I have a set which has an unknown number of objects. I want to associate a label to each one of these objects. Instead of labeling each object with a number I want to label them with letters.
For example the first object would be labeled A the second B and so on.
When I get to Z, the next object would be labeled AA
AZ? then BA, BB, BC.
ZZ? then AAA, AAB, AAC and so on.
I'm working using Mapbasic (similar to VBA), but I can't seem to wrap my head around a dynamic solution. My solution assumes that there will be a max number of objects that the set may or may not exceed.
label = pos1 & pos2
Once pos2 reaches ASCII "Z" then pos1 will be "A" and pos2 will be "A". However, if there is another object after "ZZ" this will fail.
How do I overcome this static solution?
Basically what I needed was a Base 26 Counter. The function takes a parameter like "A" or "AAA" and determines the next letter in the sequence.
Function IncrementAlpha(ByVal alpha As String) As String
Dim N As Integer
Dim num As Integer
Dim str As String
Do While Len(alpha)
num = num * 26 + (Asc(alpha) - Asc("A") + 1)
alpha = Mid$(alpha, 2,1)
Loop
N = num + 1
Do While N > 0
str = Chr$(Asc("A") + (N - 1) Mod 26) & str
N = (N - 1) \ 26
Loop
IncrementAlpha = str
End Function
If we need to convert numbers to a "letter format" where:
1 = A
26 = Z
27 = AA
702 = ZZ
703 = AAA etc
...and it needs to be in Excel VBA, then we're in luck. Excel's columns are "numbered" the same way!
Function numToLetters(num As Integer) As String
numToLetters = Split(Cells(1, num).Address(, 0), "$")(0)
End Function
Pass this function a number between 1 and 16384 and it will return a string between A and XFD.
Edit:
I guess I misread; you're not using Excel. If you're using VBA you should still be able to do this will the help of an reference to an Excel Object Library.
This should get you going in terms of the logic. Haven't tested it completely, but you should be able to work from here.
Public Function GenerateLabel(ByVal Number As Long) As String
Const TOKENS As String = "ZABCDEFGHIJKLMNOPQRSTUVWXY"
Dim i As Long
Dim j As Long
Dim Prev As String
j = 1
Prev = ""
Do While Number > 0
i = (Number Mod 26) + 1
GenerateLabel = Prev & Mid(TOKENS, i, 1)
Number = Number - 26
If j > 0 Then Prev = Mid(TOKENS, j + 1, 1)
j = j + Abs(Number Mod 26 = 0)
Loop
End Function
I'm putting together an excel spreadsheet for calculations, and I need to be able to show the formulas to go with the decisions, for the most part its pretty straight forward, but When I come to an 'if' formula in an excel cell, I don't want to show the value_if_true and value_if_false... Just the logical_test value.
Example:
Formula is: =if(and(5<=A1, A1<=10),"Pass", "Fail");
Result will be: "and(5<=A1, A1<=10)"
I need to be able to work with complex logical tests which may include nested if statements, so just splitting at the commas won't work reliably. Similarly the value_if_true and value_if_false statements could also contain if statements.
Any ideas?
If have clear understanding of what you asking for, then you can use something like this (shall be used only with IF() statement :
Function extrIf(ByVal ifstatement As Range) As String
Dim S$, sRev$, x%, k
S = Replace(Replace(ifstatement.Formula, "IF(", "\"), "),", ")|")
sRev = StrReverse(S)
If InStr(1, sRev, "|") > InStr(1, sRev, "\") Or InStr(1, sRev, "|") = 0 Then
x = InStr(1, StrReverse(Left(sRev, InStr(1, sRev, "\"))), ",") - 1
S = Mid(S, 1, Len(S) - InStr(1, sRev, "\") + x) & "|"
End If
sRev = ""
For Each k In Split(S, "|")
If k <> "" Then
If k Like "*\*" Then
sRev = sRev & ", " & Mid(k, InStr(1, k, "\") + 1, 999)
End If
End If
Next
extrIf = Mid(sRev, 3, 999)
End Function
example:
test:
Maybe this is not complete solution for you, but I think it might give you right direction.
