问题描述：
一道ACM题目,看不懂
1026 Major ScalesTimeLimit :1 Second Memorylimit :32 Megabyte
Totalsubmit :37 Accepted :20
In music,the range of audible frequencies is divided into octaves,where each octave spans frequencies within factor of 2 of one another.For example,the note called middle C corresponds to an audio frequency of 263 Hz.The octave below middle C spans the frequency range from 131.5 Hz to 263 Hz while the octave above middle C spans the range from 263 Hz to 526 Hz.
An octave contains 13 chromatic notes whose frequencies differ by a common ratio.The separation between two adjacent chromatic notes is called a half-step or semi-tone.Note that there are 12 semi-tones in an octave and therefore the frequency ratio represented by a semi-tone is 1.0593 (since 1.0593^12 = 2).A tone is two semi-tones.
While it might be convenient to use frequencies to describe musical notes,historical tradition demands that we name the notes of the chromatic scale,in order:C,C#,D,D#,E,F,F#,G,G#,A,A#,B,C,and so on,repeating the same names for each new octave.
Western music rarely uses all the notes in the chromatic scale.Instead,8 of the 13 chromatic notes are commonly used a composition.The most common such set of 8 notes is the major scale.The 8 notes of a major scale,in order,are separated by:tone,tone,semi-tone,tone,tone,tone,semi-tone.A major scale can begin with any of the chromatic notes; this note defines the key of the scale.Coincidentally,in the key of C,the major scale consists of the notes:C,D,E,F,G,A,B,C.On the other hand,in the key of F,the major scale is:F,G,A,A#,C,D,E,F.
There are other scales,notably the minor scale,and music composed in a particular scale sometimes uses notes that are not within the scale,caled accidentals.We shall concern ourselves only with music composed in a major scale with no accidentals.
Your job is to read a sequence of notes and to identify all the keys that the music might have been composed in.Your program need not have any musical ear:report a particular key if and only if all the notes come from the major scale in that key.
Input
Input contains several test cases.Each test case consists of a single line of input,containing a sequence of chromatic notes separated by white space.No input line exceeds 1000 characters.The last line of input contains the word "END".
Output
For each test case,output a line giving the possible keys,in the order given above.
Sample Input
C C D F E G A A F G B
A B C D E F G C#
C C D F E G A A F G
C C C C C
END
Sample Output
C
C F
C C# D# F G G# A#
题目大概看懂了,不过它问的是什么还不清楚.
而且为什么输入有四个,输出却只有三个.
1026 Major ScalesTimeLimit :1 Second Memorylimit :32 Megabyte
Totalsubmit :37 Accepted :20
In music,the range of audible frequencies is divided into octaves,where each octave spans frequencies within factor of 2 of one another.For example,the note called middle C corresponds to an audio frequency of 263 Hz.The octave below middle C spans the frequency range from 131.5 Hz to 263 Hz while the octave above middle C spans the range from 263 Hz to 526 Hz.
An octave contains 13 chromatic notes whose frequencies differ by a common ratio.The separation between two adjacent chromatic notes is called a half-step or semi-tone.Note that there are 12 semi-tones in an octave and therefore the frequency ratio represented by a semi-tone is 1.0593 (since 1.0593^12 = 2).A tone is two semi-tones.
While it might be convenient to use frequencies to describe musical notes,historical tradition demands that we name the notes of the chromatic scale,in order:C,C#,D,D#,E,F,F#,G,G#,A,A#,B,C,and so on,repeating the same names for each new octave.
Western music rarely uses all the notes in the chromatic scale.Instead,8 of the 13 chromatic notes are commonly used a composition.The most common such set of 8 notes is the major scale.The 8 notes of a major scale,in order,are separated by:tone,tone,semi-tone,tone,tone,tone,semi-tone.A major scale can begin with any of the chromatic notes; this note defines the key of the scale.Coincidentally,in the key of C,the major scale consists of the notes:C,D,E,F,G,A,B,C.On the other hand,in the key of F,the major scale is:F,G,A,A#,C,D,E,F.
There are other scales,notably the minor scale,and music composed in a particular scale sometimes uses notes that are not within the scale,caled accidentals.We shall concern ourselves only with music composed in a major scale with no accidentals.
Your job is to read a sequence of notes and to identify all the keys that the music might have been composed in.Your program need not have any musical ear:report a particular key if and only if all the notes come from the major scale in that key.
Input
Input contains several test cases.Each test case consists of a single line of input,containing a sequence of chromatic notes separated by white space.No input line exceeds 1000 characters.The last line of input contains the word "END".
Output
For each test case,output a line giving the possible keys,in the order given above.
Sample Input
C C D F E G A A F G B
A B C D E F G C#
C C D F E G A A F G
C C C C C
END
Sample Output
C
C F
C C# D# F G G# A#
题目大概看懂了,不过它问的是什么还不清楚.
而且为什么输入有四个,输出却只有三个.
问题解答：
我来补答展开全文阅读