {-21, 21, -34, 0, -64}

    {75, -73, 52, -60, -68}

    {21, -16, -75, -91, -16}

    Returns: 76.62563700587269

  23. {4415, -435, 6942, -4518, -4627}

    {-66, 6237, -5148, 7197, -8369}

    {-1798, 7567, -9718, 219, -3622}

    Returns: 11364.028541647205

  24. {2376, 1889, -8726, 8829, -5715}

    {-7050, -3890, -6984, 2467, -4986}

    {4344, 4925, 3739, -2739, -858}

    Returns: 5690.844877436935

  25. {-5509, -1565, -6170, 1213, -414}

    {805, -2727, -6218, -8085, -2601}

    {-9853, 6068, 1861, 6093, 9067}

    Returns: 3235.084656785191

  26. {1012195, 3114234, 4550478, -2838066, -1944254}

    {-8500478, -8201585, -2181078, 5801506, 9830135}

    {-9149587, 1355370, -4603096, 6759117, 9132989}

    Returns: 6536221.040672541

  27. {-722014, 2226631, -6390716, 5581566, -7929909}

    {1284075, 5559308, 7685412, -122898, -8099857}

    {1961063, 7448028, -4956905, -6743536, -8503243}

    Returns: 4856323.260853817

  28. {4416017, 326107, 2534620, -9329462, -9970582}

    {-760808, -281137, -9979540, -3545508, 3591297}

    {3531857, 5704425, -8095757, -398136, -2836463}

    Returns: 8460936.197452558

  29. {-771502844998, 902996822620, 37317198846, -177205078255, -427604731386}

    {772283566588, -508577767531, -729150915536, -164805652488, -803508610519}

    {741883634232, 220301255033, 795594350465, 35856570266, -934403230361}

    Returns: 1.1843232530852544E12

  30. {790037955955, 175218764906, 49178441556, 739101193618, 602924409246}

    {-885414707102, 589088585904, -416759685311, 226822031441, 920631006500}

    {31057907718, -723082751845, -952126375713, -892608145092, -461376865896}

    Returns: 4.088335377247422E11

  31. {988460610748, 831671052919, 946613606265, 654235011624, 950666308085}

    {-702705505710, 757872121376, -776672912564, -321808320990, -612585950466}

    {62162814256, 961326319412, -558026998470, -132519490, -116104090407}

    Returns: 3.127950769526655E10

  32. {161573909363, 323060738887, -995979904228, -849543838297, -989285928271}

    {-334537442199, -966234442229, -613675115423, -393181917849, -65487424907}

    {-524732814382, -354991760448, 45440812519, 6987838316, 23133788253}

    Returns: 4.0666898897496716E11

  33. {-990779714214, -20565566997, -94258718798, -535500649605, -739471246355}

    {789462026237, 123934898625, -636273777344, 624970803349, -270351862370}

    {-370843282047, 934524145795, 575653377199, -518280146638, -898566274581}

    Returns: 6.587501060248524E11

  34. {452066881476, -45847066007, -864215121691, -983868303103, 219628825911}

    {-42680688779, 9839833490, -172391791879, -148443773230, -388577675459}

    {417884438967, -853929047479, 677987748214, 186541163038, -917394827971}

    Returns: 3.905255544962377E11

  35. {-521924622083, -425749951512, 692184349300, 537506410841, 933026775634}

    {404622379372, -172662816770, -380005771264, 234166005226, 976312473997}

    {93063564627, 662006226709, -204797640735, -354432560917, 213772479449}

    Returns: 1.0994431547806343E12

  36. {107444589345, -872796885301, 258425628082, -729644466565, 377577367183}

    {684974736443, -8997611033, 508668041735, 692478545291, 533157602582}

    {813124871701, -100698120391, -709294585136, -159590153231, 34419368768}

    Returns: 6.972087060639778E10

  37. {723,-53,522,134,622}

    {552,780,-433,-319,60}

    {-744,-844,603,553,-70}

    Returns: 0.6651220764158822

  38. {-218,-210,769,761,270}

    {-531,-41,839,349,-336}

    {-209,-727,-775,-257,22}

    Returns: 3.6936677372695024

  39. {408,22,311,-268,-219}

    {231,-377,117,-795,-742}

    {333,801,-197,505,769}

    Returns: 3.605309891994234

  40. {-210267,-987807,189544,-587996,-399133}

    {612867,851883,225327,464343,538604}

    {345012,821404,-883248,-406856,-30923}

    Returns: 2.0052957152718798

  41. {-91052,167153,-799901,-541696,-703678}

    {-147052,-577766,174287,-256427,444335}

    {462375,523229,-401239,-340385,-30281}

