Statistics

Problem Statement for "TakeBus"

Problem Statement

You would like to return home from a party as soon as possible by taking a bus. You are currently standing at a bus stop that is serviced by several different routes. Each bus route takes a different amount of time to take you home, so it's not always optimal to take the first bus you see. Sometimes it's better to skip a bus and wait for a bus from another route. Fortunately for you, each route has a fixed time interval between consecutive buses arriving at this stop. You also know the time it takes each route to get you back home. Unfortunately, you have no idea when any of the previous buses were at this stop, so you don't know how long it will take for the next bus to arrive.

You will be given two int[]s - tripTime and waitTime, with the ith elements of tripTime and waitTime describing the ith route. The ith element of tripTime represents the time it takes to get home using the ith route, and the ith element of waitTime gives you the exact time interval between two consecutive buses of this route. This means you'll need to wait an integer number of minutes between 0 and (waitTime[i] - 1), inclusive, until the next bus of the ith route arrives. Each of these intervals is equally probable.

Return the minimal expected time you'll need to get home if your behavior is optimal. That is, at each moment you try to minimize the expected time using all the information about buses you have.

Definition

Class:
TakeBus
Method:
expectedTime
Parameters:
int[], int[]
Returns:
double
Method signature:
double expectedTime(int[] tripTime, int[] waitTime)
(be sure your method is public)

Notes

  • The returned value must be accurate to within a relative or absolute value of 1E-9.

Constraints

  • tripTime and waitTime will contain the same number of elements.
  • tripTime and waitTime will each contain between 1 and 50 elements, inclusive.
  • Each element of tripTime will be between 1 and 100, inclusive.
  • Each element of waitTime will be between 1 and 100, inclusive.

Examples

  1. {5}

    {2}

    Returns: 5.5

    Here the bus will come either immediately or in 1 minute, giving us an average wait time of 0.5 minutes. We spend another 5 minutes to get home.

  2. {100, 5}

    {1, 10}

    Returns: 9.5

    Here the first bus is extremely slow, so we prefer to wait for the second.

  3. {6, 5}

    {1, 10}

    Returns: 5.9

    We take the second bus only if it comes to the stop immediately. If it doesn't, we immediately take the first one.

  4. {100, 100}

    {2, 2}

    Returns: 100.25

  5. {100, 100, 100, 100, 100, 100, 100, 100, 100, 100}

    {2, 2, 2, 2, 2, 2, 2, 2, 2, 2}

    Returns: 100.0009765625

  6. {100, 100, 100}

    {2, 2, 2}

    Returns: 100.125

  7. {5, 100}

    {2, 1}

    Returns: 5.5

  8. {100, 100, 100}

    {3, 3, 3}

    Returns: 100.33333333333333

  9. {100, 100, 100, 100, 100, 100}

    {2, 4, 8, 16, 32, 64}

    Returns: 100.29334783554077

  10. {31,41,59,26,53,58}

    {27,18,28,18,49,33}

    Returns: 33.95679012345678

  11. {2, 2, 3, 11, 12, 13, 13, 14, 17, 22, 25, 25, 28, 28, 34, 35, 36, 39, 45, 45, 46, 47, 48, 59, 61, 61, 63, 66, 76, 76, 76, 79, 79, 83, 93, 95, 96}

    {28, 26, 10, 64, 43, 9, 47, 96, 1, 42, 57, 38, 13, 20, 67, 58, 76, 33, 31, 2, 26, 40, 39, 52, 1, 44, 66, 59, 91, 72, 89, 61, 41, 53, 5, 13, 15}

    Returns: 6.034340659340657

  12. {5, 7, 10, 12, 15, 15, 16, 19, 21, 22, 25, 25, 26, 36, 39, 47, 60, 62, 63, 63, 66, 68, 69, 70, 70, 79, 82, 92, 94, 96, 96, 100}

    {84, 26, 18, 89, 66, 52, 54, 30, 37, 62, 30, 97, 48, 37, 72, 75, 95, 56, 3, 79, 60, 98, 93, 76, 27, 4, 65, 100, 7, 10, 7, 36}

    Returns: 14.414977857920277

  13. {2, 8, 10, 11, 16, 19, 20, 24, 30, 32, 33, 35, 44, 46, 48, 53, 53, 53, 56, 57, 65, 65, 65, 67, 70, 73, 76, 78, 80, 89, 93, 97, 100}

    {27, 60, 39, 82, 97, 20, 43, 46, 70, 89, 12, 12, 68, 45, 65, 34, 66, 63, 9, 82, 5, 71, 33, 64, 96, 9, 68, 89, 65, 14, 99, 16, 50}

    Returns: 13.478154170430592

  14. {4, 10, 13, 20, 24, 25, 25, 26, 43, 57, 57, 59, 60, 61, 63, 70, 71, 72, 78, 79, 85, 90, 96}

    {71, 49, 10, 65, 8, 81, 59, 2, 73, 50, 51, 80, 12, 72, 12, 98, 79, 7, 22, 37, 18, 17, 22}

    Returns: 15.98232250646737

  15. {7, 7, 9, 10, 10, 10, 12, 13, 13, 14, 20, 26, 29, 42, 47, 52, 56, 57, 58, 59, 60, 60, 63, 66, 68, 68, 74, 75, 76, 78, 84, 85, 85, 86, 89, 90, 93, 93}