If the cell formula starts with an If statement then you can return the logic test (starting after the first open parenthesis) by determining the position of the first comma where the sum of the previous open parenthesis - the sum previous closed = 0.
Formulas
Function ExtractIfTest(Target As Range) As String
Dim ch As String, s As String
Dim openP As Long
Dim x As Long
s = Target.formula
For x = 5 To Len(s)
ch = Mid(s, x, 1)
If Mid(s, x, 1) = "(" Then
openP = openP + 1
ElseIf Mid(s, x, 1) = ")" Then
openP = openP - 1
ElseIf Mid(s, x, 1) = "," And openP = 0 Then
ExtractIfTest = Mid(s, 5, x - 12)
End If
Next
End Function
Results
There might be instances where the is a comma without parenthesis A1,B1. If this happens simple escape them with parenthesis (A1,B1)
I've written an UDF that extract any of the parameters of the target formula. It's close to the one in Thomas answer, but more global and takes into account strings that can enclose commas or parenthesis.
Function ExtractFormulaParameter(Target As Range, Optional Position As Long = 1) As Variant
Dim inString As Boolean
Dim formula As String
Dim st As Long, sp As Long, i As Long, c As String
Dim parenthesis As Long, comma As Long
formula = Target.formula
st = 0: sp = 0
If Position <= 0 Then ExtractFormulaParameter = CVErr(xlErrValue): Exit Function
For i = 1 To Len(formula)
c = Mid$(formula, i, 1)
If inString Then
If c = """" Then
inString = False
End If
Else
Select Case c
Case """"
inString = True
Case "("
parenthesis = parenthesis + 1
If parenthesis = 1 And Position = 1 Then
st = i + 1
End If
Case ")"
parenthesis = parenthesis - 1
If parenthesis = 0 And sp = 0 Then sp = i: Exit For
Case ","
If parenthesis = 1 Then
comma = comma + 1
If Position = 1 And comma = 1 Then sp = i: Exit For
If Position > 1 And comma = Position - 1 Then st = i + 1
If Position > 1 And comma = Position Then sp = i: Exit For
End If
Case Else
End Select
End If
Next i
If st = 0 Or sp = 0 Then
ExtractFormulaParameter = CVErr(xlErrNA)
Else
ExtractFormulaParameter = Mid$(formula, st, sp - st)
End If
End Function
By default it returns the first parameter, but you can also return the second or the third, and it should work with any formula.
Thanks for the replies all. I thought about this more, and ended up coming up with a similar solution to those posted above - essentially string manipulation to extract the text where we expect to find the logical test.
Works well enough, and I'm sure I could use it to extract further logical tests from substrings too.
I am banging my head against the wall for a while now trying different techniques.
None of them are working well.
I have two strings.
I need to compare them and get an exact percentage of match,
ie. "four score and seven years ago" TO "for scor and sevn yeres ago"
Well, I first started by comparing every word to every word, tracking every hit, and percentage = count \ numOfWords. Nope, didn't take into account misspelled words.
("four" <> "for" even though it is close)
Then I started by trying to compare every char in each char, incrementing the string char if not a match (to count for misspellings). But, I would get false hits because the first string could have every char in the second but not in the exact order of the second. ("stuff avail" <> "stu vail" (but it would come back as such, low percentage, but a hit. 9 \ 11 = 81%))
SO, I then tried comparing PAIRS of chars in each string. If string1[i] = string2[k] AND string1[i+1] = string2[k+1], increment the count, and increment the "k" when it doesn't match (to track mispellings. "for" and "four" should come back with a 75% hit.) That doesn't seem to work either. It is getting closer, but even with an exact match it is only returns 94%. And then it really gets screwed up when something is really misspelled. (Code at the bottom)
Any ideas or directions to go?
Code
count = 0
j = 0
k = 0
While j < strTempName.Length - 2 And k < strTempFile.Length - 2
' To ignore non letters or digits '
If Not strTempName(j).IsLetter(strTempName(j)) Then
j += 1
End If
' To ignore non letters or digits '
If Not strTempFile(k).IsLetter(strTempFile(k)) Then
k += 1
End If
' compare pair of chars '
While (strTempName(j) <> strTempFile(k) And _
strTempName(j + 1) <> strTempFile(k + 1) And _
k < strTempFile.Length - 2)
k += 1
End While
count += 1
j += 1
k += 1
End While
perc = count / (strTempName.Length - 1)
Edit: I have been doing some research and I think I initially found the code from here and translated it to vbnet years ago. It uses the Levenshtein string matching algorithm.
