Last week in the Chandoo.org Forums a user asked a question
“How do I convert a Roman Numeral to a Number eg: MMMCCCLVII to 3357”
User Xlstime presented the solution of:
=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)
Today we are going to look at how and why that simple formula works
As always at Formula Forensics you can follow along using a sample file: Download Sample File
Solution
Excel has a Roman function wherein =Roman(3357, 0) will return MMMCCCLVII
I knew there was no such reverse Roman function prior to Excel 2013 and so my initial thought was to look at a VBA Solution.
See notes on the Arabic Excel function at the end of the post.
However Xlstime presented =MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)
How does this work?
lets start by pulling it apart from the inside out
=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)
The Indirect Function simply takes its inputs and converts them to a Range, in this case 1:3999.
We will study why 3999 later
=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)
The next function working out is Row()
Excel will convert the function ROW(INDIRECT(“1:3999”)) to an array of Row Numbers
={1;2;3;4;5;6;7;8;9;10;11; …. 3995;3996;3997;3998;3999}
You can see this if you goto cell D7 in the Sample File, press F2 and then F9
I limited the numbers to 300 as Excel cannot display more than 8,192 digits
Stepping out one more function:
=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)
The Roman() function converts its inputs into Roman Numbers
eg: Roman(58) will return LVIII
But as we are feeding it an array of numbers from 1 to 3999 Excel handles all these and converts them to an Array of Roman Numbers
Goto D9 in the sample file =ROMAN(ROW(INDIRECT(“1:300”))) press F2 and then F9
Excel returns an array of roman numbers
={“I”;”II”;”III”;”IV”;”V”;”VI”;”VII”;”VIII”; … “CCXCVI”;”CCXCVII”;”CCXCVIII”;”CCXCIX”;”CCC”}
We have limited the example to 300 as Excel cannot display more than 8,192 characters when processing a Function using F9.
Stepping out one more function
=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)
The Excel Index() function is taking the Array of Roman Numerals and Converting it into a single Column array
This isn’t technically needed but it simplifies the solution
If you goto cell D11 in the sample file =INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0) press F2 and then F9
Excel returns an array of roman numbers
={“I”;”II”;”III”;”IV”;”V”;”VI”;”VII”;”VIII”; … “CCXCVI”;”CCXCVII”;”CCXCVIII”;”CCXCIX”;”CCC”}
This is exactly the same as the previous output from the Roman() function above, Except that it is now a Single Vertical Array. This is important for the next function.
Stepping out one more function
=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)
We can see here that the Array of Roman Numerals is now being fed into a Match() function.
Match uses the Syntax =Match(Lookup value, Lookup Array, Match Type)
Match returns the position of the Lookup value within the array
So in our example
The Lookup value is A2 or our Roman Numeral MMMCCCLVII
The Lookup Array is an array of Roman Numerals from 1 to 3999
={“I”;”II”;”III”;”IV”;”V”;”VI”;”VII”;”VIII”; … “MMMCMXCV”; “MMMCMXCVI”; “MMMCMXCVII”; “MMMCMXCVIII”; “MMMCMXCIX”}
and the Match Type is 0 or an exact Match
So the Match function will lookup the value MMMCCCLVII in the array and find it in position number 3357, which happens to correspond to the Number of the Roman Numeral and Return 3357 as the result.
Why are we limited to 3999 numbers.
The Excel Roman() function is limited to numbers up to 3999
Why 3999?
Because in Roman Numerals there is no Letter for 5,000 and 4,000 would be shown as M before the Letter for 5,000.
Why did we need the Index() function?
If you goto D17 in the sample file you will see the formula:
=MATCH(A2,ROMAN(ROW(INDIRECT(“1:3999”))),0)
It is the same formula as above but without the Index() function
You will see that it is returning a #VALUE! error
If you edit the formula with F2 and then press F9 to process the function you will see it now shows 3357
What s happening here?
Pressing F9 is the same as Array Entering the Function
so if you edit the function pressing F2 and now Array Enter the function by pressing Ctrl+Shift+Enter, excel now returns 3357
The Index() function puts a wrapper around the array for processing by the Match() function and so Array Entering is avoided.
Most array formulas that require Ctrl+Shift+Enter can be rewritten incorporating an INDEX wrapper and will not require the Ctrl+Shift+Enter confirmation.
