Statistics

Problem Statement for "CarrotJumping"

Problem Statement

Rabbits often feel hungry, so when they go out to eat carrots, they jump as quickly as possible.

Initially, rabbit Hanako stands at position init. From position x, she can jump to either position 4*x+3 or 8*x+7 in a single jump. She can jump at most 100,000 times because she gets tired by jumping.

Carrots are planted at position x if and only if x is divisible by 1,000,000,007 (i.e. carrots are planted at position 0, position 1,000,000,007, position 2,000,000,014, and so on). Return the minimal number of jumps required to reach a carrot. If it's impossible to reach a carrot using at most 100,000 jumps, return -1.

Definition

Class:
CarrotJumping
Method:
theJump
Parameters:
int
Returns:
int
Method signature:
int theJump(int init)
(be sure your method is public)

Constraints

  • init will be between 1 and 1,000,000,006, inclusive.

Examples

  1. 125000000

    Returns: 1

    She can jump from 125000000 to 1000000007.

  2. 281250001

    Returns: 2

    281250001 -> 1125000007 -> 9000000063

  3. 974579565

    Returns: -1

  4. 18426114

    Returns: 58

  5. 4530664

    Returns: 478

  6. 610

    Returns: -1

  7. 754

    Returns: -1

  8. 5000000000

    Returns: -1

  9. 579739909

    Returns: 99999

  10. 289869954

    Returns: 99999

  11. 644934980

    Returns: 99999

  12. 822467493

    Returns: 100000

  13. 411233746

    Returns: 100000

  14. 705616876

    Returns: 100000

  15. 852808441

    Returns: -1

    She can't reach any carrot by making at most 100,000 jumps.

  16. 426404220

    Returns: -1

  17. 713202113

    Returns: -1

  18. 356601056

    Returns: -1

  19. 678300531

    Returns: -1

  20. 339150265

    Returns: -1

  21. 1000000006

    Returns: -1

  22. 500000003

    Returns: -1

  23. 250000001

    Returns: 1

  24. 125000000

    Returns: 1

  25. 562500003

    Returns: 2

  26. 281250001

    Returns: 2

  27. 140625000

    Returns: 2

  28. 570312503

    Returns: 3

  29. 285156251

    Returns: 3

  30. 142578125

    Returns: 3

  31. 71289062

    Returns: 4

  32. 535644534

    Returns: 4

  33. 673399480

    Returns: 31975

  34. 610100046

    Returns: 24047

  35. 315802756

    Returns: 86744

  36. 225937957

    Returns: 72060

  37. 496178545

    Returns: 61128

  38. 453035285

    Returns: 32514

  39. 47858586

    Returns: 23997

  40. 480799171

    Returns: 82231

  41. 828067259

    Returns: 62445

  42. 895255719

    Returns: 30132

  43. 454540134

    Returns: 62962

  44. 900327479

    Returns: 91701

  45. 239594710

    Returns: -1

  46. 49592320

    Returns: -1

  47. 686088966

    Returns: -1

  48. 935467456

    Returns: -1

  49. 642858708

    Returns: -1

  50. 129938307

    Returns: -1

  51. 735946623

    Returns: -1

  52. 774009307

    Returns: -1

  53. 830378328

    Returns: -1

  54. 464244557

    Returns: -1

  55. 14646281

    Returns: -1

  56. 20735299

    Returns: -1

  57. 10000

    Returns: -1

  58. 1000170

    Returns: 6191

  59. 777

    Returns: -1

  60. 1

    Returns: -1

  61. 987654321

    Returns: -1

  62. 750000006

    Returns: -1

  63. 2

    Returns: -1

  64. 1000000004

    Returns: -1

  65. 251132667

    Returns: 479

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