Here is the code I use for that, hope it helps:
Sub Main()
Dim string1 As String = "four score and seven years ago"
Dim string2 As String = "for scor and sevn yeres ago"
Dim similarity As Single =
GetSimilarity(string1, string2)
' RESULT : 0.8
End Sub
Public Function GetSimilarity(string1 As String, string2 As String) As Single
Dim dis As Single = ComputeDistance(string1, string2)
Dim maxLen As Single = string1.Length
If maxLen < string2.Length Then
maxLen = string2.Length
End If
If maxLen = 0.0F Then
Return 1.0F
Else
Return 1.0F - dis / maxLen
End If
End Function
Private Function ComputeDistance(s As String, t As String) As Integer
Dim n As Integer = s.Length
Dim m As Integer = t.Length
Dim distance As Integer(,) = New Integer(n, m) {}
' matrix
Dim cost As Integer = 0
If n = 0 Then
Return m
End If
If m = 0 Then
Return n
End If
'init1
Dim i As Integer = 0
While i <= n
distance(i, 0) = System.Math.Max(System.Threading.Interlocked.Increment(i), i - 1)
End While
Dim j As Integer = 0
While j <= m
distance(0, j) = System.Math.Max(System.Threading.Interlocked.Increment(j), j - 1)
End While
'find min distance
For i = 1 To n
For j = 1 To m
cost = (If(t.Substring(j - 1, 1) = s.Substring(i - 1, 1), 0, 1))
distance(i, j) = Math.Min(distance(i - 1, j) + 1, Math.Min(distance(i, j - 1) + 1, distance(i - 1, j - 1) + cost))
Next
Next
Return distance(n, m)
End Function
Did not work for me unless one (or both) of following are done:
1) use option compare statement "Option Compare Text" before any Import declarations and before Class definition (i.e. the very, very first line)
2) convert both strings to lowercase using .tolower
Xavier's code must be correct to:
While i <= n
distance(i, 0) = System.Math.Min(System.Threading.Interlocked.Increment(i), i - 1)
End While
Dim j As Integer = 0
While j <= m
distance(0, j) = System.Math.Min(System.Threading.Interlocked.Increment(j), j - 1)
End While
So my professor gave me a challenge to build a decoder that could break his special formula. It was described to be 32 characters in length, alphanumeric numeric when entered but then "it has a system... the first 106 bits must be 50% 1's and the rest 0's, the remaining 22 bits are basically a hash of the previous bits so that the key can be checked..." were his exact words. Sounds to me like a 128 bit encryption with a twist. I found the below but I need VB2010 or VS2010, this says php.
<?php
function string_random($characters, $length)
{
$string = '';
for ($max = mb_strlen($characters) - 1, $i = 0; $i < $length; ++ $i)
{
$string .= mb_substr($characters, mt_rand(0, $max), 1);
}
return $string;
}
// 128 bits is 16 bytes; 2 hex digits to represent each byte
$random_128_bit_hex = string_random('0123456789abcdef', 32);
// $random_128_bit_hex might be: '4374e7bb02ae5d5bc6d0d85af78aa2ce'
Would that work? Or does it need converting? Please help. Oh and thank you :)
I wasn't promised extra credit but either way I would like to surprise him.
So the first 106 bit are 26 character and the first half of the 27.
You have first of all encode somehow the number of 0 and 1, while building the string you need to keep an eye to the number. An idea would be to build a map like this:
0 = 0000 = -4
1 = 0001 = -2
2 = 0010 = -2
3 = 0011 = 0
4 = -2
5 = 0
6 = 0
7 = +2
8 = -2
9 = 0
a = 0
b = +2
c = 0
d = +2
e = +2
f = +4
then everytime you extract a new random number you check the number associated to it and add it to a variable
balanceOfOneAndZero
your objective is have balanceOfOneAndZero = 0 when you hit your 27th character.
to do that you need a control function, that takes current balanceOfOneAndZero, the proposed character proposedChar, and current string lenght currLenght.
