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Problem Statement for "DigitStringDiv2"

Problem Statement

You are given a digit string S and a positive integer integer X. We want to select a non-empty contiguous substring of S such that:

  • The substring does not begin with the digit '0'.
  • When you convert it to a number, its value is strictly greater than X.

Two ways of selecting a substring are different if they begin or end at a different index.

Compute and return the number of ways in which we can select a substring with the above properties.

Definition

Class:
DigitStringDiv2
Method:
count
Parameters:
String, int
Returns:
int
Method signature:
int count(String S, int X)
(be sure your method is public)

Constraints

  • S will contain between 1 and 9 characters, inclusive.
  • Each character of S will be a digit ('0'-'9').
  • X will be between 0 and 777,444,111, inclusive.

Examples

  1. "0"

    1

    Returns: 0

  2. "10"

    9

    Returns: 1

  3. "471"

    47

    Returns: 2

    We can select either the substring "471" or the substring "71".

  4. "0"

    777444111

    Returns: 0

  5. "000000000"

    777444111

    Returns: 0

  6. "999999999"

    777444111

    Returns: 1

  7. "00030"

    708253

    Returns: 0

  8. "000589"

    691668

    Returns: 0

  9. "0008409"

    610805

    Returns: 0

  10. "00015496"

    307266

    Returns: 0

  11. "000953561"

    714547

    Returns: 1

  12. "45"

    0

    Returns: 3

  13. "589"

    0

    Returns: 6

  14. "8860"

    0

    Returns: 9

  15. "20463"

    0

    Returns: 11

  16. "322395"

    0

    Returns: 21

  17. "782984137"

    44633

    Returns: 14

  18. "731477481"

    25708

    Returns: 14

  19. "350085176"

    52176

    Returns: 8

  20. "203417351"

    33007

    Returns: 9

  21. "080852803"

    29582

    Returns: 7

  22. "970233950"

    84993

    Returns: 9

  23. "289775158"

    40240

    Returns: 14

  24. "528797331"

    67759

    Returns: 13

  25. "658448500"

    44534

    Returns: 15

  26. "672236426"

    24987

    Returns: 13

  27. "00007000"

    7

    Returns: 3

  28. "2222"

    97

    Returns: 3

    We can select the entire string S ("2222"). We also have two different ways to select the string "222": either we choose the first three or the last three characters of S

  29. "09"

    1

    Returns: 1

  30. "009"

    8

    Returns: 1

  31. "10100607"

    6

    Returns: 15

  32. "02355653"

    2

    Returns: 27

  33. "0011"

    1

    Returns: 1

  34. "9"

    0

    Returns: 1

  35. "009"

    1

    Returns: 1

  36. "02"

    1

    Returns: 1

  37. "1001177"

    90

    Returns: 8

  38. "1099"

    9

    Returns: 4

  39. "000000009"

    0

    Returns: 1

  40. "0022220"

    10000

    Returns: 1

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