Composer

PROBLEM STATEMENT

A chord progression is a sequence of symbols representing chords, delimited by
the '-' character.  Write a method that determines if a chord progression is
valid, according to the following rules:

- A progression must be in either a major or minor key
If the progression is in a major key, the only allowable chord symbols are
(quotes are for clarification only):
    The tonic chord: "I"
    The dominant chords: "viio", "V"
    The predominant chords: "ii", "IV"
    The six chord: "vi"
  If the progression is in a minor key, the only allowable chord symbols are:
    The tonic chord: "i"
    The dominant chords: "viio", "V"
    The predominant chords: "iio", "iv"
    The six chord: "VI"
- The last symbol must be a tonic chord
- No single chord may appear 3 or more times in a row
- A dominant chord must be immediately followed by a tonic chord, a six chord,
or another dominant chord
- A predominant chord must be immediately followed by a dominant chord or
another predominant chord
- A six chord must be immediately followed by a predominant chord or another
six chord
- A tonic chord may be followed by any chord


DEFINITION
Class: Composer
Method Name: isValid
Parameters: String
Returns: boolean
Method signature (be sure your method is public):  boolean isValid(String
chords);


NOTES
TopCoder will ensure the validity of the inputs.  Inputs are valid if all of
the following criteria are met:
- chords contains between 1 and 50 characters, inclusive
- chords contains only valid chord symbols and the character '-'.  chords will
begin and end with a valid chord symbol, and consecutive chord symbols will be
separated by a single '-'.  The valid chord symbols are "i", "I", "ii", "iio",
"iv", "IV", "V", "vi", "VI", and "viio".


Examples:
"iv-V-I"     returns false because it is not in either a major or minor key
"I-I-I"      returns false because the "I" chord is repeated 3 times in a row
"V-viio-V-I" returns true.  Even though there are 3 dominant chords in a row,
no single chord is repeated 3 times in a row
"I-IV-V"     returns false because the last symbol is not a tonic chord
"I-IV-I"     returns false because a predominant chord is immediately followed
by a tonic chord
"I-I-IV-V-I" returns true