    {38, 94, 36, 15, 30, 81, 100, 55, 84, 51, 99, 70, 16, 64, 96, 97, 36, 2, 85, 71, 16, 86, 67, 4, 1, 98, 24, 65, 88, 23, 35, 70, 83, 2, 59, 1, 67, 35}

    Returns: 13.119765647052876

  16. {3, 4, 4, 5, 6, 6, 9, 14, 15, 17, 19, 20, 21, 22, 33, 34, 38, 45, 46, 46, 47, 51, 52, 58, 58, 60, 65, 67, 68, 72, 75, 76, 77, 81, 84, 87, 89, 90, 93, 95, 98, 99}

    {64, 1, 31, 56, 53, 97, 62, 32, 96, 27, 34, 91, 78, 83, 2, 13, 8, 58, 26, 43, 57, 6, 64, 83, 96, 34, 100, 19, 86, 13, 87, 92, 34, 24, 48, 98, 98, 39, 95, 25, 82, 74}

    Returns: 3.984375

  17. {1, 1, 1, 3, 10, 12, 13, 19, 20, 21, 21, 22, 23, 28, 28, 30, 31, 33, 40, 42, 44, 48, 50, 51, 57, 59, 65, 67, 68, 75, 79, 94, 98}

    {57, 64, 6, 48, 23, 54, 92, 69, 73, 3, 86, 59, 93, 41, 18, 29, 44, 21, 99, 58, 92, 68, 80, 34, 88, 88, 33, 4, 56, 15, 68, 86, 84}

    Returns: 3.291343049463938

  18. {4, 6, 6, 13, 19, 25, 27, 35, 39, 39, 44, 46, 49, 49, 49, 53, 55, 56, 66, 69, 95, 97}

    {30, 1, 71, 82, 97, 42, 79, 57, 70, 4, 2, 7, 45, 54, 68, 21, 40, 12, 29, 27, 78, 84}

    Returns: 5.933333333333334

  19. {5, 17, 21, 30, 32, 33, 35, 36, 37, 39, 47, 50, 52, 77, 77, 83, 89, 90, 90, 94}

    {3, 16, 87, 84, 79, 33, 77, 61, 8, 22, 64, 3, 14, 21, 59, 3, 51, 61, 84, 57}

    Returns: 6.0

  20. {1, 2, 2, 3, 9, 11, 12, 13, 14, 14, 16, 17, 19, 19, 23, 26, 29, 35, 37, 39, 41, 44, 45, 45, 46, 46, 50, 50, 54, 55, 58, 60, 61, 62, 64, 69, 71, 72, 73, 79, 80, 83, 84, 85, 89, 92, 96}

    {89, 83, 20, 13, 9, 62, 80, 95, 90, 36, 98, 7, 38, 58, 26, 78, 87, 14, 87, 15, 4, 68, 45, 95, 100, 38, 98, 62, 16, 18, 82, 54, 40, 22, 97, 55, 97, 30, 16, 97, 27, 87, 81, 77, 95, 4, 17}

    Returns: 6.6792067144984415

  21. {1, 3, 7, 14, 21, 23, 23, 25, 25, 26, 28, 28, 29, 29, 32, 33, 34, 38, 40, 41, 41, 45, 46, 46, 51, 52, 54, 55, 59, 64, 66, 67, 70, 72, 73, 80, 83, 84, 84, 86, 88, 99, 100}

    {100, 95, 90, 83, 83, 82, 81, 79, 78, 77, 77, 74, 69, 66, 65, 61, 58, 56, 55, 54, 44, 42, 42, 41, 39, 38, 37, 31, 27, 27, 26, 25, 19, 18, 15, 14, 13, 13, 11, 10, 8, 7, 2}

    Returns: 23.799980340430544

  22. {1, 6, 7, 14, 15, 16, 19, 24, 25, 26, 28, 28, 28, 28, 30, 32, 33, 41, 45, 51, 52, 54, 54, 57, 58, 59, 66, 67, 69, 70, 70, 70, 71, 73, 74, 76, 76, 78, 79, 79, 82, 82, 82, 83, 86, 90, 91, 95, 97, 98}

    {98, 95, 93, 92, 92, 91, 88, 81, 80, 79, 74, 71, 70, 69, 68, 67, 66, 65, 65, 65, 64, 64, 63, 62, 61, 59, 54, 52, 46, 43, 40, 39, 38, 34, 26, 25, 25, 25, 24, 22, 20, 18, 15, 13, 13, 11, 9, 9, 7, 5}

    Returns: 22.276481599491632

  23. {11, 12, 14, 16, 19, 26, 30, 35, 44, 50, 50, 54, 57, 68, 74, 75, 78, 79, 80, 90, 93, 99}

    {99, 98, 98, 84, 78, 74, 73, 71, 61, 61, 46, 46, 32, 30, 26, 21, 17, 16, 15, 14, 13, 8}

    Returns: 28.79937486882511

  24. {5, 13, 14, 17, 18, 18, 18, 21, 22, 23, 25, 27, 33, 35, 36, 37, 41, 42, 43, 43, 50, 52, 53, 59, 59, 60, 62, 68, 74, 76, 77, 78, 79, 84, 94, 96, 97}