    Returns: 7.01066527090446

  42. {416421,744761,694408,366068,227066}

    {169639,250800,-863619,-944780,-428147}

    {-213144,-54843,266422,108121,-131670}

    Returns: 7.2346836588605274

  43. {-813795173,-901675063,949607582,773847802,67906204}

    {935916163,841096063,755285191,565644991,845600677}

    {2414564,322336010,201267517,841110409,101841040}

    Returns: 0.6220483470044802

  44. {191412548,25330472,852208937,935249975,355728666}

    {-354192358,-453083988,-280040945,-230595130,-416008282}

    {-863488304,-185120602,182234594,-156949257,337740847}

    Returns: 0.6817046925641028

  45. {634789732,286162252,-97696430,250931050,268546650}

    {-545821261,-597735530,-309332636,-257418367,-427576949}

    {-238670345,120419163,-220077466,-579166974,-229373906}

    Returns: 1.1617873668361616

  46. {-644070473,-505898794,-241611934,311074782,109845516}

    {429923693,412993506,-876672177,-944392925,-291094989}

    {659506743,481259858,683415372,-29572168,-41526482}

    Returns: 3.2731111212458712

  47. {472236428,32902662,-957901882,-79234350,-682166499}

    {356104404,121490918,-496113181,-26886209,-304617882}

    {-724190293,-293356690,936694379,75027173,537085648}

    Returns: 5.702474320675728

  48. {-346360933,326660235,-316883071,19627513,-331621967}

    {630529526,19468888,129413970,-176116349,379971693}

    {550372520,-67299926,524005324,215169101,537188859}

    Returns: 24.01534634089217

  49. {-436964726,-636225216,-356788310,-755309290,-994655050}

    {58802770,-216738105,-57309038,-608390788,-825868874}

    {-446186227,-351686075,227866252,416866556,174349613}

    Returns: 10891.721660318257

  50. {-165128603257,-434193245842,-222846253274,-491910895859,75077214319}

    {213507741934,688126689386,-976875606831,-502256659379,-856302879901}

    {-608096740843,-622426845969,-308803142300,-323133247426,-444119836446}

    Returns: 0.8481210202829673

  51. {73377724070,-39580992596,-570240219936,-626719578269,-304910606266}

    {160941463164,-11192240050,-41550600943,-127617452550,-26371420497}

    {173973017140,-605928091352,410217086192,20266531946,-97855502580}

    Returns: 0.48848231423400856

  52. {857048967127,-137161970885,63171267245,560276736251,957215586192}

    {429813720804,-33903737630,-207883952008,23974777209,342823613615}

    {-53451995014,23398876596,543079157378,504653721573,206388145377}

    Returns: 0.0

  53. {138992909661,626536434819,279835781096,-207707744062,-521900942359}

    {-505077792886,125277147210,538152607186,-92202332910,-928995002994}

    {485097040645,567993058201,-385160574518,-468056592074,-74375793270}

    Returns: 0.66047733150498

  54. {11592097204,-42975694220,-214704938695,-269272730119,-101556420745}

    {292739317498,517593338457,133245331210,358099352169,212992324354}

    {-551043679685,-938671717081,-136070857197,-523698894593,-343557268440}

    Returns: 0.6365993391192911

  55. {-146316261601,185839519999,638290099997,306134318397,578142700797}

    {-437872425207,-819354168458,144604220731,526085963982,-528115845489}

    {496703055354,631132906372,472510357062,338080506044,619036557227}

    Returns: 1.3628197230079535

  56. {730603801988,808752233045,-601931323584,-575881846565,142484670257}

    {-101974068535,-460729237003,144182869140,24597812984,-337650768165}

    {818471524593,65684910072,248103644166,-2825227341,-219499030140}

    Returns: 1.8550280706229767

  57. {-475567386864,-128186461651,-321604669727,25776255486,-51205103086}

    {-287925140077,115257955141,386132495541,789315590759,452286772948}

    {-11284791785,377976375851,-893455190075,-504194022439,-63108823292}

    Returns: 4.085619133978348

  58. {306488388579,648617759661,563359537795,221230166713,434923963188}

    {-774956391118,-631752400586,-789687899078,-932891889610,-782322145101}

    {-347488709211,-663907264611,323705436235,640123991635,-11891636487}

