Statistics

Problem Statement for "InverseCollatz"

Problem Statement

Given a positive integer j greater than 1, the corresponding Collatz sequence is produced by repeatedly applying f to j (and continues even after we reach 1). The function f behaves as follows: 
             { x/2    if x is even
   f(x)  =   {
             { 3x+1   if x is odd
Suppose someone began with the value y and has started (but not necessarily finished) generating the Collatz sequence. Each time they apply f they write down 'E' or 'O' to denote whether the argument was even or odd, respectively. Given the String s they have written down, you must return a String of the form (quotes for clarity) "ak+b". Here a and b are integers with no extra leading zeros. The returned string must make the following set the collection of all possible numbers that could have begun the sequence: 
	P = { ak + b | k >= 0 and ak + b > 1}
If there are multiple possible return values, choose the one with b minimal.

Definition

Class:
InverseCollatz
Method:
getForm
Parameters:
String
Returns:
String
Method signature:
String getForm(String s)
(be sure your method is public)

Constraints

  • s will contain between 1 and 50 characters, inclusive.
  • Each character in s will be 'E' or 'O'.
  • An 'O' will never be immediately followed by another 'O' in s.

Examples

  1. "EOEEEOEOEEEOEOEEOEEOEO"

    Returns: "32768k+30138"

  2. "OEEEEOEOEEEOEOEEOEOE"

    Returns: "8192k+4197"

  3. "EOEEEEEEEEOEOEOEOEEEOEE"

    Returns: "131072k+13482"

  4. "EOEOEEOEOEOEEOEEOEEOEEEOEOEEEEOEOEOEEOE"

    Returns: "33554432k+31532726"

  5. "OEOEEEEOEEOEOEEEOEEE"

    Returns: "16384k+6915"

  6. "OEEOEOEOEOEEEEOEEEOEOEEEEEE"

    Returns: "524288k+497513"

  7. "OEEEOEEOEOEOEEEEEEEEOEEEEOEEOEE"

    Returns: "8388608k+7526253"

  8. "EEEEEEOEOEOEOEOEOEOEOEO"

    Returns: "32768k+32704"

  9. "EOEOEEOEEEOEEOEOEEOEEEEEEEEOEEEOEEEEOEE"

    Returns: "536870912k+9580054"

  10. "OEEOEOEEOEOEOEOEOEOEEEE"

    Returns: "16384k+8569"

  11. "EEEEOEEOEEOEOEEEOEOE"

    Returns: "16384k+528"

  12. "OEEOEEOEOEOEEEEEEEEEOEEOEEOEEE"

    Returns: "4194304k+1562209"

  13. "EEOEOEEOEEOEEEEEEEEOEOEOEEEOEEOEOEEOEOEOEOEOEOEOEO"

    Returns: "8589934592k+6324799660"

  14. "EEOEEEEOEOEEEEOEEEEOEEEEEEOEOEEEEEEE"

    Returns: "536870912k+172078484"

  15. "OEEEOEOEEEOEOEOEOEEEOEOEOEEOEOEEO"

    Returns: "2097152k+127197"

  16. "EEOEEEEEEEOEEOEEOEOEEOEOEEEEOEOEE"

    Returns: "16777216k+11823956"

  17. "EEOEEEOEEEEEOEOEEEEEOEOEOEEOEEEEOEOE"

    Returns: "67108864k+9222708"

  18. "OEOEOEOEOEOEOEOEEEOEOEOEOEOEOE"

    Returns: "65536k+56575"

  19. "OEOEOEEEOEOEOEEOEOEOEOEOEEEOEOEOEOEOEEEOEEOEOE"

    Returns: "134217728k+130016567"

  20. "OEEEEOEEOEEEEOEOEOEOEOEEEEOEOEEEEEEOEEEEEEOEE"

    Returns: "8589934592k+1408901381"

  21. "EOEEOEOEEEOEEOEEEEOEOEOEOEOEEOEOEEOEOEEOEEEE"

    Returns: "536870912k+326134066"

  22. "OEOEOEOEEOEOEOEEEOEEEEEOEEEOEOEOEOEEOEE"

    Returns: "33554432k+17798127"

  23. "EOEEOEOEOEEOEEEOEEOEOEOEEOEEEEEOEEEOEOE"

    Returns: "67108864k+3911698"

  24. "OEOEEOEOEEOEOEEEOEOEEOEOEEOEOEOEEEE"

    Returns: "4194304k+1435131"

  25. "EOEEOEOEEEOEOEOEEEEOEOEEEOEEEEOEOE"

    Returns: "8388608k+6722098"

  26. "OEOEEEEEOEOEOEEEOEOEEOEEOEEEEOEEEOEOEE"

    Returns: "67108864k+9070755"

  27. "EEEOEOEEOEOEEOEOEOEEEOEOEOEE"

    Returns: "262144k+63448"

  28. "EEOEEEEEEOEOEEOEOEOEOEOEOEOEOEEEEEEEE"

    Returns: "67108864k+14310996"

  29. "EEOEOEEEOEOEEOEOEOEOEEOEEOEOEOEOEOEO"

    Returns: "4194304k+1770572"

  30. "EEOEEOEOEOEEEEOEEOEOEOEEEEEE"

    Returns: "1048576k+714532"

  31. "EEE"

    Returns: "8k+0"

    The argument was even 3 times in a row, so the original value was a positive multiple of 8.

  32. "OE"

    Returns: "2k+1"

    The initial number had to be odd. After multiplying by 3 and adding 1, the next value will definitely be even.

  33. "OEO"

    Returns: "4k+3"

  34. "EEEEOEEEEOEEEEOEEEEOEEEEOEEEEOEEEEOEEEEOEEEEOEEEEO"

    Returns: "2199023255552k+1014933810256"

  35. "EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE"

    Returns: "1125899906842624k+0"

  36. "OEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE"

    Returns: "562949953421312k+375299968947541"

  37. "OEOEOEOEOEOEOEOEOEOEOEOEOEOEOEOEOEOEOEOEOEOEOEOEOE"

    Returns: "33554432k+33554431"

  38. "OEOEEOEEEOEEEEOEEEEEOEEEEEEOEEEEOEEOEEEEEOEEEEEEEE"

    Returns: "1099511627776k+728557408267"

  39. "EOEEEOEEEEOEOEEEEEEOEEEEEEOEOEEOEOEOEOEEEEEEEOEOEE"

    Returns: "137438953472k+110210109978"

  40. "EEEEOEEEEOEEEEOEEEEOEEEEOEEEEOEEEEOEEEEOEEEEOEEEEO"

    Returns: "2199023255552k+1014933810256"

  41. "OEOEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEO"

    Returns: "2199023255552k+1343847545059"

  42. "OEEE"

    Returns: "8k+5"

  43. "EEOEOEOEOEOEOEOEOEOEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEO"

    Returns: "2199023255552k+1731857897468"

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