Statistics

Problem Statement for "TippingWaiters"

Problem Statement

In a restaurant, if you were pleased by the waiter's service, you may leave him a tip -- you pay him more than the actual value of the bill, and the waiter keeps the excess money. In some countries, not leaving a tip for the waiter is even considered impolite. During my recent holiday I was having dinner in a foreign restaurant. The pamphlet from my travel agency informed me that the proper way of tipping the waiter is the following:
  • The sum I pay must be round, i.e., divisible by 5.
  • The tip must be between 5% and 10% of the final sum I pay, inclusive.
Clearly, sometimes there may be multiple "correct" ways of settling the bill. I'd like to know exactly how many choices I have in a given situation. I could program it easily, but I was having a holiday... and so it's you who has to solve this task. You will be given:
  • an int bill -- the amount I have to pay for the dinner
  • an int cash -- the amount of money I have in my pocket
Write a function that computes how many different final sums satisfy the conditions above.

Definition

Class:
TippingWaiters
Method:
possiblePayments
Parameters:
int, int
Returns:
int
Method signature:
int possiblePayments(int bill, int cash)
(be sure your method is public)

Notes

  • Assume that both bill and cash are in dollars.
  • All the money I have is in one-dollar banknotes.

Constraints

  • bill and cash are between 1 and 2,000,000,000, inclusive.
  • bill doesn't exceed cash.

Examples

  1. 4

    100

    Returns: 0

    4 isn't a round sum, and 5 is too much.

  2. 23

    100

    Returns: 1

    The only correct choice is to pay 25 dollars, thus leaving a tip of 2 dollars.

  3. 23

    24

    Returns: 0

    The same bill, but I don't have enough money to leave an appropriate tip.

  4. 220

    239

    Returns: 1

    This time, it is appropriate to pay either 235 or 240 dollars. Sadly, I don't have enough money for the second possibility.

  5. 1234567

    12345678

    Returns: 14440

    A large bill, but with that much money I don't care.

  6. 1880000000

    1980000000

    Returns: 210527

  7. 1

    2000000000

    Returns: 0

  8. 2000000000

    2000000000

    Returns: 0

  9. 1000000000

    2000000000

    Returns: 11695907

  10. 1800000000

    2000000000

    Returns: 21052632

  11. 21345

    21532156

    Returns: 250

  12. 1

    1

    Returns: 0

  13. 1

    2

    Returns: 0

  14. 1

    5

    Returns: 0

  15. 5

    5

    Returns: 0

  16. 5

    10

    Returns: 0

  17. 10000

    100000

    Returns: 117

  18. 10000

    11000

    Returns: 95

  19. 123456789

    234567890

    Returns: 1443940

  20. 123456789

    133456789

    Returns: 700455

  21. 17100

    19000

    Returns: 201

  22. 17100

    18000

    Returns: 1

  23. 171000000

    181000000

    Returns: 200001

  24. 171000000

    190000000

    Returns: 2000001

  25. 171000000

    189999999

    Returns: 2000000

  26. 171000000

    180000001

    Returns: 1

  27. 171000000

    179999999

    Returns: 0

  28. 1880000000

    1980000000

    Returns: 210527

  29. 2000000

    2000000000

    Returns: 23392

  30. 1

    2000000000

    Returns: 0

  31. 1234567

    12345678

    Returns: 14440

  32. 23

    100

    Returns: 1

  33. 190

    200

    Returns: 1

  34. 1900000000

    2000000000

    Returns: 1

  35. 1500000000

    2000000000

    Returns: 17543860

  36. 188084

    1980605100

    Returns: 2200

  37. 18800000

    1980000000

    Returns: 219883

  38. 199999999

    199999999

    Returns: 0

  39. 18

    1980605100

    Returns: 1

  40. 1750000000

    2000000000

    Returns: 20467836

  41. 1900

    1000000

    Returns: 23

  42. 100

    2000000000

    Returns: 1

  43. 1645665466

    1999999999

    Returns: 19247549

  44. 19

    164

    Returns: 1

  45. 3243642

    2000000000

    Returns: 37938

  46. 1000000000

    2000000000

    Returns: 11695907

  47. 5

    200000000

    Returns: 0

  48. 100

    200

    Returns: 1

  49. 23

    2000000000

    Returns: 1

  50. 855

    1980000000

    Returns: 11

  51. 950

    20000

    Returns: 12

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