Rhyme Schemes
| Time Limit: 1000MS | Memory Limit: 10000K | |||
| Total Submissions: 674 | Accepted: 376 | Special Judge | ||
Description
The
rhyme scheme for a poem (or stanza of a longer poem) tells which lines
of the poem rhyme with which other lines. For example, a limerick such
as If computers that you build are quantum
Then spies of all factions will want 'em
Our codes will all fail
And they'll read our email
`Til we've crypto that's quantum and daunt 'em
Jennifer and Peter Shor (http://www.research.att.com/~shor/notapoet.html)
Has a rhyme scheme of aabba, indicating that the first, second and fifth lines rhyme and the third and fourth lines rhyme.
For a poem or stanza of four lines, there are 15 possible rhyme schemes:
aaaa, aaab, aaba, aabb, aabc, abaa, abab, abac, abba, abbb, abbc, abca, a bcb, abcc, and abcd.
Write a program to compute the number of rhyme schemes for a poem or stanza of N lines where N is an input value.
Then spies of all factions will want 'em
Our codes will all fail
And they'll read our email
`Til we've crypto that's quantum and daunt 'em
Jennifer and Peter Shor (http://www.research.att.com/~shor/notapoet.html)
Has a rhyme scheme of aabba, indicating that the first, second and fifth lines rhyme and the third and fourth lines rhyme.
For a poem or stanza of four lines, there are 15 possible rhyme schemes:
aaaa, aaab, aaba, aabb, aabc, abaa, abab, abac, abba, abbb, abbc, abca, a bcb, abcc, and abcd.
Write a program to compute the number of rhyme schemes for a poem or stanza of N lines where N is an input value.
Input
Input
will consist of a sequence of integers N, one per line, ending with a 0
(zero) to indicate the end of the data. N is the number of lines in a
poem.
Output
For
each input integer N, your program should output the value of N,
followed by a space, followed by the number of rhyme schemes for a poem
with N lines as a decimal integer with at least 12 correct significant
digits (use double precision floating point for your computations).
Sample Input
1
2
3
4
20
30
10
0
Sample Output
1 1
2 2
3 5
4 15
20 51724158235372
30 846749014511809120000000
10 115975
Source
