Is it possible to generate a table of permutations in Excel without using VBA and without using any "helper" sheets or rows/columns?
For N columns, there would be N! rows.
For example, the table for N=3 would look like this:
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
Open a blank worksheet and paste the following formula into cell A1. (I included line breaks for readability.)
= IF(ROW()<=FACT(COLUMN()-1),COLUMN(),
INDIRECT(ADDRESS(ROW()-FACT(SUMPRODUCT(((ROW()-1)>=FACT(ROW($A$2:$A$10)))+0)+1),
IF(COLUMN()=(SUMPRODUCT(((ROW()-1)>=FACT(ROW($A$2:$A$10)))+0)+2),1,COLUMN()+1))))
Simply drag this formula over N columns and then down N! rows in order to generate a full permutation table of order N.
A few things to note:
Because factorials grow very quickly, the formula above only works for N<=10. However, this isn't really a limitation because 10! = 3,628,800 which is a number that exceeds the maximum number of rows in Excel 2010 (which is 1,048,576). Therefore, Excel can't generate a permutation table for N=10 anyway.
If you want the top left of the table to be a cell other than A1, the formula can manually be modified to account for this shift. For example, if you want the table to start at A2 instead of A1, replace each instance of ROW() in the formula above with (ROW()-1).
Excluding the first row (which lists the numbers ascending) and the last row (which lists the numbers descending), the order in which the permutations are listed in this table are not in the same order as listed in the original question, but the pattern is still deterministic. See below for a screenshot of a permutation table using this formula of order 4, using conditional formatting to make it easy to spot the pattern of how the order of the permutations change as row numbers increase.
EDIT:
Another solution with all of the same properties as above except that the permutations are generated in a different order is the following:
= IF(ROW()<=FACT(COLUMN()-1),COLUMN(),
INDIRECT(ADDRESS(ROW()-FACT(SUMPRODUCT(((ROW()-1)>=FACT(ROW($A$2:$A$10)))+0)+1),COLUMN()))
+IF(ROW()<=FACT(COLUMN()),-1,
IF(INDIRECT(ADDRESS(ROW()-FACT(SUMPRODUCT(((ROW()-1)>=FACT(ROW($A$2:$A$10)))+0)+1),COLUMN()))
=INDIRECT(ADDRESS(ROW(),(SUMPRODUCT(((ROW()-1)>=FACT(ROW($A$2:$A$10)))+0)+2))),1,0)))
This formula is obviously longer than the first formula, but it still generally accomplishes the same thing: Open a blank worksheet and paste this formula into cell A1. Then drag the formula over N columns and then down N! rows in order to generate a full permutation table of order N.
As already stated, however, the order of the permutations changed as compared to the previous solution. The order of permutations in this solution is arguably better than that of the first solution because each column always contains "blocks" of numbers of the same size. See below for a screenshot of a permutation table using this formula of order 4, using conditional formatting to make it easy to spot the pattern of how the order of the permutations change as row numbers increase.
For those stumbling upon this in 2021 and beyond: if you have access to Power Query, a Cross join is a straightforward way to achieve this (and technically not VBA and doesn't use "helper" columns)
See documentation here.
Related
So I'm going to eventually have 3 sheets. Sheet 1 is where I have data (numbers for a category and a name associated with it. Sheet 2 is where I pull the top 5 users for each category. Sheet 3 is where I have a leaderboard for points gained.
Right now I'm trying to work with Sheet 2 (grab the top 5 performers from each category. I'm fairly new to Excel, but after some research it seemed that XLOOKUP would be the way to go. (i'll attach screenshots below.
I'm using this formula:
=XLOOKUP(LARGE('Cases Test for Categories'!$C$18:$C$55,1),'Cases Test for Categories'!$C$18:$C$55,'Cases Test for Categories'!$A$18:$A$55)
however when using it I get all 0's.
Here's a screenshot of values I'm trying to grab from "Warranty Service Request"
and here is a screenshot when applying my formula
The solution I would want is to grab the 5 largest numbers from sheet 1 with the person name as well.
I don't think that XLOOKUP can get you anywhere near what you want but the formula below will get you one step closer.
=INDEX(List,MATCH(LARGE(INDEX(List, ,2),1),INDEX(List,,2),0),1)
In fact, it's the explanation of that formula which will be of help. Here we go.
List is a named range, perhaps equal to your 'Cases Test for Categories'!$C$18:$C$55. The reason for using a name is obvious. It's shorter. In my test List = A2:B6, in case you want to reconstruct it. Column 1 has names, column 2 numbers.
The term INDEX(List,,2) specifies the second column of List. You can replace the '2' with a formula to specify different columns of the named range.