    {94, 91, 91, 85, 82, 79, 76, 76, 74, 68, 66, 64, 64, 59, 57, 56, 55, 54, 53, 52, 45, 42, 35, 33, 32, 31, 27, 26, 22, 20, 16, 14, 10, 9, 9, 8, 5}

    Returns: 24.055572114117652

  25. {24, 35, 39, 44, 66, 71, 80, 84, 88, 90, 92, 94}

    {98, 96, 93, 84, 76, 64, 56, 36, 35, 26, 11, 4}

    Returns: 53.82294406978099

  26. {1, 3, 4, 5, 5, 10, 10, 11, 12, 14, 15, 18, 23, 27, 28, 28, 32, 35, 35, 40, 43, 47, 48, 50, 51, 52, 58, 59, 60, 63, 66, 67, 69, 71, 71, 75, 75, 79, 79, 83, 85, 85, 86, 87, 88, 88, 92, 94, 96, 97}

    {99, 96, 96, 93, 91, 89, 86, 86, 83, 82, 80, 79, 75, 75, 75, 75, 73, 73, 69, 65, 64, 62, 62, 58, 56, 56, 55, 53, 51, 48, 48, 46, 45, 42, 42, 40, 40, 39, 30, 27, 25, 22, 20, 18, 17, 17, 17, 11, 9, 8}

    Returns: 15.232792889838908

  27. {1, 1, 4, 6, 6, 8, 8, 10, 10, 13, 17, 17, 18, 18, 20, 21, 23, 24, 29, 33, 37, 39, 41, 42, 44, 49, 49, 50, 55, 59, 62, 62, 64, 70, 72, 73, 73, 73, 77, 77, 77, 77, 80, 81, 81, 82, 83, 90, 93, 96}

    {96, 95, 92, 91, 90, 87, 85, 84, 82, 81, 78, 74, 74, 73, 71, 70, 66, 63, 62, 62, 62, 62, 51, 51, 51, 48, 42, 42, 39, 35, 34, 32, 31, 28, 27, 21, 20, 19, 18, 16, 16, 13, 8, 8, 7, 4, 4, 3, 2, 2}

    Returns: 14.30257494517852

  28. {2, 2, 3, 5, 15, 15, 19, 19, 22, 28, 28, 31, 32, 35, 38, 41, 45, 48, 49, 51, 52, 55, 55, 56, 59, 60, 60, 61, 61, 63, 63, 69, 71, 76, 77, 81, 82, 82, 84, 86, 87, 87, 88, 91, 92, 94, 95, 99, 100, 100}

    {100, 99, 98, 93, 89, 87, 87, 87, 84, 77, 77, 76, 73, 71, 70, 69, 67, 67, 65, 64, 64, 63, 59, 56, 54, 48, 44, 40, 39, 36, 35, 35, 35, 34, 33, 28, 27, 26, 26, 24, 24, 23, 15, 13, 13, 11, 10, 10, 2, 2}

    Returns: 19.917461031228893

  29. {3, 5, 5, 7, 10, 12, 14, 17, 18, 21, 25, 28, 29, 30, 30, 34, 36, 39, 40, 40, 41, 45, 45, 47, 50, 54, 55, 57, 59, 62, 64, 66, 66, 68, 72, 73, 74, 75, 80, 84, 87, 88, 88, 89, 90, 92, 95, 95, 96, 98}

    {97, 95, 94, 94, 93, 91, 90, 88, 85, 82, 80, 79, 77, 77, 74, 74, 73, 70, 68, 66, 65, 63, 60, 57, 53, 52, 40, 39, 39, 37, 35, 34, 30, 28, 23, 23, 22, 20, 17, 15, 14, 14, 13, 12, 8, 8, 5, 4, 3, 3}

    Returns: 18.827620407231784

  30. {1, 3, 4, 5, 6, 16, 19, 23, 24, 24, 28, 29, 32, 34, 38, 39, 42, 43, 44, 47, 50, 51, 52, 57, 58, 65, 67, 68, 70, 71, 72, 74, 76, 77, 80, 81, 81, 84, 85, 86, 87, 87, 87, 92, 93, 94, 95, 96, 97, 98}

    {100, 98, 96, 89, 84, 82, 82, 75, 75, 74, 74, 72, 72, 69, 65, 64, 63, 63, 61, 59, 59, 54, 52, 50, 48, 47, 45, 45, 37, 36, 35, 34, 34, 34, 33, 28, 26, 24, 19, 16, 14, 14, 13, 12, 12, 10, 9, 8, 3, 2}

    Returns: 18.529689260485277

  31. {1, 1, 1, 3, 4, 4, 6, 7, 8, 9, 9, 10, 14, 17, 23, 24, 25, 27, 30, 31, 36, 36, 37, 38, 40, 40, 41, 42, 43, 43, 44, 47, 50, 52, 53, 53, 53, 60, 61, 70, 80, 80, 84, 91, 93, 94, 94, 96, 100, 100}

    {100, 98, 96, 95, 89, 89, 89, 88, 88, 87, 77, 75, 74, 71, 68, 67, 66, 66, 63, 56, 54, 54, 51, 48, 46, 42, 42, 42, 41, 41, 41, 38, 38, 35, 33, 31, 30, 29, 28, 26, 22, 19, 19, 19, 18, 9, 9, 8, 7, 2}