Would be better to split the problem into two part. First is reaching the 26th character of the sequence with balanceOfOneAndZero between -2 and 2. Any other value is not acceptable, because your 27th character can have maximum two 1 or two 0 to completely balance the first 106 characters.
so your function should do something like (I'll write in sort of pseudo code since I don't have an IDE right now)
function checkNextLetter(Dim balanceOfOneAndZero As Integer, Dim proposedChar As Char,
Dim currentLenght as Integer) As Boolean
If( ((26 - currentLenght - 1) * 4 + 2) < MOD(Map.ValueOf(proposedChar) + balanceOfOneAndZero) ) Then
Return true
Else
Return false
ENd If
End function
This function basically check if accepting the new character will still make possible to Balance the number of 0 and 1 before the 26th character.
So your main function should have a loop every time it propose a new character, something like
proposedChar = new RandomChar
While (Not checkNextLetter(balanceOfOneAndZero, proposedChar, len(currentString))
proposedChar = new RandomChar
End While
currentString = currentString & proposedChar
this only until you hit the 26th character.
Than you have to check balanceOfOneAndZero, if its 2 you add a character that begin with 00, if it's 0 you can either have 10 or 01, if it's -2 you have to add a character that begin with 11.
After this I can't help you about the rest 22 character, since there are not enough information. You could brute force the rest
EDIT:
so to brute force the rest (il start from when you reach the 26th character):
Dim stringa1, stringa2, stringa3, stringa4 As String
If balanceOfOneAndZero = 2 Then
stringa1 = currentString & '0'
stringa2 = currentString & '1'
stringa3 = currentString & '2'
stringa4 = currentString & '3'
ELse If balanceOfOneAndZero = 0 Then
stringa1 = currentString & '4'
stringa2 = currentString & '5'
stringa3 = currentString & '6'
stringa4 = currentString & '7'
Else
stringa1 = currentString & 'c'
stringa2 = currentString & 'd'
stringa3 = currentString & 'e'
stringa4 = currentString & 'f'
End if
Function GenerateAllCombination(ByVal iLenght As Integer)
Dim arrayLista As New List(Of String)()
Dim arraySubLista As New List(Of String)()
If (iLenght > 1) Then
arraySubLista = GenerateAllCombination(iLenght -1)
for each objString As String in arraySubLista
for each ele As String in arrayValori
arrayLista.add(objString & ele)
loop
loop
Else
for each ele As String in arrayValori
arrayLista.add(ele)
loop
End If
End Function
Now if you use generateAllCombination you will have a List of string with ALL the combination of 5 character.
Now you just create 4 list by concatenating those combination with your string1 to string4 (string1 & combination) etc..
put all those result on a List of string, and you have 100% that at least ONE of the string will break your teacher code
I forgot, arrayValori must be a List with all values from "0" to "f"
How do I convert a indefinite decimal (i.e. .333333333...) to a string fraction representation (i.e. "1/3"). I am using VBA and the following is the code I used (i get an overflow error at the line "b = a Mod b":
Function GetFraction(ByVal Num As Double) As String
If Num = 0# Then
GetFraction = "None"
Else
Dim WholeNumber As Integer
Dim DecimalNumber As Double
Dim Numerator As Double
Dim Denomenator As Double
Dim a, b, t As Double
WholeNumber = Fix(Num)
DecimalNumber = Num - Fix(Num)
Numerator = DecimalNumber * 10 ^ (Len(CStr(DecimalNumber)) - 2)
Denomenator = 10 ^ (Len(CStr(DecimalNumber)) - 2)
If Numerator = 0 Then
GetFraction = WholeNumber
Else
a = Numerator
b = Denomenator
t = 0
While b <> 0
t = b
b = a Mod b
a = t
Wend
If WholeNumber = 0 Then
GetFraction = CStr(Numerator / a) & "/" & CStr(Denomenator / a)
Else
GetFraction = CStr(WholeNumber) & " " & CStr(Numerator / a) & "/" & CStr(Denomenator / a)
End If
End If
End If
End Function
As .333333333 is not 1/3 you will never get 1/3 but instead 333333333/1000000000 if you do not add some clever "un-rounding" logic.