In fact, INDEX(List,,1) does specify the first column and INDEX(List,4,1) specifies the 4th cell in that column, and that is exactly what you see in my formula. All of MATCH(LARGE(INDEX(List, ,2),1),INDEX(List,,2),0) just serves to find the row number in List, in this example the number 4.
Of course, LARGE(INDEX(List, ,2),1) returns the largest number in column2 of List. The '1' can be replaced by a formula, for example ROW()-1 which would return 1 if placed in row 2 and count up from there as it's copied down. Try =ROW()-1 in any cell in row 2 and copy the formula down.
MATCH([LARGEST],INDEX(List,,2),0) returns the row number where the largest was found, and that is the number we need to return the name from the first column of List.
This will work perfectly for one column and can easily be modified to work for different columns. Your question doesn't specify how you would like to arrange the 5 results from each category but the formula can be modified a little to accommodate whatever you want. What it can not do is to deal with ties. MATCH(LARGE can only find the first of several identical results.
To break ties in this sort of operation is complicated and must be done ether by helper columns in the data table or using VBA. It's definitely the topic of another question. For now I hope that it's a problem you will not have to anticipate.
How to reproduce cells that are in the same row a certain time? Please see the screenshot.
Use INDEX function to reference each of your text ranges as a 1D range.
Then you just need to develop two counters. The first counter will increase by 1 every 4 columns, the other will reset/loop every 4 columns. Use these counter to pull the appropriate cell address from the INDEX Function.
The following formula increases by 1 every 4 columns:
=INT((COLUMN(A:A)-1)/4)+1
The following formula loops a count of 1 to 4 as its copied to the right:
=MOD(COLUMN(A:A)-1,4)+1
Combined with with an index you can use the following formulas:
Names
=INDEX($A$1:$G$1,INT((COLUMN(A:A)-1)/4)+1)
Letters
=INDEX($A$3:$D$3,MOD(COLUMN(A:A)-1,4)+1)
Note the formula will produce an error if you pull it too far to the right as it will run out of names in the index to reference. It will work for a maximum columns Number of Names X Number of Letters, or the Maximum number of columns in your spreadsheet, which ever is smaller.
If you have Excel O365 with dynamic arrays and the SEQUENCE function, you can use these formulas in a single cell.
The results will SPILL over the requisite number of Cells, and adjust if you change the data ranges.
I used Dynamic named ranges for the two rows of information you have, but you could use Tables, or other methods:
A7: =INDEX(myMonths,1,INT(SEQUENCE(,COLUMNS(myData)*COLUMNS(myMonths),1,1/COLUMNS(myData))))
A8: =INDEX(myData,1,MOD(-1+SEQUENCE(,COLUMNS(myData)*COLUMNS(myMonths)),COLUMNS(myData))+1)
I thought a bit and figured out a simple solution as shown in the screenshot.please see the formula here
I'm looking for a way to count the number of times two cells appear side by side in Excel - like intersections. Sometimes in my data (of about 550 records) A Road will appear next to B Road, which is a count of 1. If it occurs again, later in the data the count would be 2. But if B Road appears in the first column and A Road appears in the second column, I can't find a way to make that number 3 in the count.
I've tried concatenating the data, but I need to be able to write this formula without inserting specific criteria (like searching for A Road) because it would be easier in that case to do this manually. Does anyone know if there's a formula for find the occurrence of the same two variables between two columns without specific criteria?
If the order of values in the two columns were important (i.e. A Road followed by B Road is different than B Road followed by A Road), then a simple pivot table would provide the counts you need. You would just put Col M on the rows, Col N on the columns and the count of any field as the value.
But the OP has said that A Road followed by B Road should be counted in the same total as B Road followed by A Road. Let's modify the concatenation in Col O to become =IF(M2<N2,CONCAT(M2," & ",N2),CONCAT(N2," & ",M2)). That provides a canonical form of each combination regardless of order. Having done that, then it is again an easy matter to create a pivot table that shows all the required counts -- just put the concatenated value on the rows and the count as the value.
If I correctly understand your intent, then try this array formula : =SUM(IF(EXACT(B$2:B3&C$2:C3,B3&C3),1,""))+SUM(IF(EXACT(B$2:B3&C$2:C3,C3&B3),1,"")).The second sum formula accounts for any reverse order of adjacent street occurrences.Then copy down the column as needed. Enter with Ctrl+Shift+Enter.