    Returns: 11.704015323361508

  32. {100}

    {100}

    Returns: 149.49999999999994

  33. {23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 27, 27, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28}

    {75, 78, 9, 33, 97, 81, 17, 40, 14, 24, 33, 17, 39, 53, 98, 26, 45, 64, 29, 80, 2, 2, 33, 86, 16, 72, 84, 61, 29, 72, 95, 91}

    Returns: 25.18880410210125

  34. {93, 94, 94, 94, 94, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 96, 96, 96, 96, 96, 96, 96, 96, 96, 97, 97, 97, 97, 97, 97, 97, 97, 97, 98, 98, 98, 98, 98}

    {45, 39, 19, 63, 98, 69, 47, 9, 85, 99, 86, 58, 55, 3, 31, 32, 95, 26, 53, 31, 27, 47, 40, 13, 69, 52, 99, 18, 13, 59, 8, 2, 10, 45, 13, 76, 8, 56}

    Returns: 95.35578965478794

  35. {6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11}

    {16, 27, 46, 33, 11, 91, 43, 44, 28, 47, 19, 19, 73, 61, 98, 58, 1, 91, 34, 81, 49, 88, 67, 44, 9, 24, 22, 28, 4, 83, 37, 13, 3, 98, 11, 82, 60, 84, 3, 57, 87, 50, 18, 49, 2, 4, 84, 89, 33}

    Returns: 6.622558463325687

  36. {45, 45, 45, 45, 45, 45, 46, 46, 46, 47, 47, 47, 47, 48, 48, 48, 48, 48, 49, 49, 50, 50}

    {81, 86, 68, 72, 84, 14, 65, 36, 55, 1, 82, 16, 23, 24, 58, 26, 6, 36, 15, 56, 98, 69}

    Returns: 46.68811382690145

  37. {66, 66, 66, 66, 66, 66, 66, 67, 67, 67, 67, 67, 67, 67, 68, 69, 69, 69, 69, 69, 69, 69, 70, 70, 70, 70, 70, 70, 70, 70, 70, 71, 71, 71, 71}

    {46, 33, 53, 37, 29, 6, 82, 54, 54, 83, 77, 80, 29, 33, 61, 16, 71, 5, 10, 100, 74, 65, 92, 92, 41, 71, 49, 49, 79, 83, 100, 72, 91, 76, 86}

    Returns: 67.5451650715269

  38. {84, 84, 84, 84, 84, 85, 85, 85, 85, 85, 86, 86, 87, 87, 87, 87, 87, 88, 88, 88, 88, 88, 88, 89, 89, 89, 89, 89, 89, 89, 89}

    {70, 28, 88, 43, 87, 40, 42, 1, 12, 33, 20, 39, 69, 69, 70, 54, 53, 63, 78, 72, 65, 34, 98, 4, 15, 31, 48, 31, 14, 31, 9}

    Returns: 84.90730519480522

  39. {36, 36, 36, 36, 36, 37, 37, 38, 38, 38, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40, 41, 41, 41}

    {98, 40, 71, 75, 45, 10, 1, 17, 46, 4, 19, 9, 25, 93, 96, 61, 57, 82, 22, 84, 88, 19, 92}

    Returns: 36.917911021685654

  40. {1, 3, 3, 4, 5, 10, 14, 15, 19, 19, 22, 23, 30, 31, 35, 40, 41, 43, 48, 54, 63, 64, 70, 77, 78, 81, 82, 85, 87, 90, 91, 91, 100}

    {99, 98, 94, 94, 93, 91, 90, 89, 78, 75, 69, 67, 60, 57, 49, 46, 42, 35, 32, 30, 29, 27, 26, 22, 22, 19, 18, 15, 15, 13, 6, 11, 4}

    Returns: 16.787061128399138

  41. {1, 4, 8, 9, 15, 17, 29, 35, 37, 37, 42, 50, 55, 55, 62, 62, 66, 68, 70, 71, 74, 74, 76, 80, 81, 82, 82, 87, 96}

    {93, 90, 85, 83, 77, 76, 69, 65, 59, 58, 58, 48, 46, 41, 31, 36, 29, 25, 24, 23, 23, 18, 16, 13, 13, 10, 9, 5, 1}

    Returns: 20.772667848237646

  42. {1, 3, 7, 13, 15, 16, 20, 23, 24, 30, 30, 31, 32, 38, 39, 41, 45, 48, 48, 49, 49, 49, 54, 56, 56, 62, 63, 64, 66, 66, 68, 77, 78, 78, 78, 79, 85, 87, 89, 90, 93, 93, 94, 96, 96, 99, 100}

    {99, 96, 96, 95, 94, 90, 81, 81, 80, 78, 78, 77, 67, 67, 66, 64, 64, 63, 63, 63, 61, 62, 59, 57, 56, 55, 54, 52, 41, 48, 41, 41, 37, 40, 40, 34, 34, 32, 27, 27, 22, 22, 19, 18, 6, 4, 2}

    Returns: 21.997333779729285

  43. {2, 4, 4, 5, 5, 5, 5, 7, 8, 10, 11, 11, 14, 16, 17, 19, 20, 20, 26, 28, 29, 29, 31, 31, 36, 38, 41, 42, 43, 44, 44, 46, 47, 59, 68, 70, 81, 82, 89, 89, 93, 95, 95}

