TopCoder Statistics - Problem Statement

Problem Statement

You are a point in the plane. You start at the coordinates (0, 0) and you want to flee far away, to the coordinates (10^100, 0). Your path can be any continuous curve.

You are given int[]s x and y. For each valid i, there is a guard standing on the point with coordinates (x[i], y[i]). The guards do not move. You want to avoid the guards as much as possible.

Formally, for any point P in the plane, we define its safety level S(P) as the distance to the closest guard. The safety level of a path is the minimum safety level of a point on the path. Find a path with the largest possible safety level and return its safety level.

Definition

Class:: Flee
Method:: maximalSafetyLevel
Parameters:: int[], int[]
Returns:: double
Method signature:: double maximalSafetyLevel(int[] x, int[] y)
(be sure your method is public)

Notes

Your return value must have an absolute or a relative error smaller than 1e-9.

Constraints

x will contain between 1 and 3 elements, inclusive.
x and y will contain the same number of elements.
Each element in x and y will be between -1,000 and 1,000, inclusive.

Examples

{1,1,-7}

{5,-5,0}

Returns: 5.0

You can go from (0, 0) to (10^100, 0) directly. The safety level of this path is 5, because when you are at (1, 0) the distance to the closest guard is 5.
{1,1}

{-5,-5}

Returns: 5.0990195135927845

One optimal path is the following polyline: (0, 0) -- (-100, 0) -- (-100, -10000) -- (10^100, 0).
{1,1,-8}

{5,-5,0}

Returns: 5.0990195135927845
{232,312,-432}

{498,-374,24}

Returns: 432.6661530556787
{0}

{0}

Returns: 0.0

Each valid path starts in the point (0, 0). This point contains a guard and therefore its safety level is 0. Hence, the safety level of any valid path will be 0.
{-941}

{-883}

Returns: 1290.4146620369747
{873}

{728}

Returns: 1136.7114849424192
{102,620,-161}

{781,-207,512}

Returns: 536.7168713577018
{-608}

{933}

Returns: 1113.6215694750167
{-285}

{-718}

Returns: 772.4953074291132
{-581,-81,-449}

{530,-650,-214}

Returns: 497.390188885949
{708,774,-448}

{-477,-770,-757}

Returns: 853.6937389954314
{-204,-74}

{979,658}

Returns: 662.1480197055639
{-559,865,920}

{-674,707,-127}

Returns: 875.6466182199301
{227}

{861}

Returns: 890.4212486233691
{-567}

{-94}

Returns: 574.7390712314589
{-947}

{-679}

Returns: 1165.2682094693905
{4}

{640}

Returns: 640.012499877932
{-282,959,500}

{669,405,182}

Returns: 532.0939766620179
{577,705,391}

{-912,328,-873}

Returns: 777.5660743628157
{475,-843}

{-715,697}

Returns: 858.3996738116807
{-308,963}

{412,-217}

Returns: 514.4006220836052
{-170,-290}

{-325,-199}

Returns: 351.7115295238415
{-730,-625,-492}

{770,-972,310}

Returns: 581.5187013329837
{359}

{747}

Returns: 828.7882721177948
{-360,870,-966}

{984,720,867}

Returns: 1047.7862377412675
{-487,-85,120}

{944,-161,534}

Returns: 182.06042952822008
{310}

{46}

Returns: 313.39432030590467
{-120}

{-853}

Returns: 861.3994427674074
{-170,-325,525}

{677,433,-719}

Returns: 541.4000369412622
{-676,-881,548}

{-354,4,-915}

Returns: 763.0805986263836
{-827}

{454}

Returns: 943.421962856494
{-109}

{34}

Returns: 114.17968295629481
{-843,981}

{-504,57}

Returns: 982.1736099081465
{465,166,-309}

{36,-87,36}

Returns: 187.4166481399131
{-841}

{283}

Returns: 887.3387177397367
{39,-177}

{150,158}

Returns: 154.9870962370739
{32,751,206}

{80,-553,-648}

Returns: 86.16263691415207
{976,-353}

{-264,-202}

Returns: 406.70997037200846
{23,927}

{-77,-833}

Returns: 80.36168241145776
{-110,560,70}

{731,112,732}

Returns: 571.090185522392
{57}

{731}

Returns: 733.2189304702927
{-843,-852}

{208,736}

Returns: 868.2816363369664
{-863}

{-194}

Returns: 884.5366018430216
{-416,-140,-295}

{553,-410,560}

Returns: 433.2435804486894
{278}

{-644}

Returns: 701.4413731738384
{472}

{571}

Returns: 740.8272403199007
{-996,-915}

{675,-276}

Returns: 955.7201473234725
{212,669,224}

{592,-496,-473}

Returns: 523.3593411796526
{701,618,-984}

{915,642,-783}

Returns: 891.1161540450269
{281}

{-576}

Returns: 640.8876656638042
{-13,-710,-923}

{368,164,-881}

Returns: 368.229547972457
{905,-552,521}

{424,-761,-234}

Returns: 571.1365861157906
{-717,-769,102}

{283,-703,406}

Returns: 418.6167698504206
{-231,-398,646}

{-27,-562,-252}

Returns: 232.57256931977167
{849}

{24}

Returns: 849.3391548727752
{216,751,868}

{-965,233,-946}

Returns: 786.314186569211
{610}

{-826}

Returns: 1026.8281258321667
{298,694}

{-388,-737}

Returns: 489.2320512803715
{-493}

{-631}

Returns: 800.7558928912106
{522}

{-758}

Returns: 920.3521065331463
{803,61,-251}

{-409,-800,-955}

Returns: 802.3222544588925
{169}

{-518}

Returns: 544.8715444946633
{996}

{-193}

Returns: 1014.5269833769823
{228,-265,-616}

{-116,310,61}

Returns: 255.8124312851117
{100, 100, 100 }

{-1, 0, 1 }

Returns: 100.0
{1, 1, -7 }

{5, -5, 0 }

Returns: 5.0
{1, 1, 0 }

{0, 0, 1 }

Returns: 1.0
{1, -7, 1 }

{5, 0, -5 }

Returns: 5.0
{-1000 }

{-1000 }

Returns: 1414.213562373095
{-1, 100, 100 }

{100, 100, -1 }

Returns: 100.00499987500623
{100, 100, 101 }

{100, 101, 100 }

Returns: 141.4213562373095
{1, 1, -8 }

{5, -5, 0 }

Returns: 5.0990195135927845
{10, 11, 11 }

{0, 1, -1 }

Returns: 10.0
{1, 1, 1 }

{5, 5, 5 }

Returns: 5.0990195135927845
{-4, -5, -5 }

{0, 1, -1 }

Returns: 4.0
{-500, -499, -501 }

{-500, -501, -501 }

Returns: 707.1067811865476

Statistics

Problem Statement for "Flee"

Problem Statement

Definition

Notes

Constraints

Examples