Letter Sequence Analysis

Time Limit: 1 Second    Memory Limit: 32768 KB

Cryptographic analysis makes extensive use of the frequency with which letters and letter sequences occur in a language. If an encrypted text is known to be in english, for example, a great deal can be learned from the fact that the letters E, L, N, R, S, and T are the most common ones used in written english. Even more can be learned if common letter pairs, triplets, etc. are known.

For this problem you are to write a program which accepts as input a text file of unspecified length and performs letter sequence analysis on the text. The program will report the five most frequent letter sequences for each set of sequences from one to five letters. That is it will report the individual characters which occur with the five highest frequencies, the pairs of characters which occur with the five highest frequencies, and so on up to the letter sequences of five characters which occur with the five highest frequencies.

Input

The program should consider contiguous sequences of alphabetic characters only, and case should be ignored (e.g. an `a' is the same as an `A'). A report should be produced using the format shown in the example at the end of this problem description.

Output

For each sequence length from one to five, the report should list the sequences in descending order of frequency. If there are several sequences with the same frequency then all sequences should be listed in alphabetical order as shown (list all sequences in upper case). Finally, if there are less than five distinct frequencies for a particular sequence length, simply report as many distinct frequency lists as possible.

Sample Input

Peter Piper Picks Pickles!
Cryptographic analysis makes extensive use of the frequency with which letters 
and letter sequences occur in a language. If an encrypted text is known to be 
in english, for example, a great deal can be learned from the fact that the letters 
E, L, N, R, S, and T are the most common ones used in written english. Even more 
can be learned if common letter pairs, triplets, etc. are known.
For this problem you are to write a program which accepts as input a text file 
of unspecified length and performs letter sequence analysis on the text. The 
program will report the five most frequent letter sequences for each set of 
sequences from one to five letters. That is it will report the individual characters 
which occur with the five highest frequencies, the pairs of characters which 
occur with the five highest frequencies, and so on up to the letter sequences 
of five characters which occur with the five highest frequencies.

The program should consider contiguous sequences of alphabetic characters only, 
and case should be ignored (e.g. an `a' is the same as an `A'). A report should 
be produced using the format shown in the example at the end of this problem 
description.

For each sequence length from one to five, the report should list 
the sequences in descending order of frequency. If there are several sequences 
with the same frequency then all sequences should be listed in alphabetical 
order as shown (list all sequences in upper case). Finally, if there are less 
than five distinct frequencies for a particular sequence length, simply report 
as many distinct frequency lists as possible.

Sample Output

Analysis for Letter Sequences of Length 1
-----------------------------------------
Frequency = 5, Sequence(s) = (P)
Frequency = 4, Sequence(s) = (E)
Frequency = 3, Sequence(s) = (I)
Frequency = 2, Sequence(s) = (C,K,R,S)
Frequency = 1, Sequence(s) = (L,T)

Analysis for Letter Sequences of Length 2
-----------------------------------------
Frequency = 3, Sequence(s) = (PI)
Frequency = 2, Sequence(s) = (CK,ER,IC,PE)
Frequency = 1, Sequence(s) = (ES,ET,IP,KL,KS,LE,TE)

Analysis for Letter Sequences of Length 3
-----------------------------------------
Frequency = 2, Sequence(s) = (ICK,PIC)
Frequency = 1, Sequence(s) = (CKL,CKS,ETE,IPE,KLE,LES,PER,PET,PIP,TER)

Analysis for Letter Sequences of Length 4
-----------------------------------------
Frequency = 2, Sequence(s) = (PICK)
Frequency = 1, Sequence(s) = (CKLE,ETER,ICKL,ICKS,IPER,KLES,PETE,PIPE)

Analysis for Letter Sequences of Length 5
-----------------------------------------
Frequency = 1, Sequence(s) = (CKLES,ICKLE,PETER,PICKL,PICKS,PIPER)

Analysis for Letter Sequences of Length 1
-----------------------------------------
Frequency = 201, Sequence(s) = (E)
Frequency = 112, Sequence(s) = (T)
Frequency = 96, Sequence(s) = (S)
Frequency = 90, Sequence(s) = (R)
Frequency = 84, Sequence(s) = (N)

Analysis for Letter Sequences of Length 2
-----------------------------------------
Frequency = 37, Sequence(s) = (TH)
Frequency = 33, Sequence(s) = (EN)
Frequency = 27, Sequence(s) = (HE)
Frequency = 24, Sequence(s) = (RE)
Frequency = 23, Sequence(s) = (NC)

Analysis for Letter Sequences of Length 3
-----------------------------------------
Frequency = 24, Sequence(s) = (THE)
Frequency = 21, Sequence(s) = (ENC,EQU,QUE,UEN)
Frequency = 12, Sequence(s) = (NCE,SEQ,TER)
Frequency = 9, Sequence(s) = (CES,FRE,IVE,LET,REQ,TTE)
Frequency = 8, Sequence(s) = (ETT,FIV)

Analysis for Letter Sequences of Length 4
-----------------------------------------
Frequency = 21, Sequence(s) = (EQUE,QUEN)
Frequency = 20, Sequence(s) = (UENC)
Frequency = 12, Sequence(s) = (ENCE,SEQU)
Frequency = 9, Sequence(s) = (FREQ,NCES,REQU)
Frequency = 8, Sequence(s) = (ETTE,FIVE,LETT,TTER)

Analysis for Letter Sequences of Length 5
-----------------------------------------
Frequency = 21, Sequence(s) = (EQUEN)
Frequency = 20, Sequence(s) = (QUENC)
Frequency = 12, Sequence(s) = (SEQUE,UENCE)
Frequency = 9, Sequence(s) = (ENCES,FREQU,REQUE)
Frequency = 8, Sequence(s) = (ETTER,LETTE)

Submit

Source: Mid-Central USA 1995