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  1. -- caesarsolver.hs
  2. -- this is part one of the optional programming assignment for the
  3. -- Stanford Univerity Introduction to Artificial Intelligence class
  4. -- it solves a rotating or caesar cypher by using the probabilities 
  5. -- of three letter trigrams for the english language. 
  6. -- All 26 rotations are generated, scored and the top 3 most likely
  7. -- candidates are displayed. Apologies for the Haskell, it's my first program
  8. --
  9. -- source for trigram data is here: http://h...content-available-to-author-only...l.org/~cowan/trigrams
  10. -- the trigram data is read from input
  11. -- PAC 9th January, 2012
  12.  
  13. import Data.Char (ord, chr, isUpper, isLower, toLower, isLetter, toUpper)
  14. import Data.List (sortBy)
  15. import Data.Ord (comparing)
  16. import qualified Data.Map as M
  17. import System.IO
  18. import System.Environment
  19. import Control.Monad
  20.  
  21. -- define a datatype for our map of trigram frequencies for clarity
  22. type TrigramFrequencies = M.Map String Int
  23.  
  24. -- datatype for a scored string
  25. type ScoredString = ( Double, String )
  26.  
  27. -- the code to break
  28. defaultEncodedMsg = "Esp qtcde nzyqpcpynp zy esp ezatn zq Lcetqtntlw Tyepwwtrpynp hld spwo le Olcexzfes Nzwwprp ty estd jplc."
  29.  
  30. -- Shifts a character to the right if positive, left if negative. Wraps around.
  31. shift :: Int -> Char -> Char -- Modulus handles the wraparound(shift 1 'z' = 'a')
  32. shift n c 	| isUpper c = chr $ ord 'A' + ((ord c + n - ord 'A') `mod` 26)
  33. 		| isLower c = chr $ ord 'a' + ((ord c + n - ord 'a') `mod` 26)
  34.           	| otherwise = c 
  35.  
  36. -- shifts input string by n
  37. shiftString:: Int -> String -> String
  38. shiftString n = map (shift n)
  39.  
  40. --parse a line from the trigams data file into a tuple of trigram and frequency per 10000 words
  41. parseTrigram:: String -> [ (String,Int) ]
  42. parseTrigram contents = [ lineToTuple( words x ) | x <- lines(contents), head x /= ';' ]
  43.       where lineToTuple [ trigram, frequency ] = ( trigram, read frequency :: Int)
  44.  
  45. -- loads the trigram frequency data into a Map for fast lookup
  46. -- source for trigram data is here: http://h...content-available-to-author-only...l.org/~cowan/trigrams
  47. -- we read it in from stdin
  48. -- returns an IO action yielding a Map containing a trigram and it's frequency per 10000 words
  49. loadTrigrams:: IO (TrigramFrequencies)
  50. loadTrigrams = fmap (M.fromList . parseTrigram) getContents
  51.  
  52. -- preprocess our string for trigram lookup. Converts all non letters to # and the rest to uppercase
  53. preprocessText:: String -> String
  54. preprocessText text = map processChar text
  55.          where processChar c = if isLetter c then toUpper c else '#'
  56.  
  57. -- split a string into character trigrams
  58. splitIntoTrigrams:: String -> [String] 
  59. splitIntoTrigrams str = [ take 3 $ drop x str | x <- [ 0 .. (length str - 3) ] ]
  60.  
  61. -- lookup the trigram frequencies per 10000 words. If not found it will return 0
  62. lookupTrigramFrequency:: TrigramFrequencies -> String -> Int
  63. lookupTrigramFrequency trigramFrequencies trigram = M.findWithDefault 0 trigram trigramFrequencies
  64.  
  65. -- converts a letter frequency into a probability using laplace smoothing so we don't end up with
  66. -- trigrams that were not found borking our calculations (due to multiplying by 0)
  67. laplaceSmoothedProbability:: Int -> Int -> Int -> Double
  68. laplaceSmoothedProbability frequency totalCategories k = (fromIntegral(frequency) + fromIntegral(k))/(10000.0 + fromIntegral(k)*fromIntegral(totalCategories))
  69.  
  70. -- returns the log of the probability for a trigram. We use logs so we don't endup dealing with
  71. -- really small numbers caused by multiplying small numbers. We can just sum the logs instead.
  72. calcLogOfSmoothedProbabilityForTrigram:: TrigramFrequencies -> String -> Double 
  73. calcLogOfSmoothedProbabilityForTrigram trigramFrequencies trigram = log ( laplaceSmoothedProbability (lookupTrigramFrequency trigramFrequencies trigram) (M.size trigramFrequencies) 1 )
  74.  
  75. -- calculates the score for a string based on the probabilities of all the trigrams it contains
  76. scoreString:: TrigramFrequencies -> String -> ScoredString
  77. scoreString trigramFrequencies str =  ( sum $ map ( calcLogOfSmoothedProbabilityForTrigram trigramFrequencies ) ( splitIntoTrigrams $ preprocessText str ) , str )
  78.  
  79. -- calculates the scores for all 26 rotations of the input string and returns them in descending order of score
  80. scoreAll:: TrigramFrequencies -> String -> [ ScoredString ]
  81. scoreAll trigramFrequencies str = reverse $ sortBy (comparing fst) $ map (scoreString trigramFrequencies) [ shiftString n str | n <- [1 .. 26] ]
  82.  
  83. -- displays the string along with its score
  84. displayScoredString:: (Double, String ) -> IO ()
  85. displayScoredString (score, str) = do
  86. 							putStrLn str
  87. 							putStr "score: "
  88. 							putStrLn $ show score 
  89.            						putStrLn ""
  90.  
  91. -- parse arguments, if no supplied use default
  92. parseArgs:: [String] -> String
  93. parseArgs args = if null args then defaultEncodedMsg else head args
  94.  
  95. -- entry point
  96. main = do 
  97. 		trigramFrequencies <- loadTrigrams  
  98. 		args <- getArgs
  99. 		let msg = parseArgs args
  100.           	putStrLn "Caesar Cypher Solver (ai-class)\n"
  101. 		putStrLn  "encoded message:"
  102.     		putStrLn msg
  103.     		putStrLn "\nThe top 3 candidates based on trigram letter probabilities for english language are:\n"
  104.           	let top3 = take 3 $ scoreAll trigramFrequencies msg
  105.           	mapM_ displayScoredString top3
  106.  
Success #stdin #stdout 0.03s 3808KB
comments (?)
stdin 
; English trigram frequency table
;
; This table is in the public domain, and is derived from the Brown Corpus.
; # signifies a word boundary, where words are defined as sequences of letters
;   bounded by non-letters (hence the high frequency of #S#, based on "'s").
; The numbers are frequency of the trigram in Brown per 10,000 words.
; Trigrams less frequent than that are omitted.
;
;
#TH	230
THE	192
HE#	172
#S#	129
ED#	86
#OF	81
#AN	78
OF#	77
ND#	75
#IN	71
AND	70
#TO	64
ING	62
NG#	62
ER#	61
TO#	58
ON#	58
IN#	54
IS#	49
#A#	48
#CO	47
ES#	47
ION	47
RE#	46
AS#	42
AT#	41
ENT	38
#BE	38
TIO	37
OR#	37
#HE	36
#RE	34
LY#	34
#HA	33
HER	32
FOR	32
#FO	31
#WA	31
EN#	31
AL#	30
AN#	30
#WH	29
NT#	28
#MA	27
#WI	27
HAT	27
TER	26
THA	26
ST#	26
ATI	26
HIS	26
#ON	26
ERE	26
#PR	25
#ST	25
#HI	25
TH#	25
LL#	24
#IT	23
LE#	23
CE#	23
#IS	23
#NO	23
TS#	23
ATE	22
IT#	22
VE#	22
SE#	21
ALL	21
WAS	20
UT#	20
VER	20
#SE	20
#AS	20
#WE	20
#DE	19
#CA	19
RS#	19
CH#	19
ME#	19
CON	19
ITH	18
LD#	18
THI	18
RES	18
#SO	18
TED	18
#MO	18
NCE	17
WIT	17
#SH	17
ERS	17
MEN	17
NE#	17
#AR	16
NS#	16
ONS	16
ARE	16
#DI	16
#AL	16
PRO	16
RY#	16
REA	15
EVE	15
#FR	15
STA	15
#WO	15
TE#	15
#LI	15
ESS	15
AD#	15
#SU	14
COM	14
#AT	14
IVE	14
#BU	14
#PA	14
TY#	14
#ME	14
ONE	14
BE#	14
EST	14
EAR	14
NOT	13
AY#	13
#FI	13
PER	13
OUT	13
INT	13
#SA	13
ECT	13
OT#	13
ILL	13
OME	12
#PO	12
MAN	12
#NE	12
#OR	12
#CH	12
IST	12
#HO	12
#DO	12
ICA	12
AVE	12
GHT	11
BY#	11
TIN	11
OUL	11
OM#	11
AIN	11
IGH	11
OVE	11
IDE	11
SS#	11
#UN	11
ULD	11
#EX	11
INE	11
#BY	11
DER	11
#LO	11
ORE	11
CTI	11
STR	11
#YO	10
#FA	10
NTE	10
EY#	10
ROM	10
RED	10
#LE	10
#I#	10
#PE	10
OUR	10
RAT	10
OUN	10
#LA	10
HAD	10
#TR	10
BLE	10
PRE	10
HIN	10
WHI	10
AR#	10
OTH	10
STI	10
#MI	10
FRO	10
TRA	10
YOU	10
STE	10
OW#	10
#SI	10
ITI	10
UND	10
BUT	10
ET#	10
CAL	9
ANT	9
ART	9
IC#	9
HOU	9
GE#	9
HAN	9
#GR	9
WER	9
#BA	9
ERI	9
ACT	9
ORT	9
DE#	9
COU	9
URE	9
NTI	9
TUR	9
SHE	9
TIC	9
HAV	9
HEN	9
IND	9
ERA	9
HT#	9
ENC	9
#GO	9
#BO	9
EEN	8
THO	8
HIC	8
#OU	8
US#	8
AME	8
OUS	8
DS#	8
PAR	8
ITY	8
ID#	8
NDE	8
ROU	8
WHE	8
UGH	8
#EN	8
RIN	8
ICH	8
#TE	8
USE	8
IES	8
LIN	8
CAN	8
TEN	8
EAS	8
TOR	8
MIN	7
#AC	7
NED	7
UST	7
EAT	7
KE#	7
PLA	7
HEY	7
SSI	7
#SP	7
ARD	7
TAT	7
LIT	7
OUG	7
NAL	7
#PL	7
AGE	7
MOR	7
LES	7
IR#	7
ANC	7
ABL	7
LLY	7
END	7
WOR	7
DEN	7
RD#	7
AST	7
ITE	7
#FE	7
#RA	7
ELL	7
NY#	7
#CL	7
#BR	7
TTE	7
ESE	7
ANY	7
CK#	7
#EV	7
VEN	7
RT#	7
OU#	7
IAL	7
PLE	6
DIN	6
OSE	6
EW#	6
#TA	6
CES	6
OWN	6
ONT	6
ASS	6
REC	6
INC	6
RAN	6
INS	6
#MU	6
SIN	6
NIN	6
SED	6
TAN	6
#AB	6
LAT	6
LAN	6
NAT	6
HIM	6
IME	6
#DA	6
CHA	6
NTS	6
CT#	6
ONG	6
EAD	6
REN	6
SO#	6
SHO	6
TIM	6
EME	6
RIE	6
ICE	6
SIO	6
UR#	6
LLE	6
REE	6
DIS	6
WHO	6
LEA	6
OST	6
LED	6
RAL	6
EM#	6
TIV	6
NES	6
#RO	6
CHE	6
GH#	6
BER	6
WN#	6
ONA	6
HES	6
IM#	6
LS#	6
ACE	6
APP	6
#TI	6
HAS	6
SOM	6
SON	6
WIL	6
AKE	6
RIC	6
TRI	6
ERN	5
HEI	5
POS	5
SEN	5
WE#	5
WOU	5
ACH	5
GRE	5
#AF	5
ADE	5
UNI	5
MER	5
KIN	5
#GE	5
TES	5
STO	5
SPE	5
ITS	5
NOW	5
OMP	5
OPE	5
EIR	5
NDI	5
ENE	5
#UP	5
#SC	5
EE#	5
IRE	5
HEA	5
CHI	5
POR	5
ACK	5
#YE	5
BEE	5
OD#	5
NER	5
DED	5
#PU	5
#EA	5
LAR	5
CAT	5
SEL	5
#AD	5
RIT	5
ATT	5
SID	5
ORM	5
GRA	5
ABO	5
UNT	5
HAR	5
#US	5
MAT	5
OLD	5
NGE	5
NEW	5
ANG	5
UCH	5
ANS	5
#AG	5
NST	5
#NA	5
#DR	5
ENS	5
ORD	5
THR	5
DES	5
UP#	5
ELY	5
MS#	5
HOW	5
HEM	5
EXP	5
NSI	5
#AP	5
AID	5
INA	5
ILE	5
ECO	4
ARI	4
LOW	4
ALI	4
MON	4
#IM	4
SER	4
MPL	4
SIT	4
CEN	4
UAL	4
ERY	4
NO#	4
FIC	4
WAR	4
MAR	4
TAL	4
HO#	4
IEN	4
PEN	4
SEE	4
WAY	4
ARY	4
#CR	4
#AM	4
OWE	4
ISH	4
LIC	4
SES	4
PRI	4
NTR	4
ATH	4
EAC	4
SSE	4
OMM	4
ELE	4
NLY	4
ERT	4
OOD	4
SUR	4
LON	4
#CE	4
IF#	4
TAI	4
#RI	4
ASE	4
WHA	4
INI	4
#IF	4
FAC	4
#OT	4
DAY	4
ALS	4
CRE	4
OND	4
VEL	4
ELI	4
OOK	4
NTO	4
BOU	4
OLL	4
RAC	4
PEC	4
IMP	4
ILI	4
CIA	4
REL	4
NIT	4
#VI	4
MIL	4
FIR	4
HIL	4
TRO	4
KED	4
FFE	4
GEN	4
#JU	4
TRE	4
ARS	4
RIS	4
EAL	4
NTA	4
CAR	4
RST	4
MED	4
#TW	4
LF#	4
EL#	4
LAS	4
#T#	4
FER	4
FIN	4
TLE	4
#KN	4
DY#	4
#OP	4
#QU	4
LIS	4
MBE	4
IKE	4
EED	4
SAI	4
RTI	4
MOS	4
TLY	4
RN#	3
TIE	3
ITT	3
ORK	3
SHI	3
#VE	3
ORI	3
IVI	3
ETE	3
REP	3
YEA	3
LLI	3
QUI	3
GER	3
REM	3
OLI	3
HED	3
NDS	3
ANI	3
TEM	3
UE#	3
#FU	3
PPE	3
FTE	3
GS#	3
GIN	3
COR	3
GRO	3
#GA	3
RK#	3
VES	3
OFF	3
VED	3
ONL	3
ETH	3
OIN	3
ERV	3
YS#	3
IAN	3
DUC	3
ESI	3