Here is a solution for handling numbers with periodic decimal representation I remember from school.
A number 0.abcdabcd... equals abcd/9999. So 0.23572357... equals 2357/9999 exactly. Just take that many 9s as your pattern is long. 0.11111... equals 1/9, 0.121212... equals 12/99, and so on. So try just searching a pattern and setting the denominator to the corresponding number. Of course you have to stop after some digits because you will never know if the pattern is repeated for ever or just many times. And you will hit the rounding error in the last digit, so you still need some clever logic.
This only works in Excel-VBA but since you had it tagged "VBA" I will suggest it. Excel has a custom "fraction" format that you can access via "Format Cells" (or ctrl-1 if you prefer). This particular number format is Excel-Specific and so does not work with the VBA.Format function. It does however work with the Excel Formula TEXT(). (Which is the Excel equivalent of VBA.Format. This can be accessed like So:
Sub Example()
MsgBox Excel.WorksheetFunction.Text(.3333,"# ?/?")
End Sub
To show more than one digit (Example 5/12) just up the number of question marks.
Google for "decimal to fraction" and you'll get about a gazillion results.
I really like this one, because it's simple, has source code (in RPL, similar to Forth, ~25 lines), and is pretty fast (it's written to run on a 4-bit, 4MHz CPU). The docs say:
In a book called Textbook of Algebra by G. Chrystal, 1st
edition in 1889, in Part II, Chapter 32, this improved continued fraction
algorithm is presented and proven. Odd to tell, Chrystal speaks of it as if it
were ancient knowledge.
This site seem to have a really nice implementation of this in JavaScript.
I would multiply by 10000000(or whatever you want depending on the precision), then simplify the resulting fraction (ie n*10000000/10000000)
You can approximate it. Essentially cycle through all numerators and denominators until you reach a fraction that is close to what you want.
int num = 1;
int den = 1;
double limit == 0.1;
double fraction = num / den;
while(den < 1000000 ) // some arbitrary large denominator
{
den = den + 1;
for(num = 0; num <= den; num++)
{
fraction = num / den;
if(fraction < n + limit && fraction > n - limit)
return (num + "/" + den);
}
}
This is slow and a brute force algorithm, but you should get the general idea.
In general, it'll be easier if you find the repeating part of the rational number. If you can't find that, you'll have a tough time. Let's say the number if 8.45735735735...
The answer is 8 + 45/100 + 735/999/100 = 8 1523/3330.
The whole number is 8.
Add 45/100 - which is .45, the part before the repeating part.
The repeating part is 735/999. In general, take the repeating part. Make it the numerator. The denominator is 10^(number of repeating digits) - 1.
Take the repeating part and shift it the appropriate number of digits. In this case, two, which means divide by 100, so 735/999/100.
Once you figure those parts out, you just need some code that adds and reduces fractions using greatest common fractions ...
Similar to CookieOfFortune's, but it's in VB and doesn't use as much brute force.
Dim tolerance As Double = 0.1 'Fraction has to be at least this close'
Dim decimalValue As Double = 0.125 'Original value to convert'
Dim highestDenominator = 100 'Highest denominator you`re willing to accept'
For denominator As Integer = 2 To highestDenominator - 1
'Find the closest numerator'
Dim numerator As Integer = Math.Round(denominator * decimalValue)
'Check if the fraction`s close enough'
If Abs(numerator / denominator - decimalValue) <= tolerance Then
Return numerator & "/" & denominator
End If
Next
'Didn't find one. Use the highest possible denominator'
Return Math.Round(denominator * decimalValue) & "/" & highestDenominator
...Let me know if it needs to account for values greater than 1, and I can adjust it.
EDIT: Sorry for the goofed up syntax highlighting. I can't figure out why it's all wrong. If someone knows how I can make it better, please let me know.