    Returns: 3.2114845286261224

  59. {172125756207,-136205863429,-320226573023,-11894953387,-382382028046}

    {119409202854,-326977787346,68377593469,514764583669,-352493592048}

    {511980394551,-440178858401,-449819418765,502339834187,-921078765059}

    Returns: 8.63735393004479

  60. {-309091489960,486567012906,6964919669,802623422535,644595217723}

    {-598699223155,-867698038015,558895915803,289897100943,-288900468536}

    {-879794020427,-976626298139,-472780702431,-569612980143,-773119639145}

    Returns: 3.7880208992445907

  61. {65643601889,-160608122219,184521375815,-41730348293,181645419888}

    {498455122124,929150722324,-189191912347,241503687853,46957704845}

    {80405428465,459151100353,574702089481,953447761369,232867341006}

    Returns: 11.387663656729204

  62. {61508974359,545836205542,-188675288304,-673002519487,-63583157702}

    {763777121169,568431130020,-990281448350,-794935457201,-113252164567}

    {-476296742765,-271137147278,257874081331,52714485844,-109211330667}

    Returns: 1189.3452329981974

  63. {401553548285,25366516170,-131290380872,244896651243,887505647741}

    {856778291882,937606776875,51902060694,-28926424299,292683206499}

    {292893242997,302558802275,-790858876396,-800524435674,-268313935550}

    Returns: 336.31973016386104

  64. {43269204665,364204726369,-49864048643,271071473061,638573622300}

    {11750950616,420352552306,-441040426086,-32438824396,602558464993}

    {-449238315514,-682042815909,955229694150,722425193755,-212613311863}

    Returns: 1148.297222216961

  65. {798521758402,813085939040,828802684148,843366864786,755405020156}

    {849603524724,882490143735,412801574723,445688193734,499655774431}

    {681272688079,846102406171,-489296368922,-324466650830,-563330320843}

    Returns: 626055.3912770513

  66. {-134542852745,-35929752639,-364875970632,-463489070738,-348321625140}

    {466593374444,954833710680,-458970919390,-947211255626,-484429392814}

    {375569954940,-133439760476,-544256411411,-35246695995,424666805515}

    Returns: 937281.2966503402

  67. {343759127858,722909964242,-893846610367,54030480593,293682668679}

    {203087487962,-76204951644,-108363176604,-806594275619,-371576903672}

    {831518629692,645334079686,543800242658,78338867643,408381613352}

    Returns: 827295.0325719944

  68. {282767885507,45062369976,-152207948106,-389913463637,303665588977}

    {58084234366,283511741019,197136897407,422564404060,-97782576936}

    {423541826504,-25869122981,-540267857313,-989678806798,391256809434}

    Returns: 5.557302994887904E8

  69. {-605825666093,-117327611911,932574925944,444076871762,-812881265199}

    {-553559873218,-866838372965,-251558133697,61720366050,224679439036}

    {-576642382149,-612121602390,-881554155190,-846074934949,-657514595488}

    Returns: 1.1645958576713636E9

  70. {-739894184393,-305946943779,630754711790,196807471176,-487846943332}

    {-359725747325,-306545572177,-452811869412,-505992044560,-460382522885}

    {417029837215,317655011625,-72231515931,27143309659,270832762277}

    Returns: 1.2842206256811497E9

  71. {671712870300,282763124146,-227357396180,-421832269257,413519279298}

    {777574309566,366577989616,678663829887,473165669912,927835425704}

    {-679402144507,131394954717,-906930131295,-501531581683,-627554897907}

    Returns: 3.215896304337462E11

  72. {-516559202363,-490927132640,69357396596,18093257150,-273544872746}

    {-678888581938,-958954561635,201780836147,761912795541,-469013109900}

    {-101317401151,-240322221354,-343634071839,-65624431433,-150168477583}

    Returns: 1.7906080663518707E11

  73. {-868723519885,-391514440190,431809632588,-522608526802,-426473034830}

    {-248615142512,-431358657725,165012098848,530499129274,-463321958810}

    {-544498792646,-507493309445,134658513672,60647547270,-794263870621}

    Returns: 7.48922791943506E11

  74. {-451,-493,43,-465,-239}

    {21,207,-893,83,-281}

