Formula Forensics. 009 – Pradhishnair’s Chainage Problem

Posted on January 17th, 2012 in Excel Howtos , Formula Forensics , Huis , Posts by Hui - 5 comments

A common Forum question and one that Chandoo has written about a few times is, Does my data overlap with another range?

Last week, Pradhishnair, asked in the Chandoo.org Forums I need to find if the values between range D2:E2 are overlapping in any of the following rages, if yes then where? (may be row number)”

I answered with an array formula:

{=”Overlap Row S.no. = ” &MIN(IF((D3:$D$41<=E2) *(E3:$E$41>=D2) >0, (A3:$A$41)))}

Which returns ether:

Overlap Row S.no. = x (If there is an overlap)

or

Overlap Row S.no. = 0 (If there is no overlap)

So today in Formula Forensics we will take a look at how the above formula works with a worked example.

 

Chainage

As always you can follow along with a worked example. This is a subset of Pradhishnair’s Data to simplify the length of the equations, but otherwise is the same as the original post: Download Here

Pradhishnair’s data consists of a list of chainages. Chainages are measurements of distances from a fixed point and relate to a segment of something. Chainage From is to the closest end of the segment and and Chainage To is to the furthest end of the segment and by default these are in order, that is To is always greater than From.

Using this we can check for overlapping data by simply checking if the From is less than the remaining To’s or the To value is greater than the remaining From’s

This is done for each row compared to the remaining rows of data by the array formula

=”Overlap Row S.no.: ” & MIN(IF((D3:$D$41<=E2) *(E3:$E$41>=D2) >0, (A3:$A$41))) Ctrl Shift enter

We can see that the above equation simply joins

“Overlap Row S.no.: “

To the result of

MIN(IF((D3:$D$41<=E2) *(E3:$E$41>=D2) >0, (A3:$A$41)))

Using the & operator

It will return:

Overlap Row S.no. = 0 if there is no overlap

Or

Overlap Row S.no. = x If there is an overlap.

So the function

MIN(IF((D3:$D$41<=E2) *(E3:$E$41>=D2) >0, (A3:$A$41)))

Is used to return the minimum value of an If() formula which is its only component

The If() statement usually has three components:

=If( Condition, Value if True, Value if False)

In our case, I will evaluate Row 2, Particularly Cell G2, against the remaining entries in the two lists.

=If((D3:$D$41<=E2) *(E3:$E$41>=D2) >0, (A3:$A$41))

Condition:  (D3:$D$41<=E2) *(E3:$E$41>=D2) >0

Value if True:  (A3:$A$41), This is just the S.No. in Column A

Value if False:  Note that the If statement has no Value if it is False, I could put any value there eg: -1 or 0, but Excel evaluates it to 0 anyway so it hasn’t been used.

 

The If Statement says If (D3:$D$41<=E2) *(E3:$E$41>=D2) >0, then return (A3:$A$41)

What the condition is saying is If the To Data in the Current Row, Row 2, is Greater than or equal to the other From Values or the From Data in the Current Row, Row 2, is Less than the other To Value, Then this is True

To check this, in Cell I2, enter  =(D3:$D$41<=E2) *(E3:$E$41>=D2) and evaluate it with F9 instead of Enter

Excel returns ={1;1;0;0;0;0;0;0;0}

Excel is showing us that the first and second entries have overlapping data.

Which we can see if we look at the data

The >0 at the end of the (D3:$D$41<=E2) *(E3:$E$41>=D2) >0, transforms the array of 0’s and 1’s to an array of Falses and Trues

To check this, in I3, enter  =(D3:$D$41<=E2) *(E3:$E$41>=D2)>0 and evaluate it with F9 instead of Enter

Excel returns ={TRUE;TRUE;FALSE;FALSE;FALSE;FALSE;FALSE;FALSE;FALSE}

Now the If Statement will be True for the first two entries in the array and so will evaluate the Value if True component of the If Formula:  (A3:$A$41)

We can check this

In cell I4 enter

=IF((D3:$D$41<=E2) *(E3:$E$41>=D2) >0, (A3:$A$41)) and press F9 instead of Enter

Excel returns

={2;3;FALSE;FALSE;FALSE;FALSE;FALSE;FALSE;FALSE}

Which is the array of S.No’s which match our criteria

Now Min comes in

=MIN({2;3;FALSE;FALSE;FALSE;FALSE;FALSE;FALSE;FALSE})

Min returns the Minimum of these which is 2.

And that is appended to “Overlap Row S.No. = “

To return the answer:  Overlap Row S.No. = 2

Which is the first overlapping row with Row 1

 

Custom Number Formats

You may have noticed that the numbers in Pradhishnair’s worksheet look a bit odd with a + in the middle: eg: D3 displays 142+000

Pradhishnair is using a Custom Number Format of #+000

Select a Cell, eg D2, Press Ctrl 1, Select the Number Tab

If you select these cells and Press F2 Excel will show that the cells value is 142000

But Excel is using the custom Number format of #+000 to display the number with 3 digits after the +

 

Links to Overlapping Data Posts

http://chandoo.org/wp/2010/06/01/date-overlap-formulas/

http://chandoo.org/wp/2011/03/09/ec1-machine-scheduling-in-excel/

 

Download

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

 

Other Formula Forensics Posts

You can learn more about how to pull Excel Formulas apart in the following posts

Formula Forensic Series:

 

We Need Your Help

I received 3 ideas over the Xmas break from readers, and these will feature in coming weeks.

However I do need more ideas for the rest of 2012 and so I need your help.

 

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 in Formula Forensics 003. or like 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.

 

ps: I’m traveling to Esperance; Western Australia for a short holiday with the family but have left a neat Formula Forensic for you for next week.

5 Responses to “Formula Forensics. 009 – Pradhishnair’s Chainage Problem”

  1. Nikki says:

    Thank you Guys for imparting such good knowledge and expertise daily - my brain can't handle a lot of it but you and Chandoo are not only inspirational, but aspirational as well.

    Keep doing such an awesome job

    Regards from sunny South Africa,

    Nikki 🙂

  2. Pradhish Nair says:

    The formula has been a life saver for me..

    thanks again Hui..

  3. JohnC_UK says:

    I love the information on your site. I only came across it a couple of weeks ago.

    I nicked and adapted this example but I made two changes.

    1. I changed the array formula to:

    {=MIN(IF((D3:$D$41 = D2) >0, (A3:$A$41)))}

    so the cell contains the number that overlaps - allowing me to use that elsewhere without the text causing any problems.

    2. I set a custom format of:

    "Overlap Row S.no.: "0;;

    Only those rows with non-zero values will display anything, zero values are blank and there should be no negative values.

    I'm learning a lot from your site and the explanations are the clearest I've ever read.

    Keep up the excellent work!

  4. Jakob Olsen says:

    Hi

    Thank you for this - I have really looked for something like it.
    I have one problem with it though that I can't solve.
       
    My list of entries is a list that people keep adding rows to. And I can't seem to make it work with the new rows except I have to go change the formula everytime a new row is added.
    I have tried using a tableformat in Excel but I can't seem to make that work either.
    Can you please help me?

    Y/Jakob   

  5. rohit says:

    Please Help me for Preparing bar chart with Chainage gap for particular Item in if or condition which i will get answer 1 and i can fill the cell with color by conditional formatting

    4
    1.03a
    Excavation Road
    ChK-JhB
    4450
    5550
    LHS
    33
    71990
    73090

    4
    1.3a
    Excavation Road
    ChK-JhB
    5950
    8050
    LHS
    33
    73490
    75590

    4
    1.3a
    Excavation Road
    ChK-JhB
    8550
    9175
    LHS
    33
    76090
    76715

    4
    1.3a
    Excavation Road
    ChK-JhB
    9450
    9800
    LHS
    33
    76990
    77340

    4
    1.3a
    Excavation Road
    ChK-JhB
    10350
    10590
    LHS
    33
    77890
    78130

    4
    1.3a
    Excavation Road
    ChK-JhB
    11000
    11050
    LHS
    33
    78540
    78590

    4
    1.3a
    Excavation Road
    ChK-JhB
    11235
    11285
    LHS
    33
    78775
    78825

    4
    1.3a
    Excavation Road
    ChK-JhB
    11600
    11860
    LHS
    33
    79140
    79400

    4
    1.3a
    Excavation Road
    ChK-JhB
    11900
    12100
    LHS
    33
    79440
    79640

     
    0+000
    0+100
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    0+000 - 0+090
    0+100 - 0+190
    0+200 - 0+290
    0+300 - 0+390
    0+400 - 0+490
    0+500 - 0+590
    0+600 - 0+690
    0+700 - 0+790
    0+800 - 0+890
    0+900 - 0+990

    0
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    28
    EMBANKMENT
    1
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    29
    Excavation BA
    1
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    34
    Excavation Road
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