Python has a nice routine in its fractions module. Here is the working portion that converts a n/d into the closest approximation N/D where D <= some maximum value. e.g. if you want to find the closest fraction to 0.347, let n=347,d=1000 and max_denominator be 100 and you will obtain (17, 49) which is as close as you can get for denominators less than or equal to 100. The '//' operator is integer division so that 2//3 gives 0, i.e. a//b = int(a/b).
def approxFrac(n,d,max_denominator):
#give a representation of n/d as N/D where D<=max_denominator
#from python 2.6 fractions.py
#
# reduce by gcd and only run algorithm if d>maxdenominator
g, b = n, d
while b:
g, b = b, g%b
n, d = n/g, d/g
if d <= max_denominator:
return (n,d)
nn, dd = n, d
p0, q0, p1, q1 = 0, 1, 1, 0
while True:
a = nn//dd
q2 = q0+a*q1
if q2 > max_denominator:
break
p0, q0, p1, q1 = p1, q1, p0+a*p1, q2
nn, dd = dd, nn-a*dd
k = (max_denominator-q0)//q1
bound1 = (p0+k*p1, q0+k*q1)
bound2 = (p1, q1)
if abs(bound2[0]*d - bound2[1]*n) <= abs(bound1[0]*d - bound1[1]*n):
return bound2
else:
return bound1
1/ .3333333333 = 3 because 1/3 = .3333333333333, so whatever number you get do this,
double x = 1 / yourDecimal;
int y = Math.Ceil(x);
and now Display "1/" + y
It is not allways resoluble, since not all decimals are fractions (for example PI or e).
Also, you have to round up to some length your decimal before converting.
I know this is an old thread, but I came across this problem in Word VBA. There are so many limitations due to the 8 bit (16 digit) rounding, as well as Word VBA making decimals into scientific notation etc.. but after working around all these problems, I have a nice function I'd like to share that offers a few extra features you may find helpful.
The strategy is along the lines of what Daniel Buckner wrote. Basically:
1st) decide if it's a terminating decimal or not
2nd) If yes, just set the decimal tail / 10^n and reduce the fraction.
3rd) If it doesn't terminate, try to find a repeating pattern including cases where the repetition doesn't start right away
Before I post the function, here are a few of my observations of the risks and limitations, as well as some notes that may help you understand my approach.
Risks, limitations, explanations:
-> Optional parameter "denom" allows you to specify the denominator of the fraction, if you'd like it rounded. i.e. for inches you may want 16ths used. The fractions will still be reduced, however, so 3.746 --> 3 12/16 --> 3 3/4
-> Optional parameter "buildup" set to True will build up the fraction using the equation editor, typing the text right into the active document. If you prefer to have the function simply return a flat string representation of the fraction so you can store it programmatically etc. set this to False.
-> A decimal could terminate after a bunch of repetitions... this function would assume an infinite repetition.
-> Variable type Double trades off whole number digit for decimal digits, only allowing 16 digits total (from my observations anyway!). This function assumes that if a number is using all 16 of the available digits then it must be a repeating decimal. A large number such as 123456789876.25 would be mistaken for a repeating decimal, then returned as decimal number upon failing to find a pattern.
-> To express really large terminating decimal out of 10^n, VB can only handle 10^8 is seems. I round the origninal number to 8 decimal places, losing some accuracy perhaps.
-> For the math behind converting repeating patterns to fractions check this link
-> Use Euclidean Algorithm to reduce the fraction
Ok, here it is, written as a Word Macro:
Function as_fraction(number_, Optional denom As Integer = -1, Optional buildup As Boolean = True) As String
'Selection.TypeText Text:="Received: " & CStr(number_) & vbCrLf
Dim number As Double
Dim repeat_digits As Integer, delay_digits As Integer, E_position As Integer, exponent As Integer
Dim tail_string_test As String, tail_string_original As String, num_removed As String, tail_string_removed As String, removed As String, num As String, output As String
output = "" 'string variable to build into the fraction answer
number = CDbl(number_)
'Get rid of scientific notation since this makes the string longer, fooling the function length = digits
If InStr(CStr(number_), "E+") > 0 Then 'no gigantic numbers! Return that scientific notation junk
output = CStr(number_)
GoTo all_done
End If
E_position = InStr(CStr(number), "E") 'E- since postives were handled
If E_position > 0 Then
exponent = Abs(CInt(Mid(CStr(number), E_position + 1)))
num = Mid(CStr(number_), 1, E_position) 'axe the exponent
decimalposition = InStr(num, ".") 'note the decimal position
For i_move = 1 To exponent
'move the decimal over, and insert a zero if the start of the number is reached
If InStr(num, "-") > 0 And decimalposition = 3 Then 'negative sign in front
num = "-0." & Mid(num, InStr(num, ".") - 1, 1) & Mid(num, InStr(num, ".") + 1) 'insert a zero after the negative
ElseIf decimalposition = 2 Then
num = "0." & Mid(num, InStr(num, ".") - 1, 1) & Mid(num, InStr(num, ".") + 1) 'insert in front
Else 'move the decimal over, there are digits left
num = Mid(num, 1, decimalposition - 2) & "." & Mid(num, decimalposition - 1, 1) & Mid(num, decimalposition + 1)
decimalposition = decimalposition - 1
End If
Next
Else
num = CStr(number_)
End If
'trim the digits to 15, since VB rounds the last digit which ruins the pattern. i.e. 0.5555555555555556 etc.