    {97, 94, 91, 86, 83, 80, 85, 79, 79, 76, 74, 74, 73, 58, 57, 54, 47, 52, 46, 42, 41, 40, 39, 39, 35, 33, 31, 29, 27, 23, 24, 23, 14, 12, 10, 9, 7, 7, 6, 5, 4, 1, 2}

    Returns: 12.394029929909053

  44. {4, 4, 6, 11, 12, 18, 31, 35, 35, 38, 41, 42, 43, 46, 47, 47, 48, 52, 58, 61, 63, 67, 70, 72, 75, 76, 77, 78, 83, 87, 88, 89, 90, 95, 95}

    {91, 97, 90, 88, 78, 78, 74, 74, 74, 74, 71, 68, 66, 66, 62, 65, 62, 61, 57, 54, 53, 46, 40, 37, 36, 25, 14, 13, 9, 6, 6, 4, 3, 2, 1}

    Returns: 21.301360534946262

  45. {1, 3, 4, 4, 8, 12, 17, 17, 21, 25, 25, 26, 27, 40, 45, 46, 48, 57, 61, 64, 65, 70, 79, 84, 89, 95, 96, 98}

    {100, 95, 89, 90, 87, 83, 78, 82, 77, 73, 73, 72, 69, 55, 54, 51, 51, 50, 50, 43, 38, 30, 30, 30, 18, 17, 16, 3}

    Returns: 17.68901250777995

  46. {6, 7, 12, 14, 16, 16, 18, 20, 22, 27, 30, 30, 33, 33, 34, 35, 41, 52, 52, 60, 62, 66, 77, 81, 82, 82, 85, 86, 88, 89, 89, 97}

    {97, 87, 80, 77, 72, 76, 65, 58, 58, 57, 54, 51, 49, 50, 48, 43, 40, 37, 39, 35, 30, 26, 26, 22, 22, 15, 12, 11, 11, 10, 9, 7}

    Returns: 21.9677453820467

  47. {10, 11, 14, 22, 23, 27, 33, 38, 45, 48, 53, 55, 64, 69, 72, 73, 74, 75, 87, 99}

    {98, 96, 88, 82, 75, 58, 56, 55, 52, 50, 47, 45, 39, 33, 30, 29, 19, 14, 13, 4}

    Returns: 29.88911307082131

  48. {12, 13, 14, 24, 30, 32, 37, 39, 41, 43, 46, 50, 54, 60, 65, 66, 76, 84, 87, 90, 92}

    {99, 97, 91, 90, 89, 81, 81, 79, 70, 63, 62, 58, 49, 47, 43, 42, 34, 34, 31, 20, 9}

    Returns: 33.49351871916887

  49. {3, 6, 12, 12, 13, 17, 17, 18, 22, 25, 29, 33, 35, 36, 38, 41, 42, 45, 45, 50, 51, 53, 56, 64, 66, 72, 76, 78, 83, 86, 87, 89}

    {99, 93, 84, 87, 82, 81, 79, 73, 72, 70, 70, 69, 66, 65, 64, 62, 49, 44, 45, 41, 35, 34, 32, 30, 30, 29, 29, 28, 27, 27, 20, 2}

    Returns: 21.417139956850637

  50. {2, 2, 3, 4, 4, 12, 13, 15, 17, 20, 27, 27, 32, 33, 34, 37, 39, 41, 41, 42, 45, 47, 51, 52, 53, 57, 61, 61, 63, 64, 64, 70, 71, 71, 73, 79, 79, 80, 80, 81, 87, 91, 91, 93, 94, 98}

    {37, 48, 48, 28, 57, 94, 81, 93, 42, 3, 91, 63, 18, 100, 76, 87, 25, 23, 96, 59, 18, 39, 46, 39, 17, 31, 63, 30, 36, 52, 23, 50, 64, 100, 96, 73, 53, 55, 81, 23, 48, 30, 88, 1, 6, 24}

    Returns: 9.255337986012337

  51. {6, 6, 10, 12, 13, 15, 21, 21, 22, 24, 26, 33, 35, 36, 36, 37, 39, 39, 47, 47, 48, 53, 53, 54, 61, 73, 74, 75, 86, 86, 86, 88, 90, 90, 91, 91, 91, 92, 96, 98, 99}

    {95, 67, 30, 13, 2, 83, 40, 65, 88, 95, 44, 12, 98, 24, 39, 65, 3, 5, 34, 17, 65, 78, 96, 82, 78, 9, 11, 4, 74, 29, 59, 45, 67, 87, 81, 17, 74, 76, 3, 47, 64}

    Returns: 12.931916127862706

  52. {1, 2, 4, 6, 9, 17, 21, 28, 31, 38, 39, 40, 41, 42, 49, 52, 55, 57, 61, 65, 72, 73, 79, 83, 86, 90, 91, 92, 95, 100}

    {44, 84, 38, 74, 97, 27, 84, 4, 79, 68, 99, 72, 28, 69, 97, 78, 31, 42, 72, 63, 96, 67, 28, 42, 11, 97, 86, 94, 42, 21}

