Statistics

Problem Statement for "AlternateOddEven"

Problem Statement

Consider all the positive integers with the property that their digits alternate between being odd and even. The sequence of these numbers begins as follows:

1, 2, ..., 9, 10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, ..., 96, 98, 101, 103, 105, 107, 109, 121, 123, ..., 187, 189, 210, 212, ...


Given K, which is the K-th number in this sequence?

Definition

Class:
AlternateOddEven
Method:
kth
Parameters:
long
Returns:
long
Method signature:
long kth(long K)
(be sure your method is public)

Notes

  • The answer for each valid test case is guaranteed to fit into a signed 64-bit integer.

Constraints

  • K will be between 1 and 10^11, inclusive.

Examples

  1. 9

    Returns: 9

    The first nine numbers in our sequence (positions 1 to 9) are the nine one-digit positive integers.

  2. 15

    Returns: 21

    The next six numbers (in positions 10 to 15) are 10, 12, 14, 16, 18, 21.

  3. 62

    Returns: 125

  4. 100

    Returns: 290

  5. 100000000000

    Returns: 2107276767676781

  6. 99999999978

    Returns: 2107276767676587

  7. 18875212

    Returns: 8503690525

  8. 1023996291

    Returns: 2967018549052

  9. 12707531

    Returns: 5234109012

  10. 31725021040

    Returns: 387652981054141

  11. 29

    Returns: 49

  12. 9

    Returns: 9

  13. 6

    Returns: 6

  14. 6131922347

    Returns: 36927252785474

  15. 225203

    Returns: 16181296

  16. 1593537724

    Returns: 5238721090569

  17. 27

    Returns: 45

  18. 28249938

    Returns: 16303676327

  19. 24203

    Returns: 654387

  20. 20

    Returns: 30

  21. 10031887

    Returns: 3850787834

  22. 59295962

    Returns: 49056743434

  23. 18265785185

    Returns: 167490909010321

  24. 109426

    Returns: 5678183

  25. 63637

    Returns: 2905834

  26. 938

    Returns: 6327

  27. 26384464

    Returns: 14325278529

  28. 199646

    Returns: 12561872

  29. 18123077

    Returns: 8107616385

  30. 7643600085

    Returns: 50125238169430

  31. 377978

    Returns: 34965496

  32. 724

    Returns: 4569

  33. 132257987

    Returns: 143436325634

  34. 340368

    Returns: 30563656

  35. 1106362559

    Returns: 3250301878309

  36. 4774

    Returns: 63878

  37. 98

    Returns: 276

  38. 32413536401

    Returns: 412549450129892

  39. 929407952

    Returns: 2569610925294

  40. 24

    Returns: 38

  41. 68330759201

    Returns: 987618145274383

  42. 4380811

    Returns: 989070323

  43. 186479

    Returns: 10741498

  44. 31260564

    Returns: 18769416329

  45. 11086

    Returns: 234523

  46. 8250481215

    Returns: 54565898567450

  47. 1225

    Returns: 8581

  48. 1728

    Returns: 14587

  49. 40339881793

    Returns: 527894783096147

  50. 989772

    Returns: 125052965

  51. 4

    Returns: 4

  52. 304494134

    Returns: 498723292909

  53. 34945035

    Returns: 23630309030

  54. 284009

    Returns: 23870909

  55. 1395

    Returns: 9870

  56. 33653524580

    Returns: 432589278361410

  57. 99899899933

    Returns: 2105874545276307

  58. 9879876789

    Returns: 69214321836129

  59. 1000000000

    Returns: 2921676767690

  60. 626

    Returns: 3692

  61. 1234567890

    Returns: 3810923052941

  62. 54

    Returns: 98

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