If Len(num) >= 16 Then
num = Mid(num, 1, 15)
End If
number = CDbl(num) 'num is a string representation of the decimal number, just to avoid cstr() everywhere
'Selection.TypeText Text:="number = " & CStr(number) & vbCrLf
'is it a whole number?
If Fix(number) = number Then 'whole number
output = CStr(number)
GoTo all_done
End If
decimalposition = InStr(CStr(num), ".")
'Selection.TypeText Text:="Attempting to find a fraction equivalent for " & num & vbCrLf
'is it a repeating decimal? It will have 16 digits
If denom = -1 And Len(num) >= 15 Then 'repeating decimal, unspecified denominator
tail_string_original = Mid(num, decimalposition + 1) 'digits after the decimal
delay_digits = -1 'the number of decimal place values removed from the tail, in case the repetition is delayed. i.e. 0.567777777...
Do 'loop through start points for the repeating digits
delay_digits = delay_digits + 1
If delay_digits >= Fix(Len(tail_string_original) / 2) Then
'Selection.TypeText Text:="Tried all starting points for the pattern, up to half way through the tail. None was found. I'll treat it as a terminating decimal." & vbCrLf
GoTo treat_as_terminating
End If
num_removed = Mid(num, 1, decimalposition) & Mid(num, decimalposition + 1 + delay_digits) 'original number with decimal values removed
tail_string_removed = Mid(num_removed, InStr(CStr(num_removed), ".") + 1)
repeat_digits = 0 'exponent on 10 for moving the decimal place over
'Selection.TypeText Text:="Searching " & num_removed & " for a pattern:" & vbCrLf
Do
repeat_digits = repeat_digits + 1
If repeat_digits = Len(tail_string_removed) - 1 Or repeat_digits >= 9 Then 'try removing a digit, incase the pattern is delayed
Exit Do
End If
tail_string_test = Mid(num_removed, decimalposition + 1 + repeat_digits)
'Selection.TypeText Text:=vbTab & "Comparing " & Mid(tail_string_removed, 1, Len(tail_string_removed) - repeat_digits) & " to " & tail_string_test & vbCrLf
If Mid(tail_string_removed, 1, Len(tail_string_removed) - repeat_digits) = tail_string_test Then
'Selection.TypeText Text:=num & ", " & Mid(tail_string_removed, 1, Len(tail_string_removed) - repeat_digits) & " vs " & tail_string_test & vbCrLf
GoTo foundpattern
End If
Loop
Loop 'next starting point for pattern
foundpattern:
If delay_digits = 0 Then 'found pattern right away
numerator = CLng(Mid(CStr(number), decimalposition + 1 + delay_digits, CInt(repeat_digits)))
'generate the denominator nines, same number of digits as the numerator
bottom = ""
For i_loop = 1 To repeat_digits
bottom = bottom & "9"
Next
denominator = CLng(bottom)
Else 'there were numbers before the pattern began
numerator = CLng(Mid(num, decimalposition + 1, delay_digits + repeat_digits)) - CLng(Mid(num, decimalposition + 1, delay_digits))
'i.e. x = 2.73232323232... delay_digits = 1, repeat_digits = 2, so numerator = 732 - 7 = 725
bottom = ""
For i_loop = 1 To repeat_digits
bottom = bottom & "9"
Next
For i_loop = 1 To delay_digits
bottom = bottom & "0"
Next
denominator = CLng(bottom)
'i.e. 990... 725/990 = 145/198 = 0.7323232...
