I have what I think is a interesting question, about google sheets and some Maths, here is the scenario:
4 numbers as follows:
64.20 | 107 | 535 | 1070
A reference number in which the previous numbers needs to fit leaving the minimum possible residue while setting the number of times each of them fitted in the reference number for example we could say the reference number is the following:
806.45
So here is the problem:
I'm calculating how many times those 4 numbers can fit in the reference number by starting from the higher to the lower number like this:
| 1070 | => =IF(E12/((I15+J15)+IF(H17,K17,0)+IF(H19,K19,0)) > 0,ROUNDDOWN(E12/((I15+J15)+IF(H17,K17,0)+IF(H19,K19,0))),0)
| 535 | => =IF(H15>0,ROUNDDOWN((E12-K15-IF(H17,K17,0)-IF(H19,K19,0))/(I14+J14)),ROUNDDOWN(E12/((I14+J14)+IF(H17,K17,0)+IF(H19,K19,0))))
| 107 | => =IF(OR(H15>0,H14>0),ROUNDDOWN((E12-K15-K14-IF(H17,K17,0)-IF(H19,K19,0))/(I13+J13)),ROUNDDOWN((E12-IF(H17,K17,0)-IF(H19,K19,0))/(I13+J13)))
| 64.20 | => =IF(OR(H15>0,H14>0,H13>0),ROUNDDOWN((E12-K15-K14-K13-IF(H17,K17,0)-IF(H19,K19,0))/(I12+J12)),ROUNDDOWN((E12-IF(H17,K17,0)-IF(H19,K19,0))/(I12+J12)))
As you can notice, I'm checking if the higher values has a concurrence, so I can substract the amount from the original number and calculate again how many times can fit the lower number in the result of that subtraction , you can also see that I'm including some checkboxes to the formula in order to add a fixed number to the main number.
This actually works, and as you can see in the example, the result is:
| 1070 | -> Fits 0 times
| 535 | -> Fits 1 time
| 107 | -> Fits 2 times
| 64.20 | -> Fits 0 times
The residue of 806.45 in this example is: 57.45
But each number that needs to fit on the main number needs to take in consideration others; IF you solve this exercise manually, you could get something much better.. like this:
| 1070 | -> Fits 0 times
| 535 | -> Fits 1 time
| 107 | -> Fits 0 times
| 64.20 | -> Fits 4 times
The residue of 806.45 in this example is: 14.65
When I’m talking about residue I mean the result when subtracting, I’m sorry if this is not clear, it’s hard to me to explain maths in English, since is not my native language, please see the spreadsheet and make a copy to better understand what I’m trying to do, or suggest me a way to explain it better if possible.
So what would you do to make it work more efficient and "smart" with the minimum possible residue after the calculation?
Here is the Google's spreadsheet for reference and practice, please make a copy so others can try their own solutions:
LINK TO SPREADSHEET
Thanks in advance for any help or hints.
Delete all current formulas in H12:H15.
Then place this mega-formula in H12:
=ArrayFormula(QUERY(SPLIT(FLATTEN(SPLIT(VLOOKUP(E12,QUERY(SPLIT(FLATTEN(QUERY(SPLIT(FLATTEN(QUERY(SPLIT(FLATTEN(SEQUENCE(ROUNDUP(E12/I12),1,0)&" "&I12&" / "&TRANSPOSE(SEQUENCE(ROUNDUP(E12/I13),1,0)&" "&I13)&"|"&(SEQUENCE(ROUNDUP(E12/I12),1,0)*I12)+(TRANSPOSE(SEQUENCE(ROUNDUP(E12/I13),1,0)*I13))),"|"),"Select Col1")&" / "&TRANSPOSE(SEQUENCE(ROUNDUP(E12/I14),1,0)&" "&I14)&"|"&QUERY(SPLIT(FLATTEN(SEQUENCE(ROUNDUP(E12/I12),1,0)&" "&I12&" / "&TRANSPOSE(SEQUENCE(ROUNDUP(E12/I13),1,0)&" "&I13)&"|"&((SEQUENCE(ROUNDUP(E12/I12),1,0)*I12)+(TRANSPOSE(SEQUENCE(ROUNDUP(E12/I13),1,0)*I13)))),"|"),"Select Col2")+TRANSPOSE(SEQUENCE(ROUNDUP(E12/I14),1,0)*I14)),"|"),"Select Col1")&" / "&TRANSPOSE(SEQUENCE(ROUNDUP(E12/I15),1,0)&" "&I15)&"|"&QUERY(SPLIT(FLATTEN(QUERY(SPLIT(FLATTEN(SEQUENCE(ROUNDUP(E12/I12),1,0)&" "&I12&" / "&TRANSPOSE(SEQUENCE(ROUNDUP(E12/I13),1,0)&" "&I13)&"|"&(SEQUENCE(ROUNDUP(E12/I12),1,0)*I12)+(TRANSPOSE(SEQUENCE(ROUNDUP(E12/I13),1,0)*I13))),"|"),"Select Col1")&" / "&TRANSPOSE(SEQUENCE(ROUNDUP(E12/I14),1,0)&" "&I14)&"|"&QUERY(SPLIT(FLATTEN(SEQUENCE(ROUNDUP(E12/I12),1,0)&" "&I12&" / "&TRANSPOSE(SEQUENCE(ROUNDUP(E12/I13),1,0)&" "&I13)&"|"&((SEQUENCE(ROUNDUP(E12/I12),1,0)*I12)+(TRANSPOSE(SEQUENCE(ROUNDUP(E12/I13),1,0)*I13)))),"|"),"Select Col2")+TRANSPOSE(SEQUENCE(ROUNDUP(E12/I14),1,0)*I14)),"|"),"Select Col2")+TRANSPOSE(SEQUENCE(ROUNDUP(E12/I15),1,0)*I15)),"|"),"Select Col2, Col1 WHERE Col2 <= "&E12&" ORDER BY Col2 Asc, Col1 Desc"),2,TRUE)," / ",0,0))," "),"Select Col1"))
Typically, I explain my formulas. In this case, I trust that readers will understand why I cannot explain it. I can only offer it in working order.
