Statistics

Problem Statement for "PersistentNumber"

Problem Statement

Given a number x, we can define p(x) as the product of the digits of x. We can then form a sequence x, p(x), p(p(x))... The persistence of x is then defined as the index (0-based) of the first single digit number in the sequence. For example, using 99, we get the sequence 99, 9*9 = 81, 8*1 = 8. Thus, the persistence of 99 is 2. You will be given n, and you must return its persistence.

Definition

Class:
PersistentNumber
Method:
getPersistence
Parameters:
int
Returns:
int
Method signature:
int getPersistence(int n)
(be sure your method is public)

Constraints

  • n will be between 0 and 2,000,000,000, inclusive.

Examples

  1. 99

    Returns: 2

    The example from the problem statement.

  2. 268

    Returns: 4

    The sequence here is 268, 96, 54, 20, 0.

  3. 6

    Returns: 0

    6 is already a single-digit number.

  4. 68889789

    Returns: 3

  5. 86898

    Returns: 7

  6. 438939648

    Returns: 9

  7. 999888664

    Returns: 3

  8. 1999826842

    Returns: 9

  9. 1804289383

    Returns: 1

  10. 846930886

    Returns: 1

  11. 1681692777

    Returns: 5

  12. 1714636915

    Returns: 2

  13. 1957747793

    Returns: 2

  14. 424238335

    Returns: 2

  15. 719885386

    Returns: 2

  16. 596516649

    Returns: 2

  17. 1189641421

    Returns: 4

  18. 44897763

    Returns: 2

  19. 1131176229

    Returns: 3

  20. 749241873

    Returns: 8

  21. 1632621729

    Returns: 3

  22. 1141616124

    Returns: 3

  23. 1998898814

    Returns: 5

  24. 1947346619

    Returns: 5

  25. 791698927

    Returns: 4

  26. 1117142618

    Returns: 6

  27. 434248626

    Returns: 4

  28. 1431419379

    Returns: 4

  29. 476667372

    Returns: 5

  30. 296864819

    Returns: 5

  31. 1111783898

    Returns: 5

  32. 1344247686

    Returns: 5

  33. 474613996

    Returns: 5

  34. 77211388

    Returns: 6

  35. 733327814

    Returns: 7

  36. 1669679262

    Returns: 6

  37. 164826621

    Returns: 7

  38. 717293418

    Returns: 7

  39. 67874133

    Returns: 7

  40. 1424321892

    Returns: 7

  41. 993683397

    Returns: 8

  42. 1999337836

    Returns: 8

  43. 1137638147

    Returns: 7

  44. 384696634

    Returns: 8

  45. 1743768897

    Returns: 8

  46. 894661689

    Returns: 9

  47. 362447374

    Returns: 8

  48. 232787891

    Returns: 8

  49. 1698842299

    Returns: 9

  50. 928398892

    Returns: 9

  51. 983866662

    Returns: 9

  52. 1896918466

    Returns: 9

  53. 349638498

    Returns: 9

  54. 4

    Returns: 0

  55. 9

    Returns: 0

  56. 0

    Returns: 0

  57. 1234567890

    Returns: 1

  58. 10

    Returns: 1

  59. 99

    Returns: 2

  60. 6

    Returns: 0

  61. 25

    Returns: 2

  62. 9

    Returns: 0

  63. 1043

    Returns: 1

  64. 0

    Returns: 0

  65. 33

    Returns: 1

  66. 11

    Returns: 1

  67. 268

    Returns: 4

  68. 1099

    Returns: 1

  69. 1

    Returns: 0

  70. 52

    Returns: 2

  71. 41025

    Returns: 1

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