    Returns: 12.673809801946671

  53. {1, 6, 9, 12, 15, 18, 22, 26, 34, 41, 49, 50, 55, 56, 58, 60, 62, 64, 65, 72, 85, 86, 89, 90, 95, 95, 100}

    {31, 30, 99, 6, 6, 1, 39, 33, 57, 32, 11, 77, 96, 3, 6, 88, 53, 94, 45, 9, 49, 91, 45, 64, 33, 23, 42}

    Returns: 12.212798233228337

  54. {1, 4, 6, 9, 10, 11, 12, 12, 18, 18, 22, 27, 30, 31, 32, 33, 38, 42, 44, 46, 50, 52, 58, 59, 61, 64, 64, 65, 69, 70, 72, 77, 80, 81, 83, 86, 89, 92, 92, 93, 93, 96, 97, 99, 99, 99}

    {44, 91, 80, 48, 27, 67, 44, 76, 9, 34, 14, 14, 39, 47, 5, 92, 61, 67, 79, 72, 100, 100, 15, 96, 67, 98, 2, 49, 95, 8, 82, 39, 37, 100, 100, 15, 98, 89, 93, 57, 23, 68, 38, 82, 38, 21}

    Returns: 13.329591479950304

  55. {5, 8, 11, 14, 16, 19, 20, 22, 22, 33, 36, 36, 37, 37, 39, 43, 45, 47, 47, 52, 54, 56, 57, 60, 60, 63, 69, 69, 74, 74, 78, 79, 80, 82, 85, 86, 88, 89, 90, 91, 92, 94, 95, 96, 98, 99}

    {18, 57, 7, 56, 9, 28, 43, 19, 45, 68, 17, 74, 1, 3, 20, 42, 97, 4, 11, 64, 85, 96, 29, 22, 63, 71, 5, 89, 27, 67, 90, 19, 51, 49, 13, 78, 61, 17, 56, 49, 65, 98, 86, 76, 81, 69}

    Returns: 11.971456418824836

  56. {3, 6, 9, 18, 18, 23, 29, 31, 35, 37, 44, 47, 47, 52, 57, 60, 66, 70, 74, 77, 80, 81, 84, 90, 91, 92, 95, 100}

    {71, 97, 35, 69, 27, 82, 95, 97, 43, 62, 48, 1, 98, 7, 95, 53, 22, 90, 84, 41, 6, 88, 25, 78, 69, 17, 99, 77}

    Returns: 19.273510498721205

  57. {2, 3, 7, 7, 8, 11, 14, 15, 20, 21, 21, 22, 23, 26, 35, 38, 42, 49, 49, 51, 52, 56, 59, 61, 65, 66, 67, 73, 76, 79, 80, 85, 85, 86, 86, 86, 90, 92, 93}

    {28, 54, 60, 70, 97, 86, 10, 43, 5, 63, 50, 98, 92, 30, 42, 82, 94, 23, 52, 22, 86, 6, 8, 89, 19, 68, 59, 21, 64, 70, 52, 47, 20, 1, 70, 47, 20, 7, 49}

    Returns: 11.749158702991217

  58. {3, 4, 4, 8, 14, 17, 21, 22, 24, 28, 29, 29, 32, 35, 40, 41, 43, 45, 50, 59, 60, 62, 64, 67, 71, 71, 71, 74, 80, 82, 85, 88, 90, 91, 95, 98}

    {57, 29, 98, 40, 73, 94, 73, 65, 49, 25, 29, 84, 47, 68, 10, 28, 38, 100, 93, 26, 42, 20, 79, 71, 37, 5, 41, 35, 48, 68, 78, 57, 13, 95, 67, 45}

    Returns: 13.078037766830878

  59. {1, 1, 5, 6, 7, 7, 10, 12, 13, 21, 21, 24, 28, 28, 32, 32, 34, 34, 35, 35, 37, 43, 46, 50, 52, 53, 57, 61, 70, 71, 71, 74, 80, 81, 84, 85, 90, 91, 91, 91, 93, 94, 95, 96, 100}

    {76, 40, 6, 22, 53, 48, 3, 39, 41, 22, 10, 22, 54, 46, 7, 81, 97, 59, 41, 94, 9, 16, 64, 35, 84, 95, 70, 78, 13, 19, 38, 65, 33, 32, 5, 95, 11, 94, 17, 67, 25, 64, 82, 23, 7}

    Returns: 6.663808043035869

  60. {2, 8, 13, 18, 22, 31, 57, 62, 68, 81, 89, 100}

    {34, 47, 55, 18, 46, 86, 26, 77, 58, 87, 16, 17}

    Returns: 16.092365456821035

  61. {39, 50, 76, 81}

    {16, 9, 33, 84}

    Returns: 46.499999999999986

  62. {6, 8, 10, 21, 26, 28, 35, 46, 52, 53, 69, 71, 82, 85, 86, 92, 93}

    {97, 3, 7, 39, 87, 68, 82, 87, 99, 83, 79, 85, 19, 73, 50, 55, 54}

    Returns: 8.945017182130583

  63. {44, 49, 96}

    {82, 66, 23}

    Returns: 70.60569105691056

  64. {32, 42, 43, 45, 57, 62, 96}

    {1, 73, 18, 31, 23, 66, 93}

    Returns: 32.0

  65. {19, 74}

    {26, 23}

    Returns: 31.5

  66. {7, 8, 13, 20, 42, 44, 46, 50, 66, 73, 74, 79, 99}

    {78, 16, 76, 97, 83, 4, 15, 55, 85, 43, 74, 2, 14}

    Returns: 14.761755651147102

  67. {3, 3, 4, 6, 8, 14, 19, 28, 28, 31, 34, 35, 38, 41, 44, 49, 57, 61, 69, 83, 84, 92}

