Statistics

Problem Statement for "BadClock"

Problem Statement

According to Lewis Carroll, a clock that has stopped is more accurate than one that is five minutes behind. He argues that the former is right twice a day, whereas the latter never shows the correct time. Then again, a clock that is always five minutes behind is in a sense perfectly accurate, and therefore an extraordinary specimen. More usually, a clock is ahead or behind because it runs at the wrong rate, so that its absolute discrepancy from the true time is steadily changing. If left unregulated, such a clock will show the true time at regular but perhaps lengthy intervals.

You are given two Strings of the form "hh:mm:ss". The first represents exactly the true time, while the second is exactly the time shown by an ill-tuned clock. This is an analog clock whose hour, minute, and second hands sweep continuously around the dial at a speed that is too fast or too slow by a constant factor. Both times are given in the North American style, where the hour ranges between 1 and 12, inclusive. Given an int specifying the non-zero number of seconds that the clock gains every hour, calculate the number of hours that elapse before it agrees with the true time. Your answer, a double, must be correct with either absolute or relative precision of 1.0e-9 (one billionth).

Definition

Class:
BadClock
Method:
nextAgreement
Parameters:
String, String, int
Returns:
double
Method signature:
double nextAgreement(String trueTime, String skewTime, int hourlyGain)
(be sure your method is public)

Notes

  • If hourlyGain is negative, the clock falls behind by a fixed number of seconds every hour.
  • It is not the case that the clock makes discrete jumps every so often. Rather, the hands of the clock are moving smoothly and continuously at a constant rate that is too slow or too fast relative to the true time.

Constraints

  • trueTime and skewTime each contain exactly eight characters in the format "hh:mm:ss", where the substring "hh" is a zero-padded integer between 1 and 12, inclusive, and "mm" and "ss" are zero-padded integers between 0 and 59, inclusive
  • hourlyGain is either between -1800 and -1, inclusive, or between 1 and 3600, inclusive

Examples

  1. "07:07:07"

    "07:07:07"

    1776

    Returns: 0.0

    The clock is already showing the true time.

  2. "11:59:58"

    "12:03:28"

    -3

    Returns: 70.0

    This clock loses three seconds every hour, and will catch up with the true time in exactly 70 hours.

  3. "12:03:28"

    "11:59:58"

    3

    Returns: 70.0

    This clock gains three seconds per hour.

  4. "03:03:02"

    "03:01:47"

    5

    Returns: 15.0

  5. "03:03:02"

    "03:01:47"

    -5

    Returns: 8625.0

  6. "07:08:09"

    "09:08:07"

    -321

    Returns: 22.42367601246106

  7. "11:59:59"

    "12:00:00"

    3600

    Returns: 11.999722222222223

  8. "11:59:59"

    "12:00:00"

    1

    Returns: 43199.0

  9. "12:00:00"

    "11:59:59"

    -1800

    Returns: 23.999444444444446

  10. "12:00:00"

    "11:59:59"

    -1

    Returns: 43199.0

  11. "03:03:48"

    "09:30:25"

    2337

    Returns: 8.559264013692768

  12. "03:19:53"

    "03:02:36"

    1148

    Returns: 0.9033101045296167

  13. "09:32:36"

    "07:43:29"

    1268

    Returns: 5.163249211356467

  14. "08:26:33"

    "12:21:10"

    1253

    Returns: 23.24261771747805

  15. "08:06:10"

    "01:50:05"

    -1394

    Returns: 14.802725968436155

  16. "12:12:13"

    "02:24:59"

    1756

    Returns: 20.06492027334852

  17. "12:37:35"

    "07:07:35"

    -935

    Returns: 25.02673796791444

  18. "08:13:20"

    "03:16:20"

    2437

    Returns: 7.312269183422241

  19. "02:19:21"

    "04:37:59"

    -1213

    Returns: 6.857378400659522

  20. "02:14:14"

    "03:19:15"

    833

    Returns: 47.17767106842737

  21. "11:41:13"

    "02:13:53"

    -847

    Returns: 10.814639905548997

  22. "05:05:33"

    "01:34:23"

    1883

    Returns: 6.728624535315985

  23. "08:33:09"

    "01:38:19"

    2590

    Returns: 9.61003861003861

  24. "01:03:15"

    "12:03:09"

    -1204

    Returns: 32.88538205980066

  25. "09:28:30"

    "05:12:49"

    2314

    Returns: 6.629645635263612

  26. "08:09:26"

    "08:02:26"

