# 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 "-".

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

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

Tags

1. the1 says:

This is nice. Could you also post some sample results? Not everyone has Fox Pro.

I’m busy today, but will try to digest your program later this week. In the mean while, can you provide some high-level description on your algorithm? I saw your inline comments, but there is no overview. Thanks.

2. bertcord says:

3. wOOdy says:

@ 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>

4. wOOdy says:

>> 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…

5. the1 says:

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".

6. B.Y. says:

>>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.

7. the1 says:

Calvin,

I posted my own solution at http://blogs.msdn.com/the1/archive/2004/04/02/106691.aspx

8. garrettvm says:

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.

9. Since July 4 th is nearing, I thought it would be appropriate to start my independent blog. In this first