    {27, 43, 45, 44, 5, 32, 91, 62, 7, 34, 60, 84, 85, 9, 78, 99, 79, 44, 1, 42, 29, 9}

    Returns: 8.472543871096843

  68. {10, 31, 35, 38, 44, 57, 62, 63, 76, 80, 80, 85, 92}

    {73, 92, 82, 16, 35, 67, 13, 24, 20, 28, 62, 99, 72}

    Returns: 40.356060881186544

  69. {2, 29, 73, 75, 92, 98, 100}

    {93, 56, 24, 44, 100, 79, 27}

    Returns: 42.059139784946225

  70. {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 }

    {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 }

    Returns: 1.0

  71. {1}

    {1}

    Returns: 1.0

  72. {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 }

    {100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100 }

    Returns: 2.502288483693653

  73. {100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100 }

    {100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100 }

    Returns: 101.50228848369363

  74. {100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91 }

    {100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91 }

    Returns: 95.84844007905724

  75. {72, 52, 7, 79, 39, 13, 96, 76, 83, 60, 77, 48, 69, 16, 36, 34, 65, 10, 50, 99, 59, 7, 92, 94, 42, 19, 49, 94, 37, 24, 82, 12, 52, 22, 18, 17, 30, 73, 71, 25, 38, 56, 44, 35, 49, 99, 61, 51, 86, 3 }

    {40, 49, 90, 29, 56, 38, 8, 100, 82, 47, 44, 3, 77, 63, 72, 81, 89, 1, 93, 20, 21, 84, 19, 92, 87, 66, 82, 45, 52, 89, 99, 65, 39, 28, 42, 12, 96, 46, 56, 98, 11, 34, 30, 6, 87, 95, 86, 1, 26, 39 }

    Returns: 9.753622303622302

  76. {91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100 }

    {13, 14, 13, 15, 17, 16, 14, 15, 16, 18, 19, 13, 12, 15, 16, 18, 19, 15, 14, 13, 13, 12, 16, 17, 19, 15, 13, 14, 12, 13, 14, 16, 17, 19, 13, 12, 11, 15, 18, 12, 14, 11, 12, 18, 15, 13, 16, 12, 14, 18 }

    Returns: 92.20126250177353

  77. {51, 52, 53, 54, 55, 56, 57, 58, 59, 60 }

    {4, 3, 7, 6, 2, 2, 2, 3, 4, 10 }

    Returns: 52.16666666666666

  78. {82, 88, 75, 81, 100, 75, 89, 89, 93, 85, 76, 76, 72, 98, 72, 82, 96, 73, 98, 77, 92, 95, 73, 74, 93, 93, 92, 97, 79, 76, 88, 77, 82, 89, 80, 93, 88, 90, 96, 95, 94, 92, 73, 74, 74, 85, 92, 72, 94, 99 }

    {88, 85, 93, 98, 98, 90, 94, 92, 90, 99, 87, 76, 91, 83, 89, 87, 81, 73, 75, 99, 97, 86, 91, 80, 81, 91, 77, 92, 74, 79, 80, 94, 95, 75, 77, 91, 87, 97, 82, 99, 95, 80, 97, 84, 88, 99, 79, 83, 80, 82 }

    Returns: 78.77480732166114

  79. {59, 41, 79, 76, 92, 50, 99, 20, 61, 59, 41, 79, 76, 92, 50, 99, 20, 61, 59, 41, 79, 76, 92, 50, 99, 20, 61, 59, 41, 79, 76, 92, 50, 99, 20, 61, 59, 41, 79, 76, 92, 50, 99, 20, 61 }

    {50, 51, 50, 53, 78, 50, 51, 50, 53, 78, 50, 51, 50, 53, 78, 50, 51, 50, 53, 78, 50, 51, 50, 53, 78, 50, 51, 50, 53, 78, 50, 51, 50, 53, 78, 50, 51, 50, 53, 78, 50, 51, 50, 53, 78 }

    Returns: 28.590306079664565

  80. {5, 6, 7, 5, 5, 5, 20, 19, 18, 17 }

    {10, 9, 8, 10, 10, 10, 20, 21, 22, 23 }

    Returns: 6.329133333333333

  81. {5, 10, 3, 1 }

    {7, 8, 20, 4 }

    Returns: 2.5

  82. {10, 20, 30, 40 }

    {40, 30, 20, 10 }

    Returns: 26.64166666666666

  83. {5, 2 }

    {100, 100 }

    Returns: 36.318999999999974

  84. {100, 4, 3, 2, 5, 76, 23, 54, 32, 12, 54, 23, 43, 77, 88, 59, 90, 65, 22, 11, 4, 6, 7, 8, 5, 4, 2, 23, 2, 14, 56, 44, 22 }

    {1, 3, 6, 50, 100, 43, 22, 11, 56, 53, 22, 11, 90, 32, 11, 34, 54, 32, 33, 11, 22, 33, 44, 52, 11, 3, 45, 23, 11, 44, 66, 22, 4 }

