Word games with phone numbers: 1-800-RESULTS (by CalvinH)
My boss forwarded me this blog which is a programming puzzle challenge: given a phone number, try to create a mnemonic, like 800-776-4726 is 800-PROGRAM
He knows that I’ve been writing word games on computers for years: I decoded a spelling dictionary from a commercial software product about 20 years ago, and have been using that as a source. Using Borland C about 20 years ago, my scrabble program can’t be beat<g>
So I wrote a solution to the challenge in about 100 lines of Visual FoxPro.
Today, my dictionary is a DLL COM server of size 630784, which includes 2 separate dictionaries: one with 171201 words, and the other with 53869. That’s around the same size as some pictures that my 4 Megapixel digital camera takes. So, a picture is worth 225000 words<g>
As a corollary, you might wonder how 225000 words can fit into 679k: that’s an average of 3 bytes per English word not including the dictionary logic itself! But that’s another subject.
To run the solution, you’ll need my dictionary
There are many optimizations that could be made, but they would add more lines and obscure the algorithm itself.
In any case, here’s the non-optimized solution.
There are 2 fundamental algorithms here. The first (EnumNum, 20 lines) enumerates all the possible permutations of NUMDIGS digits. It
loops through the digits, allowing each one to range through its possible values ("2" goes through "2,d,e,f")
The 2nd algorithm (DoSeparators, 13 lines) just inserts a "-" in every possible position in a NUMDIGS length string. There are NUMDIGS-1 possible places to insert a "-" (each of the gaps between each letter). The gap can be either of 2 values: a "-" or a "". Thus there are 2^(NUMDIGS-1) locations to put a "-". So the DoSeparators routine just loops from 0 TO 2^(NUMDIGS-1)-1 and uses the bits of the loop index represented in binary to insert the "-".
Click to download Dictionary.dll
CLEAR
#define NUMDIGS 10
PUBLIC ox as dictionary.dict
PUBLIC nCnt,oBrowse
ox=CREATEOBJECT('dictionary.dict') && Instantiate the dictionary COM object
ox.DictNum=2 && 1 = 171000 word dictionary, 2= 53869 word
&&This solution uses 2 parallel strings: the number to permute and a pattern
cPattern=REPLICATE("0",NUMDIGS) && like "0000000000"
&& cPattern governs the pattern of letters to use for each digit's place
&& a "0" for each digits place to indicate which letter of the digit it is (0,1,2,3). 0 indicates use the raw digit
&& At the end, it'll be "1" (for 0,1), "3" (for 2,3,4,5,6,8), or "4" for "7,9", like "3334433143"
&& Given a phone #, the # of patterns is 3^NUMDIGS if all digits are "234568"
cNumber="642-394-6369" && number of patterns is 4^8*5^2 = 1638400
cNumber=STRTRAN(cNumber,"-","") && remove dashes
CREATE TABLE phrases (phrase c(30)) && a table into which we can put partial results
CLOSE DATABASES
USE phrases SHARED && open it shared, so another instance can view/query it while we're executing
BROWSE LAST NOWAIT NAME oBrowse && show the table
nCnt=0 && count of results
dtStart=DATETIME()
EnumNum(cNumber,cPattern,1) && Call enumerator starting at 1st digit
dtEnd=DATETIME()
?"Completed Phrase search ",dtstart,dtEnd,dtEnd-dtStart
PROCEDURE EnumNum(cNumber as String,cPattern as String, nDigNum as Integer) && cNumber is raw string of digits with no separators
LOCAL i,cDigit,cPat,cStartLet,cLastPat,cNewLet
cDigit=SUBSTR(cNumber,nDigNum,1) && the digit we're working on
cPat=SUBSTR(cPattern,nDigNum,1) && where are we on this digit?
cStartLet=SUBSTR(" adgjmptw",ASC(cDigit)-47,1) && Starting letter for this digit: 0 1 2abc, 3def, 4ghi, 5jkl, 6mno, 7pqrs, 8tuv, 9wxyz
cLastpat =SUBSTR("0033333434",ASC(cDigit)-47,1) && # permutations -1 for this digit: 0 0 4, 4, 4, 4, 4, 5, 4, 5
DO WHILE .t.
IF nDigNum < NUMDIGS && we haven't enumerated all digits yet
EnumNum(cNumber,cPattern,nDigNum+1) && recur with next digit
ELSE
DoSeparators(cNumber) && Gone through all digits. Now we've got a pattern, like "nicewinfox".
ENDIF
IF cPat=cLastPat && this digit has reached the end (for '7', we've done "7","p","q","r","s")
EXIT
ENDIF
cPat = CHR(ASC(cPat)+1) && increment the pattern
cPattern=LEFT(cPattern,nDigNum-1) + cPat + SUBSTR(cPattern, nDigNum+1) && insert the new letter into the pattern
cNewlet = CHR(ASC(cStartLet)+ASC(cPat)-49) && from 'a' to 'b' or from 'n' to 'o'
cNumber=LEFT(cNumber,nDigNum-1) + cNewLet + SUBSTR(cNumber, nDigNum+1) && insert the new letter into the number
ENDDO
RETURN
&& DoSeparators: given NUMDIGS letters like "nicewinfox", insert "-" into all positions to create phrases, then test them
&& For NUMDIGS, (NUMDIGS-1) locations to insert a separator. It's either there or not, so 2^(NUMDIGS-1) permutations
PROCEDURE DoSeparators(cNumber as String)
LOCAL i,j,k,cstr
FOR i = 0 TO 2^(NUMDIGS-1)-1 && loop on # possible separator positions. For 10 digits, it's 512
cPhrase=SUBSTR(cNumber,1,1) && first char can't be a separator
FOR j = 1 TO NUMDIGS-1 && for each of the positions, construct a multi-word phrase like "nice-win-fox"
IF BITTEST(i,j-1) && add a separator (BITTEST(1024,10) is true because the 10th bit is 1)
cPhrase=cPhrase+'-'
ENDIF
cPhrase=cPhrase+SUBSTR(cNumber,j+1,1) && add a letter
ENDFOR && for each digit
TestPhrase(cPhrase+"-") && add a trailing "-"
ENDFOR && try next separator position
RETURN
PROCEDURE TestPhrase(cPhrase as String) && given a phrase like "645-fox-test" see if all alpha sequences are in dictionary
LOCAL cStr,nDash
nCnt=nCnt+1
IF MOD(nCnt,100000)=0
?nCnt,TRANSFORM(LOG10(nCnt),"999.9"),"phrases checked",cPhrase
ENDIF
cStr=cPhrase
DO WHILE .t.