End If
Else ' terminating decimal
treat_as_terminating:
'grab just the decimal trail
If denom = -1 Then
number = Math.Round(number, 8) 'reduce to fewer decimal places to avoid overload
'is it a whole number now?
If Fix(number) = number Then 'whole number
output = CStr(number)
GoTo all_done
End If
num = CStr(number)
numerator = CLng(Mid(num, decimalposition + 1))
denominator = 10 ^ (Len(num) - InStr(num, "."))
Else 'express as a fraction rounded to the nearest denom'th reduced
numerator1 = CDbl("0" & Mid(CStr(num), decimalposition))
numerator = CInt(Math.Round(numerator1 * denom))
denominator = CInt(denom)
End If
End If
'reduce the fraction if possible using Euclidean Algorithm
a = CLng(numerator)
b = CLng(denominator)
Dim t As Long
Do While b <> 0
t = b
b = a Mod b
a = t
Loop
gcd_ = a
numerator = numerator / gcd_
denominator = denominator / gcd_
whole_part = CLng(Mid(num, 1, decimalposition - 1))
'only write a whole number if the number is absolutely greater than zero, or will round to be so.
If whole_part <> 0 Or (whole_part = 0 And numerator = denominator) Then
'case where fraction rounds to whole
If numerator = denominator Then
'increase the whole by 1 absolutely
whole_part = (whole_part / Abs(whole_part)) * (Abs(whole_part) + 1)
End If
output = CStr(whole_part) & " "
End If
'if fraction rounded to a whole, it is already included in the whole number
If numerator <> 0 And numerator <> denominator Then
'negative sign may have been missed, if whole number was -0
If whole_part = 0 And number_ < 0 Then
numerator = -numerator
End If
output = output & CStr(numerator) & "/" & CStr(denominator) & " "
End If
If whole_part = 0 And numerator = 0 Then
output = "0"
End If
all_done:
If buildup = True Then 'build up the equation with a pretty fraction at the current selection range
Dim objRange As Range
Dim objEq As OMath
Dim AC As OMathAutoCorrectEntry
Application.OMathAutoCorrect.UseOutsideOMath = True
Set objRange = Selection.Range
objRange.Text = output
For Each AC In Application.OMathAutoCorrect.Entries
With objRange
If InStr(.Text, AC.Name) > 0 Then
.Text = Replace(.Text, AC.Name, AC.Value)
End If
End With
Next AC
Set objRange = Selection.OMaths.Add(objRange)
Set objEq = objRange.OMaths(1)
objEq.buildup
'Place the cursor at the end of the equation, outside of the OMaths object
objRange.OMaths(1).Range.Select
Selection.Collapse direction:=wdCollapseEnd
Selection.MoveRight Unit:=wdCharacter, count:=1
as_fraction = "" 'just a dummy return to make the function happy
Else 'just return a flat string value
as_fraction = output
End If
End Function
I shared an answer at this link : https://stackoverflow.com/a/57517128/11933717
It's also an iterative function, but unlike finding numerator and denominator in a nested loop, it just tests numerators only and so, should be faster.
Here is how it works :
It assumes that, based on the user input x, you want to find 2 integers n / m .
n/m = x , meaning that
n/x should give an almost integer m
Say one needs to find a fraction for x = 2.428571. Putting the int 2 aside for later, the algo starts by setting n and x and iterates n :
// n / x = m ( we need m to be an integer )
// n = 1 ; x = .428571 ;
1 / .428571 = 2.333335 (not close to an integer, n++)
2 / .428571 = 4.666671 (not close to an integer, n++)
3 / .428571 = 7.000007
At this point n = 3, we consider that m = 7.000007 is integer enough --based on some kind of accuracy the programmer decides-- and we reply the user
2.428571 = 2 + 3/7
= 14/7 + 3/7
= 17/7