    Returns: 3.7913388429752075

  85. {70, 20, 30, 40 }

    {40, 30, 70, 10 }

    Returns: 34.1595238095238

  86. {1, 2, 3 }

    {10, 8, 3 }

    Returns: 3.1499999999999995

  87. {20, 30, 10, 50, 10, 59, 29, 17, 38, 29, 17, 39, 20, 17 }

    {80, 23, 29, 38, 18, 47, 17, 29, 19, 29, 39, 19, 39, 10 }

    Returns: 16.60373385367439

  88. {100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91 }

    {100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91 }

    Returns: 95.84844007905724

  89. {72, 52, 7, 79, 39, 13, 96, 76, 83, 60, 77, 48, 69, 16, 36, 34, 65, 10, 50, 99, 59, 7, 92, 94, 42, 19, 49, 94, 37, 24, 82, 12, 52, 22, 18, 17, 30, 73, 71, 25, 38, 56, 44, 35, 49, 99, 61, 51, 86, 3 }

    {40, 49, 90, 29, 56, 38, 8, 100, 82, 47, 44, 3, 77, 63, 72, 81, 89, 1, 93, 20, 21, 84, 19, 92, 87, 66, 82, 45, 52, 89, 99, 65, 39, 28, 42, 12, 96, 46, 56, 98, 11, 34, 30, 6, 87, 95, 86, 1, 26, 39 }

    Returns: 9.753622303622302

  90. {91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100 }

    {13, 14, 13, 15, 17, 16, 14, 15, 16, 18, 19, 13, 12, 15, 16, 18, 19, 15, 14, 13, 13, 12, 16, 17, 19, 15, 13, 14, 12, 13, 14, 16, 17, 19, 13, 12, 11, 15, 18, 12, 14, 11, 12, 18, 15, 13, 16, 12, 14, 18 }

    Returns: 92.20126250177353

  91. {51, 52, 53, 54, 55, 56, 57, 58, 59, 60 }

    {4, 3, 7, 6, 2, 2, 2, 3, 4, 10 }

    Returns: 52.16666666666666

  92. {82, 88, 75, 81, 100, 75, 89, 89, 93, 85, 76, 76, 72, 98, 72, 82, 96, 73, 98, 77, 92, 95, 73, 74, 93, 93, 92, 97, 79, 76, 88, 77, 82, 89, 80, 93, 88, 90, 96, 95, 94, 92, 73, 74, 74, 85, 92, 72, 94, 99 }

    {88, 85, 93, 98, 98, 90, 94, 92, 90, 99, 87, 76, 91, 83, 89, 87, 81, 73, 75, 99, 97, 86, 91, 80, 81, 91, 77, 92, 74, 79, 80, 94, 95, 75, 77, 91, 87, 97, 82, 99, 95, 80, 97, 84, 88, 99, 79, 83, 80, 82 }

    Returns: 78.77480732166114

  93. {59, 41, 79, 76, 92, 50, 99, 20, 61, 59, 41, 79, 76, 92, 50, 99, 20, 61, 59, 41, 79, 76, 92, 50, 99, 20, 61, 59, 41, 79, 76, 92, 50, 99, 20, 61, 59, 41, 79, 76, 92, 50, 99, 20, 61 }

    {50, 51, 50, 53, 78, 50, 51, 50, 53, 78, 50, 51, 50, 53, 78, 50, 51, 50, 53, 78, 50, 51, 50, 53, 78, 50, 51, 50, 53, 78, 50, 51, 50, 53, 78, 50, 51, 50, 53, 78, 50, 51, 50, 53, 78 }

    Returns: 28.590306079664565

  94. {5, 6, 7, 5, 5, 5, 20, 19, 18, 17 }

    {10, 9, 8, 10, 10, 10, 20, 21, 22, 23 }

    Returns: 6.329133333333333

  95. {5, 10, 3, 1 }

    {7, 8, 20, 4 }

    Returns: 2.5

  96. {10, 20, 30, 40 }

    {40, 30, 20, 10 }

    Returns: 26.64166666666666

  97. {5, 2 }

    {100, 100 }

    Returns: 36.318999999999974

  98. {100, 4, 3, 2, 5, 76, 23, 54, 32, 12, 54, 23, 43, 77, 88, 59, 90, 65, 22, 11, 4, 6, 7, 8, 5, 4, 2, 23, 2, 14, 56, 44, 22 }

    {1, 3, 6, 50, 100, 43, 22, 11, 56, 53, 22, 11, 90, 32, 11, 34, 54, 32, 33, 11, 22, 33, 44, 52, 11, 3, 45, 23, 11, 44, 66, 22, 4 }

    Returns: 3.7913388429752075

  99. {70, 20, 30, 40 }

    {40, 30, 70, 10 }

    Returns: 34.1595238095238

  100. {1, 2, 3 }

    {10, 8, 3 }

    Returns: 3.1499999999999995

  101. {20, 30, 10, 50, 10, 59, 29, 17, 38, 29, 17, 39, 20, 17 }

    {80, 23, 29, 38, 18, 47, 17, 29, 19, 29, 39, 19, 39, 10 }

    Returns: 16.60373385367439

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: