Statistics

Problem Statement for "BaseMystery"

Problem Statement

The base of a number system is the number of different values each digit can represent. For example, in base-2 (binary), there are 2 values each digit can take: 0 and 1. In base-10, a digit can take values 0 through 9, inclusive. Sometimes, it is difficult to determine which base a numerical expression is in. An equation is valid for a given base if all of the digits are less than the base, and the numerical meaning of the equation is correct. For example, "1+1=10" for base-10 satisfies the rule that the digits are all less than 10, but 1+1 = 2 in base-10, so the equation is not correct for base-10.

If we assume that the characters '0'-'9' represent the values 0 - 9, and the characters 'A'-'J' represent the values 10 - 19, then we can represent numbers with a base up to 20. The equation will be in the following form: 

<num>+<num>=<num>

Where each <num> is a String consisting of characters '0'-'9' and 'A'-'J', which does not have any extra leading zeros, and is at most 5 digits long.

Given an equation as defined above, you should return which bases in the range of 2 to 20, inclusive, are valid for the equation. Return the bases in a int[] in ascending order.

Definition

Class:
BaseMystery
Method:
getBase
Parameters:
String
Returns:
int[]
Method signature:
int[] getBase(String equation)
(be sure your method is public)

Constraints

  • equation will be of the form "+="
  • Each in equation will have between 1 and 5 characters, inclusive.
  • Each in equation will consist only of numeric digits '0' - '9' and capital letters 'A' - 'J', and will not have extra leading zeros.

Examples

  1. "1+1=2"

    Returns: { 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

    The only base which this does not work for is base-2. In base 2, 2 is represented by "10"

  2. "1+1=10"

    Returns: { 2 }

    The same equation valid for base 2.

  3. "1+1=3"

    Returns: { }

    1+1 is never 3, no matter what base you are in.

  4. "ABCD+211=B000"

    Returns: { 14 }

    In base-14, the digits are 0-9, A-D. Adding one to the ones column yields 10 base-14, which carries over to make the 10's column a 'D'. Adding 1 to that column yields 10 again, which carries and makes the 100's column a 'C'. Adding 2 to C yields 10 again, which adds 1 to the 1000's column, resulting in B000.

  5. "ABCD+322=B000"

    Returns: { 15 }

    For base-15, we have increased the number required to wrap to 0 by 1.

  6. "1+0=1"

    Returns: { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

    This is valid for all bases.

  7. "GHIJ+1111=HJ00"

    Returns: { 20 }

  8. "1234+8765=9999"

    Returns: { 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

  9. "1234+8766=10000"

    Returns: { 10 }

  10. "JJJJ+JJJJ=1JJJI"

    Returns: { 20 }

  11. "A9A9A+9A9A9=JJJJJ"

    Returns: { 20 }

  12. "I63+81G=1780"

    Returns: { 19 }

  13. "28H77+E8=7D37C"

    Returns: { }

  14. "E8+CDJE=CEE2"

    Returns: { 20 }

  15. "9+4FAIH=4FAJ6"

    Returns: { 20 }

  16. "F4+AH1=BC5"

    Returns: { 20 }

  17. "JB+11H9=F9F"

    Returns: { }

  18. "4CCF+4=4CD0"

    Returns: { 19 }

  19. "6+I3=I9"

    Returns: { 19, 20 }

  20. "6F+I=7D"

    Returns: { 20 }

  21. "8+A78=A85"

    Returns: { 11 }

  22. "JI+A14=EDGD"

    Returns: { }

  23. "26C+G20EA=G2323"

    Returns: { 19 }

  24. "7B+I23E3=I242E"

    Returns: { 19 }

  25. "I0HE+6=I0I1"

    Returns: { 19 }

  26. "9+D82=D8B"

    Returns: { 14, 15, 16, 17, 18, 19, 20 }

  27. "5+5499=549E"

    Returns: { 15, 16, 17, 18, 19, 20 }

  28. "3+1=4"

    Returns: { 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

  29. "94529+58=94581"

    Returns: { 16 }

  30. "E+3D8=2J1A3"

    Returns: { }

  31. "BE+7FB=875"

    Returns: { 20 }

  32. "BI2B2+3I7DJ=2"

    Returns: { }

  33. "29+8=37"

    Returns: { 10 }

  34. "FI+64B7=6575"

    Returns: { 20 }

  35. "AJBD+3BF=B338"

    Returns: { 20 }

  36. "7H+JE6=71"

    Returns: { }

  37. "J+B21=BF"

    Returns: { }

  38. "27829+B=27831"

    Returns: { 19 }

  39. "1GGH+H36=2F14"

    Returns: { 19 }

  40. "IE30+I9H8=1I518"

    Returns: { 19 }

  41. "JH+I40=J3H"

    Returns: { 20 }

  42. "H1FI+73FHA=81HE9"

    Returns: { 19 }

  43. "ACC4+329C7=3D46B"

    Returns: { 18 }

  44. "JHEGI+JF1=JIEBJ"

    Returns: { 20 }

  45. "E+B21C=B227"

    Returns: { 19 }

  46. "G04+CCHJ=D8I3"

    Returns: { 20 }

  47. "34G74+G=1027"

    Returns: { }

  48. "9F+2BDA=2B2D"

    Returns: { }

  49. "C+603=60F"

    Returns: { 16, 17, 18, 19, 20 }

  50. "E+H7AD=H7B7"

    Returns: { 20 }

  51. "F248G+8AC=F2D2B"

    Returns: { 17 }

  52. "C3+4F6D=4G1G"

    Returns: { 17 }

  53. "G24+F=G32"

    Returns: { 17 }

  54. "DFF+E6=ED4"

    Returns: { 17 }

  55. "2JB2+AF58H=17"

    Returns: { }

  56. "9+23=32"

    Returns: { 10 }

  57. "B0+JAGF=JB7F"

    Returns: { 20 }

  58. "873+1GICD=1H80G"

    Returns: { 19 }

  59. "BFA2E+33C=BFD66"

    Returns: { 20 }

  60. "D+AE=BC"

    Returns: { 15 }

  61. "69+7F7=84G"

    Returns: { 17 }

  62. "1234+8765=9999"

    Returns: { 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

  63. "0+0=0"

    Returns: { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

  64. "1+A=0"

    Returns: { }

  65. "1A+1=2"

    Returns: { }

  66. "1+1=2"

    Returns: { 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

  67. "A+0=A"

    Returns: { 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

  68. "9+3=2"

    Returns: { }

  69. "FFFF+1=FFFG"

    Returns: { 17, 18, 19, 20 }

  70. "A+2=11"

    Returns: { 11 }

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