The Excel Arabic Function
In 2013, Microsoft introduced the Arabic function to Excel
To use simply use =Arabic(A2) or =Arabic(“MMMCCCLVII”)
You can read about the Syntax of the function in the Excel Help.
Download
You can download a copy of the above file and follow along, Download Sample File.
A Challenge
Can you solve the problem another way ?
Post your solutions in the comments below.
Other Posts in this Series
The Formula Forensics Series contains a wealth of useful solutions and information specifically about how Normal Formula and specifically Array Formula work.
You can learn more about how to pull Excel Formulas apart in the following posts: http://chandoo.org/wp/formula-forensics-homepage/
If you have a formula and you want to understand how it works contact Hui and it may be featured in future posts.
15 Responses to “Compare 2 Lists Visually and Highlight Matches”
Hi,
I solved this in a little different way.
We have 2 lists, one starts at A1 and other at B1, both are vertical arrays.
First thing is define 2 named ranges, list1 and list2:
list1 refers to "=OFFSET(Sheet1!$A$1;0;0;SUMPRODUCT(--(Sheet1!$A$1:$A$1000""));1)"
list2 refers to "=OFFSET(Sheet1!$A$1;0;0;SUMPRODUCT(--(Sheet1!$B$1:$B$1000""));1)"
this way lists will be dynamically sized when you had or remove elements (you can't have blanks and you can't have more than 1000 elements).
Then I use conditional formatting in column A when this formula is true:
"=NOT(ISERROR(MATCH(A1;list2;0)))"
and "=NOT(ISERROR(MATCH(B1;list1;0)))" to list2.
This way we eliminate the need for auxiliary columns or lists.
Hope you like my way! 😀
Nunes
Simple conditional formatting formula.
Assuming lists vertical lists starting in A1 & B1
To highlight just one column (assume B for example)
Conditional formatting>New Rule>by formula
=MATCH(B1,$A$1:$A$99,0)
Set the cell fill to what ever color you prefer & press OK
To highlight both columns repeat with this formula for cell in column A
=MATCH(A1,$B$1:$B$99,0)
This approach doesn't require named fields or addtl columns
glw
Say I had 1 list in A2:A20 and another in B2:B20.
To format all the items in column A that are repeated in column B I would use the following Conditional Formatting rule.
=IF(ISNA(VLOOKUP(A2,$B$2:$B$20,1,false)),true,false)
All the duplicates are highlighted. It us a very simple example of comparison.
I may be missing something here, but I usually highlight both my lists by holding ctrl eg A1:A20 E10:E40 then choose conditional formatting from the ribbon and then highlight duplicates, and this does it?
Lee, I was perplexed as well. I do the same thing you do with the conditional formating. A drag and click to highlight range and choose highlight duplicates does the trick for me.
I believe these methods are to check if an item from one list also appears in the other list. So if an item mentioned many times in one list if also mentioned in the other list or not.
The Conditional Formatting highlight duplicates feature will do this, but it will also highlight an item if it appears multiple times in the one column or list.
Hi, I would just like to know (if you are willing to share) which image editing program you use to make your image like above, like they are torn apart from bottom? I've been looking for long.
@i48998
Chandoo is on Holidays, but Chandoo uses Paint.Net
Paint.net is a free download available at http://www.paint.net/
.
I use CorelDraw/PhotoPaint
.
We both use the Snipping Tool (a freebe with Win Vista/10)
.
We both use Camtasia for doing screen captures to make animated GIFs where you see animation.
Here is how I would accomplish
(1) Define Names: List_1, List_2
(2) =ISNA(MATCH(D4,List_2,0))-1 (Conditional Format formula List_1)
(3) =ISNA(MATCH(D4,List_1,0))-1 (Conditional Format formula List_2)
ISNA will return 1 if NO Match and O if Match by adding a -1 will make: NO Match 0 and Match a -1 which is True
Hi all
this my first Post here
i think we can take Unique List for tow list to know what is not Duplicate By this Array formula
=IFERROR(INDEX($D$6:$D$33,SMALL(IF(ISERROR(MATCH($D$6:$D$33,$B$6:$B$33,0)),ROW($D$6:$D$33)-ROW($D$6)+1),ROWS($J$5:J5))),"")
and this one for Duplicate Value
=IFERROR(INDEX($D$6:$D$33,SMALL(IF(ISNUMBER(MATCH($D$6:$D$33,$B$6:$B$33,0)),ROW($D$6:$D$33)-ROW($D$6)+1),ROWS($J$5:J5))),"")
Don't forget to Enter This Formula by Pressing Ctrl+Shift+Enter
without wanting to ruthlessly self promote here, I do have an addin that does neatly compare two ranges, not just in columns, so you might want to check that out.
