Statistics

Problem Statement for "NonDeterministicSubstring"

Problem Statement

You are given two Strings: A and B. Each character in A is either '0' or '1'. Each character in B is '0', '1', or '?'.


A string C matches B if we can change B into C by changing each '?' in B either to '0' or to '1'. Different occurrences of '?' may be changed to different digits. For example, C = "0101" matches B = "01??". Note that each character in C must be either '0' or '1', there cannot be any '?' remaining.


Consider all possible strings that match B. How many of these strings occur as a (contiguous) substring in A? Compute and return their number. Note that we only count each good string once, even if it has multiple occurrences in A.

Definition

Class:
NonDeterministicSubstring
Method:
ways
Parameters:
String, String
Returns:
long
Method signature:
long ways(String A, String B)
(be sure your method is public)

Constraints

  • A will contain between 1 and 50 characters, inclusive.
  • B will contain between 1 and 50 characters, inclusive.
  • Each character in A will be '0' or '1'.
  • Each character in B will be '0', '1' or '?'.

Examples

  1. "00010001"

    "??"

    Returns: 3

    There are four strings that match B: the strings "00", "01", "10", and "11". Out of these, the string "11" does not occur in A as a substring. The other three do occur, hence the answer is 3.

  2. "00000000"

    "??0??0"

    Returns: 1

    There are 16 different strings that match B, but out of those only the string "000000" is a substring of A.

  3. "001010101100010111010"

    "???"

    Returns: 8

    Each of the 8 strings that match B occurs somewhere in A.

  4. "00101"

    "??????"

    Returns: 0

    Here, the length of B is greater than the length of A. Clearly, a string that matches this B cannot be a substring of this A.

  5. "1101010101111010101011111111110001010101"

    "???????????????????????????????????"

    Returns: 6

  6. "1100011000010000001011000010101110110"

    "?011101??000?0"

    Returns: 0

  7. "0010111100001001111111010101001000"

    "1?100???00??1???000"

    Returns: 0

  8. "01001001111011101100010010111111001111111110101110"

    "10?1111"

    Returns: 2

  9. "1110110111001001110001001101000011011111101100001"

    "0"

    Returns: 1

  10. "101101101010100101100100011111001100111010110"

    "?10100?1?0110?00100?1???01??1100"

    Returns: 0

  11. "00100011100011000110111010011011011000001"

    "11111?110010?001?1100?01001111110110"

    Returns: 0

  12. "0100000010111001010101"

    "0110?1000"

    Returns: 0

  13. "11001111000001"

    "10001011?10?"

    Returns: 0

  14. "1000001011111000000111101001101001111"

    "010101?"

    Returns: 0

  15. "1111011111001010001111101000100111011110101011010"

    "10111?11?110????010?0110??01100??0?1?0?1000000?"

    Returns: 0

  16. "11111110011100000110000101111010001110100110"

    "0???01???????"

    Returns: 3

  17. "1111011000"

    "0?1?????0"

    Returns: 0

  18. "1010011100001000101101010101"

    "????????????????0??????"

    Returns: 2

  19. "11100000110110100000111100111100011110011101010101"

    "????0?????10????????0"

    Returns: 1

  20. "111101011101010110000000110101100111110"

    "10??1?0??1???1??"

    Returns: 0

  21. "111100001111000110001"

    "?????????0????1??"

    Returns: 0

  22. "11010000111100001011100111101011000001111100010001"

    "????"

    Returns: 16

  23. "01110000110001110001101111000011"

    "???????????0?0??1?0"

    Returns: 0

  24. "1110011111100010011101101100010000101111110"

    "1???????0?0??????0?????????1???????0??"

    Returns: 0

  25. "11000000001101100010000101000100011111000010000"

    "???10????1"

    Returns: 2

  26. "1011111111110111101000001110101011100000010"

    "??????1??"

    Returns: 18

  27. "001111010111011011100000101111111110"

    "1?????1??????????????0??00?????????"

    Returns: 0

  28. "00111011111110110011010101110111001011110001101110"

    "????1?????0"

    Returns: 12

  29. "110011011001011111110100011101100"

    "?00?????0????1??1???????1???1?0??"

    Returns: 0

  30. "0010010011000001000000011001111000111000111"

    "??0??1????00?"

    Returns: 1

  31. "000010011110111000"

    "??0?1?????"

    Returns: 3

  32. "110101111101010000010100111110111010100"

    "????????1????11???????????0????"

    Returns: 0

  33. "110101111110000001010100101011111"

    "????0??????????????1??????"

    Returns: 2

  34. "011100101001010110010001011000011101"

    "???0?1?????????????????????????????"

    Returns: 1

  35. "0011100011011000101010000101011010"

    "0????????????????1?????"

    Returns: 2

  36. "00000000100"

    "?????????"

    Returns: 3

  37. "0011001000100"

    "????????"

    Returns: 6

  38. "000000000100001000000001000011000000000010000"

    "??????0?????????????????????"

    Returns: 15

  39. "0100010000000000"

    "?????????"

    Returns: 7

  40. "000000000000000000000100000000000010"

    "?"

    Returns: 2

  41. "0000100000001000000010010001000000100000000"

    "0"

    Returns: 1

  42. "000000000100010000010001000100"

    "???????????????"

    Returns: 16

  43. "00001000"

    "??????"

    Returns: 3

  44. "000000010000000000000"

    "?????"

    Returns: 6

  45. "000010000000000000001"

    "?????????????"

    Returns: 7

  46. "011"

    "?00"

    Returns: 0

  47. "1111111111111111111111111111111111111111"

    "????????????????????????????????????????"

    Returns: 1

  48. "10"

    "01"

    Returns: 0

  49. "0"

    "????"

    Returns: 0

  50. "10101"

    "1????"

    Returns: 1

  51. "0101010101010111100101010"

    "??"

    Returns: 4

  52. "100"

    "?1?"

    Returns: 0

  53. "1111"

    "0000"

    Returns: 0

  54. "0001"

    "01"

    Returns: 1

  55. "0"

    "0"

    Returns: 1

  56. "000"

    "11?"

    Returns: 0

  57. "11111"

    "11"

    Returns: 1

  58. "10101010101010101010101010101010101010101010101010"

    "??????????????????????????????????????????????????"

    Returns: 1

  59. "11111111111111111111111111111111111111111111111"

    "???????????????????????????????????????????11"

    Returns: 1

  60. "01"

    "01"

    Returns: 1

  61. "00010001"

    "10"

    Returns: 1

  62. "01"

    "?1"

    Returns: 1

  63. "00"

    "?"

    Returns: 1

  64. "011110"

    "10"

    Returns: 1

  65. "11"

    "01"

    Returns: 0

  66. "00"

    "11"

    Returns: 0

  67. "0000000"

    "??"

    Returns: 1

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