    -687

    Returns: 62.2707423580786

  27. "10:31:51"

    "07:46:55"

    758

    Returns: 13.055408970976254

  28. "04:06:48"

    "03:43:32"

    -626

    Returns: 66.77955271565496

  29. "11:03:13"

    "11:52:32"

    2938

    Returns: 13.696732471068755

  30. "05:12:08"

    "10:02:47"

    778

    Returns: 33.11182519280206

  31. "06:47:01"

    "12:44:23"

    598

    Returns: 36.38461538461539

  32. "06:07:41"

    "11:35:41"

    -809

    Returns: 24.326328800988875

  33. "02:19:20"

    "12:02:21"

    -1595

    Returns: 21.93166144200627

  34. "01:20:50"

    "02:30:50"

    2033

    Returns: 19.183472700442696

  35. "06:31:44"

    "03:21:48"

    566

    Returns: 20.13427561837456

  36. "10:12:36"

    "02:22:26"

    2720

    Returns: 10.371323529411764

  37. "03:19:54"

    "06:36:45"

    -243

    Returns: 48.60493827160494

  38. "04:38:33"

    "03:58:06"

    1948

    Returns: 1.245893223819302

  39. "06:23:13"

    "07:09:08"

    294

    Returns: 137.56802721088437

  40. "09:29:37"

    "07:31:34"

    2821

    Returns: 2.510811768876285

  41. "07:13:08"

    "05:34:25"

    -30

    Returns: 1242.5666666666666

  42. "12:23:43"

    "12:41:31"

    513

    Returns: 82.12865497076024

  43. "10:53:16"

    "02:34:07"

    688

    Returns: 43.530523255813954

  44. "02:58:27"

    "07:39:07"

    1091

    Returns: 24.161319890009167

  45. "06:30:06"

    "07:11:10"

    1440

    Returns: 28.288888888888888

  46. "10:01:11"

    "07:55:33"

    -1445

    Returns: 24.679584775086504

  47. "06:45:33"

    "04:59:39"

    -1684

    Returns: 21.880047505938244

  48. "08:38:09"

    "01:16:04"

    2267

    Returns: 11.700485222761358

  49. "06:47:39"

    "07:14:00"

    -478

    Returns: 3.307531380753138

  50. "08:50:39"

    "07:46:03"

    1402

    Returns: 2.7646219686162623

  51. "08:59:12"

    "10:10:06"

    3340

    Returns: 11.660479041916167

  52. "09:45:50"

    "01:18:19"

    671

    Returns: 45.38152011922504

  53. "12:17:03"

    "08:41:13"

    1363

    Returns: 9.501100513573

  54. "02:54:06"

    "01:09:13"

    2736

    Returns: 2.3000730994152048

  55. "11:32:05"

    "03:04:14"

    3568

    Returns: 8.540078475336323

  56. "03:55:13"

    "10:20:27"

    3382

    Returns: 5.9390892962743935

  57. "07:49:08"

    "07:29:41"

    3471

    Returns: 0.3362143474503025

  58. "07:08:53"

    "06:37:56"

    2462

    Returns: 0.7542648253452477

  59. "02:13:31"

    "03:09:54"

    2599

    Returns: 15.320123124278568

  60. "01:31:08"

    "11:33:39"

    2776

    Returns: 2.539265129682997

  61. "01:37:21"

    "01:00:49"

    1313

    Returns: 1.6694592536176696

  62. "09:07:52"

    "12:17:00"

    1576

    Returns: 20.210659898477157

  63. "05:24:05"

    "07:56:20"

    2830

    Returns: 12.037102473498233

  64. "10:58:21"

    "09:46:49"

    1364

    Returns: 3.1466275659824046

  65. "06:28:42"

    "09:12:25"

    -1700

    Returns: 5.778235294117647

  66. "12:32:25"

    "12:21:32"

    1271

    Returns: 0.5137686860739575

  67. "09:29:55"

    "09:57:26"

    3186

    Returns: 13.041117388575016

  68. "05:13:37"

    "08:23:58"

    230

    Returns: 138.1695652173913

  69. "05:41:30"

    "11:40:51"

    2705

    Returns: 7.999630314232902

  70. "01:28:54"

    "01:47:13"

    -1030

    Returns: 1.0669902912621358

  71. "02:48:53"

    "04:14:55"

    273

    Returns: 139.33333333333334

  72. "01:54:33"

    "03:49:31"

    -161

    Returns: 42.84472049689441

  73. "11:39:59"