Having said that this is a pretty neat solution if you dont want to be going down the VBA or purchase route. I like it
however, could you not do something with the remove duplicates feature in Excel 2010 and then compare the resulting data set?
Hi, Chandoo! I've found yesterday your Excel website... What can I say? It's just awesome, Excellent. Being a developer for 30 years, more than 15 with Office products, and wow!, how many things I discovered in a couple of hours, and what pretty resolved.
I decided to take the long path of the newbies and read all your examples and write down by myself all of them, and when I arrived to this (the comparison of two lists) I think I've found a problem:
a) in "Step 4: Apply conditional formatting to Second List - Use the same logic, but this time the rule becomes =COUNTIF(count1s,$H6)" it should say "Step 4: Apply conditional formatting to Second List - Use the same logic, but this time the rule becomes =COUNTIF(count1s,$H6)>0", but this is a typing error that I believe all of us here might have discovered and corrected
b) the very problem: I wrote down two different lists, in different ranges, and with different number of elements, I specified the equivalent conditional formats, et non voilá!, I didn't get what expected. So I downloaded your example book, I checked range names, formulaes, conditional formats and all OK. So I copied -just values- from my book to yours, and I still couldn't achieve the goal.
I'm using Excel 2010 in spanish, I'm from Buenos Aires (Argentina), and my book is at your disposition whenever you considerate it appropiate.
Thanks in advance for your time, and again my congratulations for your work here.
Best regards.
SirJB7
Comparison of 2 lists visually with highlights
Author: SirJB7 / Date: 11-Dic-2011
Pros: no duplicated tables, no matrix formulaes, no named ranges, no VBA code, just conditional formatting
Cons: not found yet, comments and observations welcome
Features:
a) standard problem: highlights in orange/yellow elements existing in the other list
b) optimized problem: idem a) plus highlights in red/violet first occurrence of elements existing in the other list
Sheet contents:
a) conditional format, 1 rule per list (2 methods used)
A1:A20, first list
B1:B20, second list
a1) range A1:A20, condition =NO(ESERROR(BUSCARV(A1;B$1:B$20;1;FALSO))), format Orange ---> in english: =NOT(ISERROR(VLOOKUP(A1,B$1:B$20,1,FALSE)))
a2) range B1:B20, condition =CONTAR.SI(A$1:A$20;B1)>0, format Yellow ---> in english: =COUNTIF(A$1:A$20,B1)>0
b) conditional format, 2 rules per list (2 methods used)
D1:D20, first list
E1:E20, second list
b1) range E1:E20, condition 1 =Y(NO(ESERROR(BUSCARV(D1;E$1:E$20;1;FALSO)));COINCIDIR(D1;D$1:D$20;0)=FILA(D1)), format Red ---> in english: =AND(NOT(ISERROR(VLOOKUP(D1,E$1:E$20,1,FALSE))),MATCH(D1,D$1:D$20,0)=ROW(D1))
same range, condition 2 and format 2, same as a1)
b2) range E1:E20, condition =Y(CONTAR.SI(D$1:D$20;E1)>0;COINCIDIR(E1;E$1:E$20;0)=FILA(E1)), format Violet ---> in english: =AND(COUNTIF(D$1:D$20,E1)>0,MATCH(E1,E$1:E$20,0)=ROW(E1))
same range, condition 2 and format 2, same as a2)
Personally I like the a2) and b2) solutions, I think the formulaes are prettier.
I still don't know the rules of this website and forum, but it any precept is infringed I'm willing to share the workbook with the solution. If it breaks a rule, I apologize and promise that won't happen again.
Best regards for all!
Dear All i have a complicated situation...
1. I have two sheets of data Sheet1 and Sheet2 (from various sources) - Both of these contain data matching and Not matching as well..
2. Now for me i need to build an excel where in i need to get sheet 3 with values that are present in a column of Sheet 1.
What ever Sheet 1 doesn't have i dont want those rows from sheet 2 to be populated into Sheet3.
Can any one help me out.
Hi Team
The above example is to compare partial name from 2 different columns.
If I want to cross check it in a single column. I have both correct and partial correct/match entries in a column. Is there any way I can find both the entries in the column.
Regards