# Lookup for a value in Unsorted data

#### stakar

##### Active Member
Hi!
I have 2 columns A & B that their data are like these
A B
500 0
501 1
502 5
503 0
504 2
505 2
506 4
507 0
508 3
509 5
510 1
511 0

I want to keep the data on column B that way (unsorted) but i want to find the first position the 0, the 1, the 5 etc. is, starting from bottom to top. and for return to get the value of the column A.
So if i want to find the 0 i ll get as result the 511
So if i want to find the 5 i ll get as result the 509
So if i want to find the 4 i ll get as result the 506 and goes on.

Stathis

##### MrExcel MVP
stakar said:
Hi!
I have 2 columns A & B that their data are like these
A B
500 0
501 1
502 5
503 0
504 2
505 2
506 4
507 0
508 3
509 5
510 1
511 0

I want to keep the data on column B that way (unsorted) but i want to find the first position the 0, the 1, the 5 etc. is, starting from bottom to top. and for return to get the value of the column A.
So if i want to find the 0 i ll get as result the 511
So if i want to find the 5 i ll get as result the 509
So if i want to find the 4 i ll get as result the 506 and goes on...
Book1
ABCDE
1XYYX
250000
350111
450252
550303
650424
750525
85064
95070
105083
115095
125101
135110
 Sheet1

The formula in E2, which is copied down, is:

=LOOKUP(2,1/(\$B\$2:\$B\$13=D2),\$A\$2:\$A\$13)

#### stakar

##### Active Member
Thanks a lot!!
It was exactly what i wanted to do!!

Stathis

#### just_jon

##### Legend
Now, that's slick. #### RalphA

##### Well-known Member
Just Jon has expressed his appreciation for Aladin's solution! Me, I can see the brilliant results, but, when I find the description for LOOKUP, I find:
=LOOKUP(lookup_value,lookup_vector,result_vector).

Would you be so kind as to explain the logic of your formula (for E2)?:
=LOOKUP(2,1/(\$B\$2:\$B\$13=D2),\$A\$2:\$A\$13)

From the description, your formula would seem to indicate that:
lookup_value=2
lookup_vector = 1/(\$B\$2:\$B\$13=D2)

I just can't understand what is going on here??? Thanks.

#### fairwinds

##### MrExcel MVP
RalphA said:
Just Jon has expressed his appreciation for Aladin's solution! Me, I can see the brilliant results...

Well it's briliant!

1/(\$B\$2:\$B\$13=D2) is the lookup array, an array that will look something like:

#DIV/0!, #DIV/0!, 1, #DIV/0!, 1, #DIV/0!

Looking up 2 in that will return the position of the last "1".

#### RalphA

##### Well-known Member
Thank you, Fairwinds! I understood it, pretty much, to mean that it returns the error code for division by 0 when the value in parenthesis is false (a 0), and it returns a 1 for 1/1 when true. I usually have only a vague glimmer of understanding how the handling of arrays is done, but, this time, I do believe I was able to follow your detailed explanations. Thanks again! However... (sorry), I still don't understand how it can report the position of the fourth (the last) 0 in the data range. Also, how does it determine the correct answer for the one instance of 4?

#### fairwinds

##### MrExcel MVP
Looking up 2 here is the same principal as using "BigNum". I'm sure you can find an explanation if you search for Aladins posts on BigNum.

##### MrExcel MVP
RalphA said:
...However... (sorry), I still don't understand how it can report the position of the fourth (the last) 0 in the data range. Also, how does it determine the correct answer for the one instance of 4?
RalphA said:
...However... (sorry), I still don't understand how it can report the position of the fourth (the last) 0 in the data range. Also, how does it determine the correct answer for the one instance of 4?
Fairwinds's explanation/exposition is just about right.

=LOOKUP(2,1/(\$B\$2:\$B\$13=D2),\$A\$2:\$A\$13)

is structured as:

LOOKUP(LookupValue,LookupVector,ResultVector)

where a vector can be an array like {2,3,7,9} or range object like X3:X6.

The way the formula is set up exploits the fact that

(A)

LOOKUP(n,Ref)
VLOOKUP(n,Ref,1,1)
INDEX(Ref,MATCH(n,Ref,1)

will all return the last numerical value from Ref when n is a number that cannot occur in Ref, an example use of which is:

=LOOKUP(9.99999999999999E+307,A:A);

And the fact that

(B)

the lookup functions ignore error values.

Since the LookupVector in the formula of interest, that is,

1/(\$B\$2:\$B\$13=D2),

is an array object, I should also add the fact that

(C)

the LOOKUP function is capable of returning computed arrays, without control+shift+enter (SumProduct is another example).

Understanding (A) is essential. It's the topic of a discussion in:

http://tinyurl.com/5l4j7

Since

=LOOKUP(9.99999999999999E+307,A2:A25)

returns the last numerical value from A2:A25, which is not perse the last value, the following is an obvious extension:

=LOOKUP(9.99999999999999E+307,A2:A25,B2:B25)

will return the value from B2:B25 which is associated with the last numerical value in A2:A25. (9.99999999999999E+307 is often referred to as BigNum.)

Given the foregoing,

=LOOKUP(2,1/(\$B\$2:\$B\$13=D2),\$A\$2:\$A\$13)

becomes intelligible for:

The lookup value 2 is a BigNum with respect to 1/(\$B\$2:\$B\$13=D2), because 1 divided by any number cannot be equal to or greater than 2. One can replace 2, if so desired, with the BigNum itself (that is: 9.99999999999999E+307).

(\$B\$2:\$B\$13=D2)

is a conditional that is bound to evaluate to an array consisting of logical values like:

{TRUE;FALSE;FALSE;TRUE;FALSE;FALSE;FALSE;TRUE;FALSE;FALSE;FALSE;TRUE}

Then:

1/{TRUE;FALSE;FALSE;TRUE;FALSE;FALSE;FALSE;TRUE;FALSE;FALSE;FALSE;TRUE}

Since 1 and 0 are Excel's numerical equivalents of TRUE and FALSE under coercion, we get a calculated array like:

{1;#DIV/0!;#DIV/0!;1;#DIV/0!;#DIV/0!;#DIV/0!;1;#DIV/0!;#DIV/0!;#DIV/0!;1}

Since the last numerical value is the 12th item in the foregoing array, LOOKUP will retrieve the 12th item from \$A\$2:\$A\$13, the ResultVector.

Let's take up the formula which corresponds to D6 housing 4 (See the exhibit in my original post)...

=LOOKUP(2,1/(\$B\$2:\$B\$13=D6),\$A\$2:\$A\$13)

===>

=LOOKUP(2,1/({0;1;5;0;2;2;4;0;3;5;1;0}=4),{500;501;502;503;504;505;506;507;508;509;510;511})

===> (after the divison)

=LOOKUP(2,{#DIV/0!;#DIV/0!;#DIV/0!;#DIV/0!;#DIV/0!;#DIV/0!;1;#DIV/0!;#DIV/0!;#DIV/0!;#DIV/0!;#DIV/0!},{500;501;502;503;504;505;506;507;508;509;510;511})

As can be seen, the last numerical value (the last instance of 1) is the 7th item. As it so happens, the last numerical value here is also the only numerical value. Hereafter LOOKUP proceeds to fetch the 7th item from

{500;501;502;503;504;505;506;507;508;509;510;511}

which is: 506.

Hope the foregoing is filling in fairwinds's correct exposition at those places where you wanted to have more info.

#### fairwinds

##### MrExcel MVP
Thanks for this excelent explanation.

Now, next time I only need to post a link. :wink:

• proficient

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