EXCEL EXPERTS: Formula Forensics No. 003

Formula Forensics No. 003 – Lukes Reward:
Hello everyone. My name is Luke M, and I’ve been coming to Chandoo’s site for about a year now.
I love solving problems, and helping people out on the forums.
Due partly to Hui’s challenge about submitting articles, and 3G’s comment the other day about this particular formula, I decided to try my hand at writing an article.
I Hope it helps explain some cool Excel tricks that I like to use.

The Problem

Often, I see a request from an individual asking for a formula that will be able to generate a list based off of some criteria, with no spaces/blanks.
As Chandoo & Hui have often pointed out, there’s not much Excel can’t do if you know the right functions to use.
Today, we’ll take a look at how we can accomplish this particular task.

Suppose I want to be able to generate a list of all the Vegetables.
In cell E2, I put this array formula:
=IF(COUNTIF(A:A,$D$2) < ROWS($E$2:E2), “”, INDEX(B:B, SMALL( IF($A$2:$A$10 =$D$2, ROW( $A$2:$A$10)), ROW(A1))))
Remember, array formulas need to be confirmed using Ctrl+Shift+Enter, and will have curly brackets { } around the formula if done correctly.
I then copy the cell downward as far as I think will ever be necessary to display all the records (i.e. E7).

Lets Look Inside

Let’s take a closer look at how the formula works.

Front Half

First, let’s look at the IF function’s logic check.
=IF(COUNTIF(A:A,$D$2)<ROWS($E$2:E2),”", INDEX(B:B, SMALL( IF($A$2:$A$10 = $D$2, ROW($A$2:$A$10)), ROW(A1))))
We’re using the COUNTIF function to determine the total number of records that meet our criteria. We’re then comparing this to a ROWS function. The ROWS function simply returns the number of rows given in the argument. Note that the first part of the range callout uses an absolute reference and will not change, while the latter part is relative and will change as the formula is copied down. Thus, in the first cell, the ROWS function evaluates to 1. The next cell, it will evaluate to 2, then 3, and so on. So, the IF statement is checking to see if the number of records returned so far (i.e., formula used) is greater than the total number of possible records. If this is true, return a blank (i.e., “”).

Back Half

The latter half of the formula is where things get tricky.
For this part, let’s work our way from the inside out.
We start off with another IF function:
INDEX(B:B,SMALL(IF($A$2:$A$10=$D$2, ROW($B$2:$B$10)), ROW(A1))))
This section compares A2:A10 with our criteria given in cell D2. So, the array if A2:A10 starts off looking like this:
{Fruit, Fruit, Vegetable, Vegetable, Fruit, Vegetable, “”, “”, “”}
When we compare it with the criteria, it becomes this:
{False, False, True, True, False, True, False, False, False}
Looking at the return values in our IF function, we see that only a True result is stated, the ROW.

INDEX(B:B,SMALL(IF($A$2:$A$10=$D$2, ROW($A$2:$A$10)), ROW(A1))))
So, each True value from the array above will be replaced with the corresponding Row value.
This causes the array to become this:
{False, False, 4, 5, False, 7, False, False, False}
Now that we have a nice array with some numbers in it, this gets fed into the SMALL function.
INDEX(B:B,SMALL(IF($A$2:$A$10=$D$2, ROW($A$2:$A$10)), ROW(A1))))

The ROW function at the end will serve as a type of counter.
In E2, where we initially place the formula, this will evaluate to 1, thus telling the SMALL function to return the 1^st smallest number.
In E3, it will evaluate to 2, and the SMALL function will return the 2^nd smallest number, and so.
So, taking the 1^st smallest number from our array, we get the number 4.
We then take this to the INDEX function
INDEX(B:B,SMALL(IF($A$2:$A$10=$D$2, ROW($A$2:$A$10)), ROW(A1))))
Note that we need to callout the entire column, since we are plugging in row numbers.
The 4^th row in column B leads us to the value “Broccoli”.
The next formula will return the 5^th row, “Spinach”.
The 3^rd formula will return the 7^th row, “Peas”.

This method can be adapted for use with multiple criteria. We would just need to expand the IF function logic checks so that only the correct rows are returned.

PS. If it gets too confusing, the first part of the formula can be omitted.
=IF(COUNTIF(A:A,$D$2)<ROWS($E$2:E2),”", INDEX(B:B, SMALL( IF($A$2:$A$10 = $D$2, ROW($A$2:$A$10)), ROW(A1))))
It is just there to hide any unwanted #NUM errors after all the pertinent records have been displayed.

DOWNLOAD

You can download a copy of the above file and follow along, Download Here.

THANK-YOU and a CHALLENGE

Firstly a Congratulations to Luke M on taking up the challenge and on your First Post at Chandoo.org.
Thank-you for explaining to us all how this formula, which has appeared a number of times on the Chandoo.org Forums, works.
The contents of the Post are published as Luke submitted it with only minor formatting changes.

My Challenge to you is this:
If you have a neat formula that you would like to share and explain, try putting pen to paper and draft up a Post as Luke Did above.
If you have a formula that you would like explained but don’t want to write a post also send it in to Chandoo or Hui.
Send it to Chandoo or Hui.