    "06:44:20"

    -760

    Returns: 33.501315789473686

  74. "03:51:05"

    "07:18:32"

    1506

    Returns: 20.4203187250996

  75. "10:42:30"

    "07:40:38"

    145

    Returns: 75.2551724137931

  76. "08:04:01"

    "11:25:21"

    685

    Returns: 45.43065693430657

  77. "04:39:48"

    "10:03:14"

    2745

    Returns: 8.668123861566485

  78. "07:44:37"

    "02:36:26"

    3321

    Returns: 5.567901234567901

  79. "01:45:45"

    "11:17:38"

    -585

    Returns: 58.654700854700856

  80. "09:30:27"

    "03:54:36"

    2328

    Returns: 8.655927835051546

  81. "07:47:34"

    "05:13:01"

    3054

    Returns: 3.036345776031434

  82. "01:16:03"

    "06:16:31"

    640

    Returns: 39.33125

  83. "03:30:18"

    "04:44:34"

    2553

    Returns: 15.17587152369761

  84. "02:34:34"

    "02:17:25"

    -57

    Returns: 739.8421052631579

  85. "01:55:48"

    "11:05:51"

    -1500

    Returns: 22.002

  86. "03:47:18"

    "07:42:24"

    -1770

    Returns: 7.969491525423729

  87. "11:10:46"

    "06:30:15"

    3158

    Returns: 5.329639012032932

  88. "04:40:01"

    "02:14:50"

    -1195

    Returns: 28.861087866108786

  89. "07:07:08"

    "10:08:20"

    2668

    Returns: 12.116941529235381

  90. "05:38:32"

    "03:07:31"

    -1409

    Returns: 24.229240596167493

  91. "01:09:31"

    "05:37:53"

    -1349

    Returns: 11.936249073387694

  92. "10:57:32"

    "01:42:35"

    1454

    Returns: 22.900275103163686

  93. "09:49:14"

    "07:23:34"

    -887

    Returns: 38.8500563697858

  94. "03:30:11"

    "03:44:36"

    -1097

    Returns: 0.7885141294439381

  95. "11:43:37"

    "02:35:23"

    -1543

    Returns: 6.679196370706416

  96. "09:02:33"

    "03:09:46"

    -1514

    Returns: 14.552840158520475

  97. "04:53:25"

    "12:15:18"

    943

    Returns: 17.695652173913043

  98. "07:26:29"

    "12:29:13"

    -222

    Returns: 81.81981981981981

  99. "10:28:13"

    "12:19:28"

    2182

    Returns: 16.73923006416132

  100. "11:37:47"

    "06:30:41"

    -740

    Returns: 33.47837837837838

  101. "07:08:09"

    "09:08:07"

    -321

    Returns: 22.42367601246106

  102. "03:03:02"

    "03:01:47"

    -5

    Returns: 8625.0

  103. "07:07:07"

    "07:07:07"

    1776

    Returns: 0.0

  104. "03:03:02"

    "03:01:47"

    -10

    Returns: 4312.5

  105. "11:59:58"

    "12:03:28"

    3

    Returns: 14330.0

  106. "03:03:03"

    "03:03:02"

    -1

    Returns: 43199.0

  107. "11:00:00"

    "11:00:01"

    3600

    Returns: 11.999722222222223

  108. "07:07:07"

    "01:01:01"

    -1

    Returns: 21234.0

  109. "03:03:02"

    "03:01:47"

    -37

    Returns: 1165.5405405405406

  110. "01:01:01"

    "03:03:03"

    1

    Returns: 35878.0

  111. "07:08:09"

    "09:08:07"

    2

    Returns: 18001.0

  112. "01:00:00"

    "01:00:01"

    1

    Returns: 43199.0

  113. "12:00:00"

    "12:00:00"

    4

    Returns: 0.0

  114. "01:01:01"

    "01:01:02"

    1

    Returns: 43199.0

  115. "05:00:00"

    "06:00:00"

    1

    Returns: 39600.0

  116. "03:01:47"

    "03:03:02"

    5

    Returns: 8625.0

  117. "10:00:01"

    "10:00:02"

    1

    Returns: 43199.0

  118. "08:00:00"

    "10:00:00"

    10

    Returns: 3600.0

  119. "07:07:07"

    "07:07:07"

    -2

    Returns: 0.0

  120. "03:03:02"

    "03:04:47"

    3

    Returns: 14365.0

  121. "03:03:02"

    "03:01:47"

    -13

    Returns: 3317.3076923076924

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