RIA	3
MET	3
TIL	3
MUS	3
ISE	3
ONC	3
RGE	3
CER	3
ULT	3
FUL	3
#OV	3
SUC	3
ULA	3
LIE	3
#PI	3
QUE	3
RET	3
ARR	3
LIK	3
TAR	3
TEL	3
SH#	3
COL	3
USI	3
BEC	3
TRU	3
WIN	3
MY#	3
IRS	3
IED	3
LAC	3
#VA	3
ETT	3
ITA	3
EQU	3
HOL	3
LOO	3
#GI	3
ORS	3
RSE	3
LET	3
IGN	3
IOU	3
TON	3
MAY	3
VIN	3
ERM	3
ROP	3
TOO	3
#BI	3
OSS	3
RTH	3
MIS	3
IL#	3
#HU	3
ISS	3
MES	3
ECE	3
ECI	3
OTE	3
#FL	3
URN	3
AM#	3
CLE	3
CHO	3
RAI	3
ICI	3
#BL	3
RON	3
AIL	3
PON	3
NGS	3
#JO	3
TWO	3
ARL	3
AIR	3
BLI	3
ELF	3
CED	3
SEC	3
GET	3
#EL	3
HOS	3
PEA	3
LIG	3
NSE	3
#CU	3
LLO	3
CTE	3
ISI	3
EAN	3
RCH	3
WO#	3
UES	3
HEL	3
ATU	3
#MY	3
DIT	3
EDI	3
KS#	3
MAL	3
HRO	3
VID	3
CUL	3
ANN	3
RTA	3
HOR	3
DID	3
DO#	3
UTI	3
RIG	3
RMA	3
#RU	3
LEC	3
NIS	3
AFT	3
AYS	3
WEL	3
CLA	3
ETI	3
POL	3
PS#	3
GES	3
IZE	3
ROV	3
DEA	3
FFI	3
SHA	3
WEE	3
SIS	3
RAD	2
AUS	2
OMI	2
ARK	2
ECA	2
GAI	2
KNO	2
#DU	2
NOR	2
URI	2
RNE	2
MEA	2
EPT	2
XPE	2
ALE	2
EMB	2
UCT	2
DOW	2
ACC	2
ICT	2
#CI	2
UTH	2
AGA	2
RIO	2
RCE	2
ADI	2
EET	2
#MR	2
URS	2
ARG	2
CAU	2
ROW	2
ESP	2
LEN	2
TTL	2
EMP	2
STU	2
TAK	2
LOS	2
ARA	2
ILD	2
PAT	2
FOU	2
BRO	2
TCH	2
TIT	2
MAK	2
EFO	2
EXT	2
NNE	2
RM#	2
ICK	2
CIE	2
SOU	2
PED	2
QUA	2
MIT	2
SPO	2
OL#	2
IMA	2
FRE	2
BET	2
IFI	2
OLE	2
BAC	2
SIG	2
ASI	2
MAD	2
OOL	2
STS	2
SCH	2
ENG	2
RDE	2
ROB	2
HOO	2
ELO	2
IAT	2
BRI	2
CIT	2
UBL	2
MPA	2
BIL	2
ORY	2
NCI	2
#SL	2
VAL	2
LT#	2
CAM	2
OCK	2
RRI	2
RTE	2
RLY	2
DIC	2
ITU	2
HAL	2
DRE	2
ORA	2
RAM	2
IFF	2
#EM	2
OK#	2
JUS	2
REF	2
OLO	2
CUR	2
LSO	2
FE#	2
REV	2
MPO	2
#KI	2
#OB	2
#SM	2
LEM	2
ULL	2
EMA	2
ARM	2
SUP	2
NGL	2
TAB	2
EVI	2
OVI	2
UDE	2
DON	2
NIC	2
LAY	2
REG	2
UTE	2
IBL	2
ROS	2
RRE	2
YIN	2
IFE	2
OCI	2
#TU	2
TUD	2
EIN	2
BEL	2
UNC	2
URA	2
TRY	2
VIS	2
#PH	2
CAS	2
ISC	2
TIA	2
PIN	2
#WR	2
LIF	2
RIV	2
SOC	2
GAN	2
EMS	2
ALT	2
NTL	2
PAN	2
SUB	2
#KE	2
#SY	2
PE#	2
DEC	2
CKE	2
GO#	2
CTO	2
FEE	2
EFF	2
CTU	2
HOM	2
HAP	2
UL#	2
CRI	2
DEV	2
#AU	2
ELA	2
ROO	2
#NU	2
AF#	2
AMP	2
LER	2
PPO	2
LOC	2
AMI	2