    {41,-487,51,-135,-394}

    Returns: 0.0

  75. {309,167,52,-19,-462}

    {-935,725,-586,244,112}

    {-714,-718,-386,-388,270}

    Returns: 998.0816942698726

  76. {127,-81,-391,-633,93}

    {82,329,237,371,-31}

    {5,-405,-56,-213,258}

    Returns: 0.0

  77. {425,-354,-565,-116,-238}

    {-247,-731,-727,-403,-558}

    {722,329,89,271,306}

    Returns: 10.15831627126388

  78. {-710,-11,331,-720,-639}

    {-492,-144,-141,-720,-847}

    {-432,-396,-276,-296,-290}

    Returns: 82.09153527735442

  79. {320811,611754,-137833,-931879,-349993}

    {-86993,-570437,209676,132795,-834093}

    {-447549,-538074,-224894,262021,80971}

    Returns: 0.0

  80. {46006,718290,424760,614137,254312}

    {444425,-159566,-14641,-244174,613641}

    {595399,-168151,273715,112873,33351}

    Returns: 0.0

  81. {-28199,-178685,-253928,-377182,245541}

    {-61587,-439315,-628179,223458,-535496}

    {-470975,46789,305671,-496811,-186257}

    Returns: 0.0

  82. {-393637,-275627,579197,335335,-396248}

    {380209,-22216,66239,78699,116085}

    {508638,647228,-594390,-268366,709700}

    Returns: 1.4058312609462817

  83. {-200451,435769,292148,-549429,-693046}

    {272436,29751,185388,203847,359488}

    {232086,-538426,-139941,205628,604113}

    Returns: 3.0229288528333536

  84. {-104913,45005,705618,603479,-459104}

    {221075,532597,-248126,-29677,346443}

    {-262495,617044,-908292,-427317,-180079}

    Returns: 7.84221493296157

  85. {-380069655,427336032,688620700,166051364,-633503762}

    {-169478230,404538335,514745497,294331173,-198553699}

    {666857415,257635734,508829517,6441951,28062622}

    Returns: 0.0

  86. {-325899255,-182156598,-59698406,-448357447,-837016488}

    {-687280127,-71678813,-401637845,-357321095,-313004345}

    {155554680,-447557268,-86932314,-205070274,-323208234}

    Returns: 0.0

  87. {-685797503,-116182682,-863273641,-244980209,-422456347}

    {192923552,282583484,-371551129,906157142,341682461}

    {304031161,-597356955,370159869,-135878535,-69749827}

    Returns: 0.0

  88. {367456159,508024110,226888208,-3771771,558500034}

    {-61727838,-196818353,73362677,257844808,-282517251}

    {792943806,867317255,718570357,-26603194,270890603}

    Returns: 1.3706170543676417

  89. {170900742,776058204,411072882,526431840,-318897762}

    {265491323,585219645,413975972,539701597,71488627}

    {277363458,131591930,44887435,-506769106,-128521555}

    Returns: 0.8895144764137544

  90. {200695035,635575595,-222070482,917419273,-298588922}

    {287850158,-82375928,263036582,-65833544,456420818}

    {355470402,-180996292,-856050132,626684064,-183976606}

    Returns: 1.1527106383634467

  91. {373831397,811436377,626447729,558820045,-63773590}

    {396997771,461203667,173232471,684968967,332791866}

    {17908255,337851777,-76302126,432062158,-302035274}

    Returns: 4.224359480563519

  92. {128114704,102715424,342077244,247795614,632237627}

    {-289885350,-478581621,-368883693,-235036386,118206776}

    {-50666204,-41909378,464910500,202743735,954216731}

    Returns: 0.8715332784608337

  93. {915670226,258074545,367794588,82812307,455425697}

    {-201400202,770309648,-707955047,-23618168,-310991148}

    {512958893,765419176,-219041518,78834734,124250705}

    Returns: 10.826836715172417

  94. {814063788,65189048,619350606,-309248322,724208056}

    {775551865,-397396693,887373002,-983870972,426413360}

    {202599381,125677809,-82381383,87217023,325851327}

    Returns: 5681.791079095976

  95. {215509818,-408603036,-11031390,-96546609,499807621}

    {439945788,-471885414,135505162,-15969813,895123424}

    {33269802,-773114628,-10390044,-369922413,774162002}

    Returns: 7172.580905985616

  96. {9649339,-8366015,511116983,-375459071,-626191217}

    {755457806,-132074076,770675822,300278353,292660443}

    {437666225,-267368440,-281364645,624422045,983928977}

    Returns: 654.5662040272705