I have a spreadsheet and I need to match the two columns together. However "Dove code" is 3600 rows and "code 2" is 1100. They all have the same codes as you can see in the image but you can also see where it starts changing and I need to have the codes all line up so I can see the gaps. I have already arranged them all alphabetically and its the "code 2" that would need to match up to "Dove code
If the above solution would result in too much shunting and vba is not an option, there's another way. Copy the first column and use 'remove duplicates' on it. Now you have an index list, put numbers from 1 to x in the column on the right of it.
Insert a column between the two lists and right of the second one.
Assuming that the index list is in F and the numbers in G, put this formula in the cell right of the first cell in the larger list:
=VLOOKUP(A2,$F$2:$G$500,2,FALSE)
Adjust the range accordingly. Put the same formula in the cell right of the first cell in the shorter list, with of course C2 instead of A2. Copy both formules to the end of the list.
Now both columns have an index on every row. You can match them using data sort, but for that you need to add dummies in the index columns.
Put this formula in the cell right of your basic index list: =countif(B:B,G2)
And this one in the cell right of that: =countif(D:D,G2)
Now you know how many times each record arises in both lists. Just add extra numbers manually so that both formulas turn up the same result. You should be able to do that really fast. If you have 200 records that are used 2 times in the first column and not in the second one, just copy the index of those 200 records and paste them twice. The countif's will automatically update.
You can use an extra column to calculate the difference between the two counts and use data sort on your basic index list to sort on the diferences.
After that just use data sort.
IF my directions are clear enough, this shouldn't cost you more than 10 minutes.
Edit:
Here's an example: http://img14.imageshack.us/img14/6366/k8pg.jpg
Without VBA I do this (for columns with a limited number of mismatches!) by adding a formula such as =INDIRECT("A"&ROW())<>INDIRECT("B"&ROW()) in a helper column. Working downwards, every time you see a TRUE shunt the appropriate column down to suit. But it may be only just about viable for 1100 rows!
I'm performing array calculations that are taking a long time to complete. I'd like to optimize my formulas some more. All of the formulas are of the same nature - they perform some high-level function (Average, Slope, Min, Max) across a column of values. However, not all cells in a column are included in the array. I use multiple IF criteria to choose which cells get included. All comparisons are made to the current row. Here's an example of the data:
A B C D E
1 Company Generation Date Value ToCalculate
2 Abc 1 1/1/2010 5.6
3 ... ... ... ... ...
E would look something like this
{=Average(If(A2=A2:A1000, If(B2=B2:B1000, If(C2 > C2:C1000, D2:D1000))))}
So once E2 is calculated then I have to autofill down column E. Column F, G, H, ... Uses the same approach, either selects different values to operate on or a different function to perform. My dataset is quite large, and with only a few of these the spreadsheet is taking an hour plus to compute. Every so often I'll add a fourth criteria, all other criteria being the same.
Is there an efficiency? Some thoughts:
Can I use a single array per column instead of thousands per column?
Can I condense the first three criteria so that the output is row numbers? Perhaps then subsequent formulas won't have to search for multiple criteria but can just perform the function?
or somehow build the crtieria up? So a new column returns all rows where the company is the same. another column returns all rows from the first column where generation is the same...and so on...
For the Average you can do without arrays:
=AVERAGEIFS(D2:D$1000,A2:A$1000,A2,B2:B$1000,B2,C2:C$1000,"<="&C2)
As there is also a COUNTIFS and a SUMIFS, I think your slopes could be calculated the same way.
For the rest of the functions (max, min, etc), we should analyze case by case.
I did a slight performance test, and this is apparently better, but of course my datasets are just mocked.
HTH!
Note: Excel 2007 and up only!
Edit - Answering your comment.
Without knowing the dimensions of the problem is difficult to give advice, but I'll risk one anyway:
You could write a VBA function that:
1) Generates a new sheet for each company-generation pair
2) Sorts the data in those sheets by date
3) Adds the formulas to those sheets (no conditionals needed in this context)
4) Recalculates and Gets the results from those formulas and populates the original sheet
5) Deletes the auxiliary sheets
To capture the rows and re-use try this approach:
Sort the data by Company & Generation.
Make a unique list of Companies & generations (use Advanced Filter, Unique Only, Copy)
For each Company generation pair in the list build 2 columns of formulae. First column gives the count of rows in the data for this pair (use COUNTIFS), second column gives the first row in the data for this pair (=first row for previous pair+count of rows for previous pair). Then you can use a function like OFFSET to return only the rows of data for the Company-Generation pair and embed this inside the final function/array formula (AVERAGEIFS etc) You could extend this sort and count approach to include dates if you wanted. There is a drawback that if the list of cities and generations change you have to change the list of uniques and associated formulas. There are examples of this approach on my website athttp://www.decisionmodels.com/optspeedk.htmhttp://www.decisionmodels.com/optspeedj.htm