FF#	2
ILY	2
OSI	2
EGA	2
SIB	2
#NI	2
NDA	2
GIV	2
VIC	2
HIG	2
EMO	2
ROA	2
SIC	2
IA#	2
#ES	2
DIF	2
PAS	2
CLU	2
MME	2
TIS	2
TWE	2
DEP	2
NK#	2
TUA	2
LEG	2
IP#	2
ANO	2
CY#	2
SPI	2
PLI	2
NEE	2
NCH	2
#VO	2
ATO	2
#GU	2
GED	2
ANE	2
OGR	2
EEM	2
IMI	2
CLO	2
SOL	2
INK	2
RDS	2
BEF	2
MIC	2
ROD	2
CTS	2
DIE	2
#OW	2
BOR	2
HRE	2
MEM	2
TEE	2
BOT	2
HIP	2
ROC	2
SET	2
ROL	2
DGE	2
ODE	2
ENI	2
DIA	2
ANA	2
UMB	2
#EF	2
AUT	2
SAM	2
MOT	2
SSU	2
IET	2
URT	2
WS#	2
EIG	2
JEC	2
ORG	2
RNI	2
TTI	2
KEN	2
ORL	2
RUS	2
RVE	2
BAS	2
MOV	2
FIE	2
OKE	1
ELD	1
WAT	1
ORN	1
INF	1
OTI	1
PT#	1
UPP	1
MAI	1
GOO	1
MUC	1
EGI	1
TOW	1
POI	1
EOP	1
#OL	1
OPL	1
AVI	1
ROG	1
PTI	1
SMA	1
SEA	1
ROT	1
ETA	1
EDU	1
URC	1
UME	1
FT#	1
RMI	1
FAR	1
CEP	1
PUB	1
PEO	1
CRO	1
LOR	1
RIB	1
LUE	1
SCO	1
NEV	1
EXC	1
EEP	1
RTS	1
MOU	1
LVE	1
RVI	1
APE	1
ISM	1
LOG	1
ERC	1
MSE	1
LOP	1
FEC	1
RSO	1
#JA	1
EPA	1
LAI	1
RLD	1
TEA	1
RKE	1
UNG	1
YST	1
AW#	1
ADD	1
SCR	1
RIM	1
DIV	1
ODU	1
#ED	1
LIV	1
OLU	1
RAG	1
ASH	1
UM#	1
OES	1
INV	1
HY#	1
ONO	1
INU	1
DEL	1
TOM	1
VOL	1
CAP	1
ONI	1
ICU	1
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DRO	1
stdout 
Caesar Cypher Solver (ai-class)

encoded message:
Esp qtcde nzyqpcpynp zy esp ezatn zq Lcetqtntlw Tyepwwtrpynp hld spwo le Olcexzfes Nzwwprp ty estd jplc.

The top 3 candidates based on trigram letter probabilities for english language are:

The first conference on the topic of Artificial Intelligence was held at Dartmouth College in this year.
score: -742.9796021883617

Nby zclmn wihzylyhwy ih nby nijcw iz Ulnczcwcuf Chnyffcayhwy qum byfx un Xulngionb Wiffyay ch nbcm syul.
score: -913.8004146160043

Esp qtcde nzyqpcpynp zy esp ezatn zq Lcetqtntlw Tyepwwtrpynp hld spwo le Olcexzfes Nzwwprp ty estd jplc.
score: -921.9751546970537
https://ideone.com/KU0ky
language:
Haskell (ghc 8.4.4)
created:
12 years ago
visibility:
public

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