一道ACM题目,看不懂1026 Major ScalesTimeLimit :1 Second Memorylimit :32 Megabyte Totalsubmit :37 Accepted :20In music,the range of audible frequencies is divided into octaves,where each octave spans frequencies within factor of 2 of one another

一道ACM题目,看不懂1026 Major ScalesTimeLimit :1 Second Memorylimit :32 Megabyte Totalsubmit :37 Accepted :20In music,the range of audible frequencies is divided into octaves,where each octave spans frequencies within factor of 2 of one another
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.

一道ACM题目,看不懂1026 Major ScalesTimeLimit :1 Second Memorylimit :32 Megabyte Totalsubmit :37 Accepted :20In music,the range of audible frequencies is divided into octaves,where each octave spans frequencies within factor of 2 of one another
这道题目和乐理有关系.题目大意是输入一串或多串半音符序列(每串用一行表示,每个半音符间用空格隔开),然后程序要判断每串音符可能采用了哪些调号,再输出(每个调号间用空格隔开).
1) 半音符序列为:C C# D D# E F F# G G# A A# B C .(每两个代号之间相差半音)
2) 大调音阶(major scale)的定义:可以任何一个半音符开始(此半音符即称为此串音符的调号)的由8个半音符组成的任意排序的序列,但这8个半音符是根据"全音-全音-半音-全音-全音-全音-半音"这个规律来挑选的.即第一个半音符与第二个半音符之间相差全音(即两个半音),第二音与第三音间也是相差全音,第三音与第四音间相差半音,如此类推.
所以,程序应该先根据以上先定义出所有可能的大调音阶(major scale),如:
C大调(the major scale in the key of C)由以下8个半音符组成:
C D E F G A B C
C#大调:C# D# F F# G# A# C C#
D大调:D E F# G A B C# D
.
题目所举例子的解释:
第一行:C C D F E G A A F G B,去除重复的半音符后剩下C D E F G A B,然后程序与所有的大调比较,发现能全部包括这7个半音符的调号只有C,所以输出"C"
第二行:A B C D E F G C#,程序与所有的大调比较,发现没有一个调号的大调能全部包括这8个半音符,所以输出为空
第三行:C C D F E G A A F G,去除重复的半音符后剩下C D E F G A,然后程序与所有的大调比较,发现能全部包括这6个半音符的调号有C和F,所以输出"C F"
第四行:C C C C C,去除重复的半音符后剩下C,然后程序与所有的大调比较,发现能包括这一个半音符的调号有C,C#,D#,F,G,G#,A#这7种,所以输出"C C# D# F G G# A#"