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Problem Statement for "DigitFiller"

Problem Statement

You have k objects divided evenly into num piles. Unfortunately, some of the digits of k may have been erased (replaced with 'X's in the input). Return the number of possible values that k could have been.

Definition

Class:
DigitFiller
Method:
howMany
Parameters:
String, int
Returns:
long
Method signature:
long howMany(String k, int num)
(be sure your method is public)

Constraints

  • k will contain between 2 and 18 characters inclusive.
  • Each character in k will be a digit ('0'-'9') or 'X'.
  • Character 0 of k will be a positive digit ('1'-'9').
  • num will be between 1 and 10000 inclusive.
  • The return value will be at least 1.

Examples

  1. "8X"

    9

    Returns: 1

    Since the objects are divided evenly into 9 piles, 81 is the only possible solution.

  2. "1XX"

    10

    Returns: 10

    Here there are 10 possible values k could have been.

  3. "14"

    7

    Returns: 1

    None of the digits are missing.

  4. "9999999999999X"

    3

    Returns: 4

  5. "23X34XX24XX34X"

    17

    Returns: 58823

  6. "9XXXXXXXXXXXXXXXXX"

    1

    Returns: 100000000000000000

  7. "9X9X"

    9999

    Returns: 1

  8. "7XXX"

    7234

    Returns: 1

  9. "123829382XX"

    99

    Returns: 1

  10. "3X8XXX99X04XXXXX7X"

    8543

    Returns: 11705428

  11. "70XX3XXX7X1"

    6563

    Returns: 150

  12. "9X5X4XXX883X61X6X"

    9099

    Returns: 10990

  13. "33X78X0131XX2X"

    8758

    Returns: 12

  14. "5X11087XX5XX"

    7880

    Returns: 11

  15. "5XXX34XX27"

    3399

    Returns: 29

  16. "4346XX7X"

    89

    Returns: 10

  17. "73X3X06X5XXX"

    6035

    Returns: 140

  18. "28XXX2"

    3448

    Returns: 1

  19. "28X5XX3X7XX15XXX"

    8107

    Returns: 123372

  20. "5X84XXXX"

    4531

    Returns: 23

  21. "9227XXXX"

    2986

    Returns: 4

  22. "66XX665XXXXX5XX3"

    3227

    Returns: 309886

  23. "9XXXXX8"

    4052

    Returns: 49

  24. "3X46XXX31XX2X3XX6"

    6116

    Returns: 326988

  25. "74XX66X13XXX0"

    1769

    Returns: 566

  26. "9XX56X8X3XX"

    3296

    Returns: 293

  27. "65X6XX2X"

    119

    Returns: 80

  28. "68XXXX6XXXXX"

    9138

    Returns: 109433

  29. "4XXXXXX"

    1632

    Returns: 613

  30. "2X5XXX319X22XX8XXX"

    8114

    Returns: 1232437

  31. "5X812XXX"

    2751

    Returns: 5

  32. "13XXXX"

    2282

    Returns: 5

  33. "23XXX8XXXX"

    175

    Returns: 57143

  34. "7XXX2X5713XX2"

    4116

    Returns: 485

  35. "3XXX0X52X7X80X1XX"

    6376

    Returns: 150610

  36. "2XX9X3XXXX9"

    1567

    Returns: 6381

  37. "72XXX2XXX6"

    8319

    Returns: 123

  38. "3XX8X9XX88X9X2XXX"

    2690

    Returns: 3717482

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