  97. {-313990744774,73988719756,-721631885089,442306508501,93650402740}

    {5445036328,101685977629,23211423643,311934247546,-12321343734}

    {363877599543,36021254105,336387379640,-647181656674,391367820562}

    Returns: 4.3967441985085834E11

  98. {-282914487032,-340172339203,-397430191374,-249380134390,-349983194606}

    {295370910113,306509632948,317648355783,211375067992,463362588338}

    {-588160670006,-273173982764,41812704478,-707919018624,-348643980593}

    Returns: 4442.70295334497

  99. {-588757801808,-375218109932,192333475780,122097374800,903188654006}

    {558502720871,405236872282,547931559550,323318367327,312747213766}

    {-992254928835,-517726698958,-469003010030,-18836624617,504415293954}

    Returns: 6324.909285736298

  100. {-158953872694,-36871750362,218272187704,-133923188812,-97912811520}

    {660557775154,272438090054,-308728648684,465991538148,466497932604}

    {199804813437,136579119393,24184416049,176970047554,168191966416}

    Returns: 2.864835514455998

  101. {-607578891642,-305773127014,-434823113509,-349478918652,-824040461403}

    {608888695084,512560072820,923154778588,-212300716452,-430238177691}

    {827984375633,248155559792,672390804446,-20486113675,714936273360}

    Returns: 11.599585685716132

  102. {480159445203,557390326787,844063535492,939621271727,-993783770604}

    {253663438509,495131530972,418026319576,392324582444,-136618256159}

    {88587181123,-611921092218,-7759640253,193627510402,-427920957364}

    Returns: 5.877640321878839

  103. {327956086169,-329090270377,-368905300234,248326026455,-737243508365}

    {-297727886583,-295448980927,98551324409,490272724089,493691082575}

    {773626789476,229961783438,72619884405,458942991410,-356554517649}

    Returns: 0.40593345606566916

  104. {-56054837153,-345039000427,407634778472,-375252371141,232929326122}

    {-196732846085,-375617839519,172434244582,-476457440035,-17847852651}

    {-8428309409,-750970330685,448901679169,-94487287349,734113711869}

    Returns: 0.5041021549825931

  105. {-35896982043,-740392976720,-649522989895,-433579972794,54973004780}

    {-700858286661,-207109544644,-36743905281,-539166735334,-530492647298}

    {575474508284,-29539988449,-232899642164,374647086775,372114854570}

    Returns: 0.6601010441907063

  106. {715095688881,-498876821103,-974074367478,-657276003228,-569416864150}

    {438018731899,625184696989,41904323779,430757905919,-20484331251}

    {42961224245,-560810437498,-861130389715,-660917088237,-659873169134}

    Returns: 0.0

  107. {-506340867437,-559442925820,-259016818221,-388498145443,-441600203826}

    {-716084183416,281746516277,447424915655,-993468283521,4362416172}

    {154036275507,-567312152234,-498258028894,417503792534,-303844635207}

    Returns: 0.0

  108. {635036338657,417126266619,580737624974,444454427787,335499391768}

    {426196130786,-160599959740,34541332607,-209728336198,-503126381461}

    {-528245773130,436474811490,-61706080580,428564511610,910924803920}

    Returns: 0.0

  109. {0, 0, 0, 0, 1 }

    {0, 0, 1, 1, 0 }

    {0, 1, 0, 1, 0 }

    Returns: 1.118033988749895

  110. {-1000000000000, -1000000000000, -1000000000000, -1000000000000, -999999999999 }

    {-1000000000000, 1000000000000, -999999999999, 1000000000000, -999999999998 }

    {-1000000000000, 999999999999, -999999999998, 1000000000000, -999999999998 }

    Returns: 1.0

  111. {0, 0, 0, 0, 1 }

    {0, 0, 2, 2, 1 }

    {0, 2, 0, 1, 2 }

    Returns: 1.0

  112. {999999999999, 0, 0, 1000000000000, 1000000000000 }

    {1, 999999999999, 1000000000000, 1, 1000000000000 }

    {999999999999, 0, 0, 1000000000000, 1 }

    Returns: 7.071067811858403E11

  113. {0, 0, 0, 0, 1 }

    {0, -999999999999, 0, 1, 0 }

    {1000000000000, 0, 0, 1, 0 }

    Returns: 1.0

  114. {1, 2, 0, 3, 4 }

    {0, 0, 0, 0, 0 }

    {0, 0, 0, 0, 0 }

    Returns: 0.0

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
This problem was used for: