Statistics

Problem Statement for "AirlineInternet"

Problem Statement

An airline wishes to supply passengers with Internet access on its flights. To do so, it is going to to install powerful radio transceivers on all of its aircraft and at the airports it operates from. The airports will be connected to the Internet and the aircraft will be able to access the connection via a radio link to any airport that is within the range of its tranceiver. Aircraft will also be able to relay the Internet connection on to other aircraft that are within range, so even if an aircraft cannot communicate directly with an airport, it may be able to access the Internet via another aircraft. The cost of the radio equipment is proportional to its range and the airline wishes to supply the Internet connection at minimal cost. It therefore wants your help in determining the minimum transceiver range required such that all of the aircraft can access the Internet all of the time.

The area that the airline operates in is represented as a 2-D cartesian plane. You are given a String[] airports containing the locations of the airports that the airline operates from. Each element will contain two space-separated integers, formatted without leading zeros, giving the x- and y-coordinates of an airport. You are also given the flight-schedule in a String[] flights. Each element of flights describes a single flight and will be formatted "<start> <destination> <take-off time> <landing time>" (quotes for clarity). All elements are integers formatted without leading zeros. <start> and <destination> reference zero-based indexes of airports in airports. The aircraft starts out at the airport referenced by <start> at time <take-off time>, and flies in a straight line at constant speed to the airport referenced in <destination>, arriving at <landing time>. All radio tranceivers have the same range R and an aircraft can communicate with an airport or another aircraft if the in-plane distance between the two is no greater than R. An aircraft can access the Internet if it can either communicate with an airport, or it can communicate with another aircraft that can access the Internet (directly or indirectly). Return a double containing the minimum value of R which ensures that all aircraft can access the Internet at all times.

Definition

Class:
AirlineInternet
Method:
minimumRange
Parameters:
String[], String[]
Returns:
double
Method signature:
double minimumRange(String[] airportLocations, String[] flights)
(be sure your method is public)

Notes

  • Your return value must be accurate to within an absolute or relative tolerance of 1E-9.

Constraints

  • airportLocations will contain between 2 and 10 elements, inclusive.
  • Each element of airportLocations will contain 2 space-separated integers, formatted without leading zeros, between 0 and 1000, inclusive.
  • The elements of airportLocations will be distinct.
  • flights will contain between 1 and 20 elements, inclusive.
  • Each element of flights will be formatted "<start> <destination> <take-off time> <landing time>" (quotes for clarity).
  • <start> and <destination> will be integers, formatted without leading zeros, between 0 and N-1, inclusive, where N is the number of elements in airportLocations.
  • <take-off time> and <landing time> will be integers, formatted without leading zeros, between 0 and 1000, inclusive.
  • In each element of flights, <start> and <destination> will be distinct and <take-off time> will be strictly less than <landing time>.

Examples

  1. {"0 0","100 0"}

    {"0 1 0 100"}

    Returns: 50.0

    A single aircraft flies between two airports. It is farthest from an airport when it is exactly halfway between them, so the minimum required range is half the distance between the two airports.

  2. {"0 0","100 0"}

    {"0 1 0 100","0 1 25 125","0 1 50 150","0 1 75 175"}

    Returns: 25.0

    This time, four aircraft fly between the same two airports, setting off at intervals of 25 time units. The aircraft closer to the airports can relay the connection to those farther away, so the minimum required range is shorter.

  3. {"25 100","0 50","90 150","22 22","60 1","95 8","12 40"}

    {"0 1 0 500","2 5 10 300","2 0 100 200" ,"3 6 150 400","4 5 50 450","5 1 0 300" ,"2 6 10 100"}

    Returns: 64.28201130009927

  4. {"0 0","50 0","100 0"}

    {"0 1 0 100"}

    Returns: 25.0

    All airports have radio transceivers, even if no aircraft fly to or from them.

  5. {"0 0","100 0"}

    {"0 1 0 100","0 1 10 110","0 1 20 120","0 1 30 130","0 1 40 140"}

    Returns: 30.0

  6. {"417 262","519 592","941 778"}

    {"0 1 376 534","0 2 603 763","1 0 137 431" ,"0 1 525 583","2 1 367 551","0 1 953 996" ,"0 1 668 886"}

    Returns: 246.618769031594

  7. {"461 168","693 177","693 310","821 244","837 808"}

    {"2 0 374 643","3 0 541 776","4 2 205 393","0 1 55 680","4 1 739 873","0 3 351 570","0 1 579 700"}

    Returns: 259.6240036821721

  8. {"169 25","269 781","712 883","813 889"}

    {"0 2 167 532","0 2 972 982","0 2 327 936","2 0 68 176","1 0 723 845","0 2 665 920","1 2 281 399","0 2 685 955","0 2 155 697"}

    Returns: 420.0059861811434

  9. {"101 591","283 183","346 696","436 638","738 46"}

    {"3 0 855 890","2 0 260 698","3 4 229 743" ,"1 2 519 898","3 1 863 955","4 0 407 993" ,"2 4 872 969","0 3 320 663"}

    Returns: 298.18759041416865

  10. {"157 964","215 237","569 565","750 164"}

    {"1 3 254 859","0 1 980 997","2 3 586 595","0 2 916 993","3 2 733 965","3 2 743 830","1 2 318 725","3 0 290 544","1 0 754 943","0 2 830 918"}

    Returns: 359.2437159929716

  11. {"212 732","438 538","549 103"}

    {"0 2 749 796","1 0 130 504","1 0 29 209","2 1 907 924","1 0 698 804"}

    Returns: 231.2072987869912

  12. {"198 704","680 993","95 557"}

    {"1 0 369 757","0 2 652 796","0 1 647 739","0 2 317 393","1 0 816 957","0 1 435 684","0 2 538 934","0 2 4 408"}

    Returns: 281.0004448395056

  13. {"152 998","656 487","75 999","913 535"}

    {"1 0 347 530","0 3 75 819","3 1 893 935" ,"1 0 971 992","2 0 471 887","2 0 924 955"}

    Returns: 358.8652253980556

  14. {"502 58","542 342","797 657","815 767"}

    {"0 1 653 975","2 0 778 783","3 2 463 644","0 1 39 304","2 0 663 931","1 0 640 835","0 3 830 874"}

    Returns: 207.7792776343636

  15. {"123 994","525 84","624 601","734 32"}

    {"0 2 15 598","1 3 43 311","0 3 813 946","3 2 879 962","0 2 467 679","0 3 611 955","3 2 442 662"}

    Returns: 337.67905744443965

  16. {"271 730","280 990","359 938","642 970","654 121","781 132","864 807","870 287","96 285","971 711"}

    {"6 2 449 748","0 1 240 838","4 8 962 991","6 1 85 527","0 6 233 739","6 4 542 694","2 0 609 877","5 0 2 524","6 9 881 913","4 0 386 753","4 0 774 971","5 0 856 886","7 5 346 613","2 0 748 859","9 2 122 608","0 3 13 214","0 2 260 370","5 2 423 921","0 1 243 418","0 5 476 713"}

    Returns: 358.97298714202395

  17. {"119 209","284 82","308 872","326 650","372 603","58 829","79 555","857 643","908 0","971 447"}

    {"9 6 292 863","5 7 763 794","0 2 783 789","4 6 839 842","3 8 640 932","7 8 995 1000","2 0 107 753","6 0 241 434","8 2 167 390","3 6 610 837","0 5 234 964","6 0 680 785","0 4 434 851","0 2 4 601","8 0 98 643","0 9 802 882","5 0 952 962","5 4 68 475","8 5 149 896","8 4 401 806"}

    Returns: 366.6144143757617

  18. {"2 372","373 156","398 9","446 380","5 383","598 68","620 654","790 440","939 730","956 951"}

    {"2 5 789 992","3 5 816 830","5 4 781 819","4 1 331 907","9 8 659 965","4 3 414 449","8 9 605 877","0 5 283 700","2 0 652 858","0 8 10 364","1 8 266 504","6 0 600 862","0 3 894 910","1 5 147 260","1 5 915 997","2 6 41 871","6 8 642 935","0 5 822 932","6 0 323 856","8 2 933 958"}

    Returns: 233.26494337238677

  19. {"12 673","189 260","229 869","296 855","542 746","690 801","730 725","835 541","867 128","891 82"}

    {"6 2 311 532","6 2 569 987","3 4 631 819","2 0 837 951","4 0 264 486","8 0 700 709","0 4 397 939","0 2 935 960","6 8 554 935","0 6 237 883","4 8 745 991","2 4 790 828","7 1 40 343","0 5 722 935","6 0 681 765","7 1 369 868","4 0 275 972","6 2 805 891","5 0 755 897","8 0 980 993"}

    Returns: 359.07044357655184

  20. {"107 73","273 257","288 422","314 23","340 63","457 993","5 310","536 759","683 68","706 695"}

    {"8 0 672 814","0 4 595 937","3 0 920 1000","2 5 489 784","6 0 450 882","4 2 631 852","0 2 821 965","4 0 768 856","4 3 85 738","3 8 990 991","3 4 872 919","2 0 433 571","6 5 80 663","2 4 183 887","6 0 184 1000","0 8 794 912","8 4 466 690","6 0 609 987","0 8 375 657","0 8 537 852"}

    Returns: 279.16281511739953

  21. {"135 221","222 744","253 845","288 79","336 423","460 49","748 542","838 897","915 192","93 319"}

    {"3 1 609 917","5 3 6 574","2 0 162 960","6 2 616 923","0 4 610 745","2 8 343 450","8 6 553 966","4 6 773 989","0 2 92 130","4 0 470 862","6 5 110 154","0 2 9 799","0 6 641 958","6 7 869 906","5 0 790 890","0 6 320 485","0 2 407 972","3 0 979 993","3 5 134 449","2 8 541 686"}

    Returns: 286.17560681614907

  22. {"110 142","266 187","367 111","420 0","533 532","581 677","662 442","921 381","929 718","956 450"}

    {"4 0 849 915","5 0 949 984","0 3 514 932","0 4 468 932","0 1 224 586","4 0 720 754","8 2 226 743","5 4 976 983","5 8 930 998","0 2 19 943","8 0 89 194","8 1 366 964","5 8 527 543","4 0 636 875","0 4 862 996","5 2 562 563","0 6 222 365","3 6 535 655","4 3 896 943","8 0 341 479"}

    Returns: 225.63963403218418

  23. {"156 132","169 795","277 687","291 511","495 427","53 62","542 778","823 1","83 747","918 59"}

    {"7 2 714 956","2 8 19 35","2 3 799 984","6 8 604 981","2 0 624 852","6 9 933 953","2 7 871 933","0 6 956 991","0 6 152 382","2 5 240 978","6 3 581 890","7 0 996 997","4 5 777 821","4 8 120 528","5 2 848 935","0 4 823 990","4 2 70 669","2 1 904 918","5 9 857 979","8 0 802 979"}

    Returns: 339.87129917073025

  24. {"0 0","1000 0","1000 1","1000 2","1000 3"}

    {"0 1 0 10","0 2 0 11","0 3 0 12","0 4 0 13","0 1 0 14","0 2 0 15","0 3 0 16","0 4 0 17","0 1 0 18","0 2 0 19","0 3 0 20","0 4 0 21","0 1 0 22","0 2 0 23","0 3 0 24","0 4 0 25","0 1 0 26","0 2 0 27","0 3 0 28","0 4 0 29"}

    Returns: 256.4111143955015

  25. {"366 310","385 945","433 139","443 696","495 854","505 733","537 977","544 239","713 209","819 665"}

    {"8 3 86 98","8 2 80 84","6 2 19 28","0 6 80 89","5 4 96 99","0 4 9 58","4 2 23 67","0 2 55 71","8 9 5 22","0 8 71 81","4 0 91 97","4 5 98 100","5 0 22 87","5 2 11 61","8 4 17 97","6 4 53 91","9 0 95 100","7 5 26 43","9 4 39 51","9 2 43 69"}

    Returns: 242.52710172768974

  26. {"319 253","349 643","40 477","406 725","428 133","618 695","664 284","714 185","815 190","86 312"}

    {"9 1 76 94","4 8 52 91","6 9 27 39","5 0 87 95","0 6 61 92","2 3 65 84","4 8 59 72","5 0 37 70","0 2 31 36","0 8 27 71","0 9 83 87","0 6 77 91","0 4 17 62","0 6 34 92","0 1 83 88","8 4 89 96","4 9 61 64","5 6 35 83","0 5 79 98","8 5 52 64"}

    Returns: 211.34383671388258

  27. {"116 880","220 239","489 480","634 743","787 851","817 308","845 213","875 746","904 619","959 240"}

    {"5 2 40 47","8 4 39 81","8 0 36 77","7 5 5 65","9 0 92 94","0 4 90 95","0 4 91 97","4 8 36 85","4 2 63 80","6 0 13 99","4 8 78 82","4 8 85 99","4 2 98 100","0 6 73 83","0 7 83 94","0 2 37 68","0 8 62 71","9 0 68 99","2 6 91 92","2 6 17 46"}

    Returns: 269.3242189396867

  28. {"133 314","190 667","292 524","518 586","637 989","646 53","752 398","896 616","934 432","969 743"}

    {"5 4 82 90","0 2 44 62","6 3 17 47","6 5 68 69","0 9 45 94","7 2 18 89","3 0 23 86","5 0 65 98","4 8 80 97","7 0 36 81","4 6 55 98","5 4 76 84","8 5 60 85","7 0 57 68","2 8 12 63","2 6 49 79","0 5 62 94","8 5 21 46","0 4 81 96","8 4 52 61"}

    Returns: 256.7963252515923

  29. {"248 382","346 840","415 302","466 967","473 553","555 143","816 450","838 564","892 963","952 841"}

    {"5 8 72 86","2 8 90 98","4 2 31 89","4 3 14 25","8 0 70 98","4 2 30 65","4 9 58 89","2 6 52 85","2 6 12 26","0 8 95 98","2 0 49 89","0 2 70 86","8 2 12 15","9 7 91 94","8 9 88 90","8 9 5 10","4 6 11 84","4 8 35 65","5 2 44 54","8 3 5 88"}

    Returns: 233.2853717440139

  30. {"149 273","256 958","277 14","369 166","526 98","59 815","691 117","866 376","892 590","988 737"}

    {"0 3 30 88","3 4 91 93","2 6 95 97","8 1 38 89","1 6 39 67","0 7 87 90","5 6 73 98","6 8 29 40","6 5 66 88","8 6 74 81","0 8 40 96","0 4 74 86","5 6 75 94","4 3 27 80","8 6 11 45","5 4 39 53","0 8 58 91","7 2 99 100","2 0 64 86","4 0 40 48"}

    Returns: 367.39624385668367

  31. {"196 80","308 74","364 690","533 436","58 473","582 49","600 967","675 580","719 833","858 455"}

    {"3 8 57 69","3 5 20 100","3 4 85 91","8 4 39 66","2 0 20 85","7 0 74 82","4 0 14 44","0 1 96 97","0 1 79 85","0 7 8 88","6 5 62 98","0 2 6 84","8 7 82 89","1 6 95 99","5 0 33 71","0 2 60 98","2 0 13 62","2 4 68 79","9 8 26 46","6 0 30 92"}

    Returns: 236.57060044993915

  32. {"335 833","406 441","462 789","504 174","674 2","711 577","714 530","878 412","908 887","945 549"}

    {"6 5 88 98","0 6 16 24","0 2 86 93","1 9 74 76","0 2 78 83","6 8 87 95","0 8 49 92","8 9 50 64","8 1 31 87","4 0 59 100","8 2 29 88","4 6 16 68","6 0 24 31","5 4 51 61","7 2 82 88","5 3 96 100","9 2 78 100","0 8 24 44","4 2 1 16","4 6 78 88"}

    Returns: 221.8119184010991

  33. {"285 906","533 262","584 251","617 756","623 711","634 695","827 554","829 413","920 650","968 690"}

    {"7 6 78 96","7 9 25 84","2 0 60 95","0 2 1 95","0 9 46 62","0 5 81 82","6 0 14 74","9 8 21 44","0 1 81 91","4 5 79 82","4 7 40 64","8 5 78 90","0 5 90 91","0 2 32 71","6 5 28 52","0 8 53 94","5 0 44 98","3 0 18 82","0 5 58 78","2 3 41 81"}

    Returns: 248.03814970878705

  34. {"146 253","303 175","411 187","436 391","565 405","64 206","647 672","687 996","710 907","951 458"}

    {"8 4 26 83","6 4 99 100","8 0 6 36","8 0 36 50","6 3 58 72","8 6 33 96","9 8 18 58","8 4 71 73","9 2 16 85","5 0 39 97","8 6 68 77","8 6 86 88","0 7 27 37","4 5 74 88","0 6 15 36","4 7 91 95","4 7 32 73","5 0 46 92","5 0 13 31","0 2 97 100"}

    Returns: 211.58906693495885

  35. {"14 869","228 564","247 619","330 821","332 162","412 180","539 139","666 519","722 743","938 461"}

    {"0 8 5 72","0 9 29 53","3 6 76 90","8 0 78 82","6 2 51 73","5 2 15 85","5 0 17 71","4 5 23 60","2 5 40 57","8 0 33 81","0 2 59 99","6 0 75 82","8 0 71 81","6 4 66 72","4 2 64 71","0 2 36 70","2 0 91 93","8 2 16 52","9 4 92 99","0 8 2 14"}

    Returns: 236.23492119750847

  36. {"136 863","177 903","302 954","309 773","372 760","376 941","481 452","727 838","809 746","943 262"}

    {"4 2 16 84","8 9 36 69","6 4 34 51","5 4 14 75","0 4 89 91","7 4 80 93","6 4 37 73","2 7 48 72","8 4 79 88","0 2 79 100","0 2 80 92","3 4 54 75","4 3 19 23","2 8 35 74","6 0 50 77","8 3 46 99","6 0 11 32","4 9 91 93","0 3 5 57","8 0 71 96"}

    Returns: 263.75180895498966

  37. {"146 758","156 415","156 534","276 937","401 562","498 352","633 712","706 255","864 793","966 943"}

    {"2 7 13 99","1 2 49 88","3 1 36 95","0 4 55 71","6 7 30 36","1 9 81 93","0 8 71 85","8 6 24 56","4 7 10 68","2 0 44 95","2 1 35 65","8 2 57 84","2 6 76 100","4 9 80 87","0 4 88 97","5 4 53 100","8 5 3 83","1 0 18 42","7 2 11 93","4 6 83 97"}

    Returns: 197.5383984922363

  38. {"144 366","285 452","374 251","494 84","542 342","614 897","665 817","749 538","857 70","963 817"}

    {"0 1 99 100","6 3 46 64","4 6 8 67","2 0 30 42","3 6 94 98","2 0 76 92","6 0 37 49","7 0 63 96","4 2 8 18","7 0 98 99","0 8 50 51","4 8 41 87","7 5 47 85","2 0 31 74","0 1 89 94","4 0 27 67","5 1 17 26","2 6 11 65","7 0 75 81","0 5 16 47"}

    Returns: 255.73685645263805

  39. {"141 839","146 661","248 204","49 36","55 674","660 625","670 968","749 181","841 96","970 16"}

    {"2 6 96 98","0 4 71 91","4 9 61 68","7 4 77 98","0 2 75 99","2 9 91 98","6 4 49 76","0 2 8 54","7 8 67 83","2 7 89 93","5 0 76 90","0 6 64 97","8 6 98 99","6 8 50 93","0 6 80 91","0 8 25 34","9 8 77 90","6 3 86 96","2 0 71 73","2 0 48 72"}

    Returns: 298.1947982123529

  40. {"168 72","273 918","309 15","315 695","359 240","478 960","734 275","747 538","811 810","841 72"}

    {"4 9 66 85","2 6 10 29","5 0 21 37","4 6 29 46","2 5 17 99","3 6 16 82","5 3 88 90","6 2 71 75","1 8 99 100","7 9 94 95","4 0 36 90","6 4 86 100","6 7 33 67","6 0 83 92","8 1 64 98","6 5 61 88","4 5 94 95","2 7 92 93","8 4 16 78","5 0 58 82"}

    Returns: 236.523003893958

  41. {"171 336","287 304","38 363","407 326","476 1","506 881","705 930","743 455","834 755","985 777"}

    {"6 0 88 98","4 6 79 85","8 0 85 93","4 8 10 60","9 7 7 51","1 4 36 61","8 4 66 83","7 4 44 79","4 5 14 63","8 0 97 99","8 7 63 87","6 5 7 42","0 4 42 62","2 0 54 63","8 9 53 95","0 4 36 69","0 8 91 92","6 2 48 65","1 4 37 57","3 1 24 93"}

    Returns: 284.62206264067163

  42. {"131 21","152 891","261 105","394 979","479 207","557 46","633 882","649 835","783 68","968 983"}

    {"0 7 48 86","2 1 29 42","0 8 82 89","0 9 5 59","4 8 34 64","5 8 74 94","1 8 76 99","5 2 6 21","5 0 5 19","9 1 8 56","2 4 88 98","8 2 62 90","8 0 43 80","5 8 12 83","5 6 91 98","7 1 95 96","8 2 1 32","0 6 9 15","5 4 91 97","3 0 60 72"}

    Returns: 396.7609481791254

  43. {"180 267","323 459","460 838","471 19","589 307","608 978","675 516","818 522","938 623","983 29"}

    {"9 4 10 48","2 0 78 84","1 0 64 79","0 4 62 97","5 9 59 83","0 6 49 85","2 4 92 96","0 3 73 94","0 5 81 92","0 6 27 66","0 6 23 53","7 0 82 86","6 0 32 56","6 4 83 98","4 8 85 93","3 8 78 81","5 4 75 81","6 8 96 99","8 4 15 67","0 2 54 90"}

    Returns: 260.3098290838234

  44. {"194 176","288 520","330 12","350 351","375 776","473 767","551 89","652 118","926 859","975 779"}

    {"8 6 94 98","6 0 3 37","6 0 22 90","2 9 0 95","8 0 64 86","2 5 16 64","0 5 8 30","0 2 30 93","9 5 71 84","0 5 10 38","6 4 95 98","7 3 77 81","4 1 78 87","6 0 30 35","8 1 69 97","0 8 73 91","8 0 52 77","5 0 77 87","3 8 17 42","0 6 63 71"}

    Returns: 346.1068830731408

  45. {"17 936","277 961","320 185","35 668","392 675","513 911","60 215","633 632","719 934","89 222"}

    {"2 4 45 80","8 2 93 94","2 4 97 98","5 2 60 83","6 8 59 73","1 9 67 90","8 0 33 41","0 4 25 64","6 1 58 74","5 6 87 90","2 0 4 20","0 8 42 95","0 8 71 78","0 8 29 62","2 4 6 25","0 4 10 84","4 8 32 69","3 0 13 53","9 0 41 49","4 2 98 100"}

    Returns: 263.0017456990797

  46. {"144 832","24 518","245 325","408 368","505 754","73 771","743 339","905 570","965 116","988 746"}

    {"8 2 3 89","7 0 38 70","0 8 86 89","0 8 94 100","2 4 57 100","8 7 21 91","4 0 56 97","8 6 91 92","0 8 45 48","8 2 74 93","6 5 9 83","3 8 25 98","8 7 99 100","2 8 83 99","7 8 29 42","7 4 91 92","6 5 66 98","4 0 50 54","4 0 94 98","0 1 76 81"}

    Returns: 225.28149653732402

  47. {"0 135","16 603","260 625","41 34","418 597","635 159","769 165","769 793","900 19","97 625"}

    {"4 0 32 44","8 0 20 72","7 4 93 96","5 6 33 93","2 0 1 40","4 0 47 75","5 3 9 16","0 6 9 22","4 0 61 93","6 5 54 77","4 2 33 49","2 8 24 97","0 5 16 20","0 1 39 77","4 0 48 49","2 8 80 96","0 6 69 87","9 2 41 70","1 0 99 100","4 0 9 62"}

    Returns: 297.50398887937513

  48. {"137 709","15 125","152 263","326 785","503 888","628 939","752 450","834 537","965 246","999 21"}

    {"4 0 74 80","2 6 53 91","4 8 52 62","8 0 63 75","0 7 95 97","2 8 34 66","5 6 84 97","5 6 75 91","0 1 73 77","0 7 83 99","2 0 83 92","0 6 41 99","1 8 51 82","0 3 99 100","9 8 42 94","0 6 55 94","6 8 19 84","0 3 93 95","8 5 59 82","0 2 35 86"}

    Returns: 331.37234028790965

  49. {"0 0","1 0"}

    {"0 1 0 20","0 1 1 21","0 1 2 22","0 1 3 23","0 1 4 24","0 1 5 25","0 1 6 26","0 1 7 27","0 1 8 28","0 1 9 29","0 1 10 30","0 1 11 31","0 1 12 32","0 1 13 33","0 1 14 34","0 1 15 35","0 1 16 36","0 1 17 37","0 1 18 38","0 1 19 39"}

    Returns: 0.04999999999999986

  50. {"0 0","1000 1000"}

    {"0 1 0 20","0 1 1 21","0 1 2 22","0 1 3 23","0 1 4 24","0 1 5 25","0 1 6 26","0 1 7 27","0 1 8 28","0 1 9 29","0 1 10 30","0 1 11 31","0 1 12 32","0 1 13 33","0 1 14 34","0 1 15 35","0 1 16 36","0 1 17 37","0 1 18 38","0 1 19 39"}

    Returns: 70.71067811865476

  51. {"0 0","0 1000","1000 0","1000 1000","500 500","499 499","501 501","501 499","499 501","500 501"}

    {"0 3 0 1000","0 3 0 1000","0 3 0 1000","0 3 0 1000","0 3 0 1000", "3 0 0 1000","3 0 0 1000","3 0 0 1000","3 0 0 1000","3 0 0 1000", "1 2 0 1000","1 2 0 1000","1 2 0 1000","1 2 0 1000","1 2 0 1000", "2 1 0 1000","2 1 0 1000","2 1 0 1000","2 1 0 1000","2 1 0 1000"}

    Returns: 352.8462838120872

  52. {"101 591", "283 183", "346 696", "436 638", "738 46" }

    {"3 0 855 890", "2 0 260 698", "3 4 229 743", "1 2 519 898", "3 1 863 955", "4 0 407 993", "2 4 872 969", "0 3 320 663" }

    Returns: 298.18759041416865

  53. {"0 0", "199 1", "201 2", "399 3", "602 5", "807 12", "987 333", "999 657", "994 899", "998 998" }

    {"0 6 0 1", "1 7 0 1", "2 8 0 1", "3 9 0 1", "4 6 0 1", "5 7 0 1", "1 8 0 1", "2 9 0 1", "3 6 0 1", "4 7 0 1", "5 8 0 1", "0 9 0 1", "6 0 0 1", "7 0 0 1", "8 0 0 1", "9 0 0 1", "7 2 0 1", "7 3 0 1" }

    Returns: 212.9147462285361

  54. {"0 0", "1000 0" }

    {"0 1 1 2" }

    Returns: 500.0

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