nDash=AT("-",cStr)
IF nDash = 0 && we parsed all words
EXIT
ENDIF
cWord=LEFT(cStr,nDash-1) && the first word before the dash
cStr=SUBSTR(cStr,nDash+1) && the rest of the string
IF !TestWord(cWord) && if it's not a word
RETURN
ENDIF
ENDDO
INSERT INTO phrases VALUES (LEFT(cPhrase,LEN(cPhrase)-1)) && Bingo! remove trailing '-'
RETURN
PROCEDURE TestWord(cWord as String) as Boolean
LOCAL i
IF ISDIGIT(cWord) && if it starts with a digit
FOR i = 2 TO LEN(cWord)
IF !ISDIGIT(SUBSTR(cWord,i,1)) && if they're not all digits
RETURN .f.
ENDIF
ENDFOR
ELSE
FOR i = 2 TO LEN(cWord) && starts with a char, lets ensure the rest are chars
IF ISDIGIT(SUBSTR(cWord,i,1))
RETURN .f.
ENDIF
ENDFOR
IF !ox.isWord(cWord)
RETURN .f.
ENDIF
ENDIF
RETURN .t.
Here are the first 20 results:
6423946369
6-423946369
64-23946369
6-4-23946369
642-3946369
6-42-3946369
64-2-3946369
6-4-2-3946369
6423-946369
6-423-946369
64-23-946369
6-4-23-946369
642-3-946369
6-42-3-946369
64-2-3-946369
6-4-2-3-946369
64239-46369
6-4239-46369
64-239-46369
6-4-239-46369
You can see that the dashes are being inserted into the number in a binary fashion: 0000, 0001, 0010, 0011, etc.
One optimization: when inserting the separators: each partial word must be either all digits or all letters. Also, don't insert a separator between 2 digits.
Another optimization: if we constrain the words to be at least a certain length, we won't get silly results like a-i-i-a-i-a-i-i-i-a
A major optimization: after we have examined all phrases that start with "642-", we can use the same stored results for all 3 letter combinations of 642 (like "mda") that are stored in the cursor. Permutations of the last 7 digits have already been calculated and put in the cursor.
We could also limit all digit words to 1 or 2 in length
The contents of the dictionary are also important. If it is a true spell checker dictionary, then it contains things like b, c, d, e, f.
These are not spelling errors, but they're not words either. Many spelling dictionaries also contain abbreviations, like ny, md, etc.
nice-window
Because the results are in a cursor, it's easy to do a query:
SELECT * from phrases WHERE AT("fox",phrase)>0
nice-win-fox
Comments
- Anonymous
March 31, 2004
The comment has been removed - Anonymous
March 31, 2004
you have some mad skillzzz - Anonymous
March 31, 2004
@ The1:
>> Not everyone has FoxPro
Come on... It's in your MSDN package. See DVD2488 or CD2014. Just install it (It's one of the most wellbehavest MS apps I know: Doesn't alter anything on your PC, doesn't depend on anything. You could even just copy the directories to your PC and start working)
@CalvinRH:
Seems the download is not yet working. Using MSVCR80.dll? Is that already compiled in VFP9? Any chance you recompile that puppy with the currently released version? <g> - Anonymous
March 31, 2004
Ah, now the download is working.
>> that’s an average of 2.8 bytes per English word not including the dictionary logic itself! But that’s another subject.<<
Which I would be very interested in.. <g> Are you using an IDX file for lookup? (For the Non-FoxPro folks: IDX is an Indexfile, which internally uses a compressed storage) Together with an empty dummy DBF, built on the fly, a INDEXSEEK() could just return a "Yes/No" on a search... - Anonymous
April 01, 2004
Calvin,
A minor thing: in your comments you said EnumNum() enumerates all the possible permutations of NUMDIGS digits. The term permutation means a ordering of a sequence (e.g. "1923" is a permutation of "1239"). I think you actually mean "combinations". - Anonymous
April 02, 2004
>>you might wonder how 225000 words can fit into 679k: that’s an average of 3 bytes per English word not including the dictionary logic itself! But that’s another subject.
This is a good subject for a programming challenge: compress a dictionary. - Anonymous
April 02, 2004
Calvin,
I posted my own solution at http://blogs.msdn.com/the1/archive/2004/04/02/106691.aspx - Anonymous
April 12, 2004
Actually, they are neither permutations nor combinations. Since these terms are being used "expressively" rather than "precisely" either is probably descriptively OK here. The counting examples most likely make clear what is going on. Counting problems vary a lot and include much more than the basic permutation or combination--many are really hard. - Anonymous
September 27, 2007
Since July 4 th is nearing, I thought it would be appropriate to start my independent blog. In this first