To briefly give the general idea, this formula figures out how many times each of the four numbers fits into the target number alone and then adds every possible combination of all of those. Those are then limited to only the combinations less than the target number and sorted smallest to largest in total. Then a VLOOKUP looks up the target number in that list, returns the closest match, SPLITs the multiples from the amounts (which, in the end, have been concatenated into long strings), and returns only the multiples.
I have a table which includes large number of calculated columns based on other calculated columns. So there are:
x, f(x),g(f(x)),h(g(x)... and so on. Each function uses a large number of fields, so that writing out the formulas from first principles is tedious and error-prone.
I am aware of this solution using sub-queries. However, this becomes increasingly impractical as columns become calculated based on other calculated columns which themselves are calculated. You would need a subquery for every level of calculation. For wide tables like mine, this would be prone to error.
I thought of a different solution, which is firstly to fill the calculated columns with dummy numbers, and then use UPDATE to calculate columns in the sequence desired.
Here is a MWE (not the real thing):
create table a (x ,y,z);
insert into a(x,y,z)
values (1,1,1),(2,1,1);
update a
set y = x,
z = 7 * y;
select * from a;
Currently this doesn't work, and the calculation for z uses the un-refreshed value of y.
To solve this, I have to separate the update statements
update a
set y = 3 * x;
update a
set z = 7 * y;
My question: is there any way to tell SQLITE to complete the calculations for the first line in the UPDATE statement, and then proceeed, so I can bundle all my calculations under one UPDATE statement?
The only database I know that uses the changed values of columns in expressions in an UPDATE statement is MySql.
The standard behavior is to use the stored values.
In your case there is an easy solution.
The new value for y is 3 * x so instead of:
z = 7 * y
use:
z = 7 * (3 * x)
or
z = 21 * x
and your statement will be:
update a
set y = 3 * x,
z = 21 * x;
See the demo.
Results:
| x | y | z |
| --- | --- | --- |
| 1 | 3 | 21 |
| 2 | 6 | 42 |
I have a stream of numbers and in every cycle I need to count the average of last N of them. This can be, of course, solved using an array where I store the last N numbers and in every cycle I shift it, add the new one and count the average.
N = 3
+---+-----+
| a | avg |
+---+-----+
| 1 | |
| 2 | |
| 3 | 2.0 |
| 4 | 3.0 |
| 3 | 3.3 |
| 3 | 3.3 |
| 5 | 3.7 |
| 4 | 4.0 |
| 5 | 4.7 |
+---+-----+
First N numbers (where there "isn't enough data for counting the average") doesn't interest me much, so the results there may be anything/undefined.
My question is, can this be done without using an array, that is, with static amount of memory? If so, then how?
I'll do the coding myself - I just need to know the theory.
Thanks
Think of this as a black box containing some state. If you control the input stream, you can draw conclusions on the state. In your sliding window array-based approach, it is kind of obvious that if you feed a bunch of zeros into the algorithm after the original input, you get a bunch of averages with a decreasing number of non-zero values taken into account. The last one has just one original non-zero value, so if you multiply that my N you get the last input back. Using that and the second-to-last output which accounts for two non-zero inputs, you can reconstruct the second-to-last input, and so on.
So essentially your algorithm needs to maintain sufficient state to reconstruct the last N elements of input, at least if you formulate it as an on-line algorithm. I don't think an off-line algorithm can do any better, except if you consider it reading the input multiple times, but I don't have as strong an agument for that.
Of course, in some theoretical models you can avoid the array and e.g. encode all the state into a single arbitrary length integer, but that's just cheating the theory, and doesn't make any difference in practice.
I am quite a beginner in Data Warehouse Design. I have red some theory, but recently met a practical problem with a design of a OLAP cube. I use star schema.
Lets say I have 2 dimension tables and 1 fact table:
Dimension Gazetteer:
dimension_id
country_name
province_name
district_name
Dimension Device:
dimension_id
device_category
device_subcategory
Fact table:
gazetteer_id
device_dimension_id
hazard_id (measure column)
area_m2 (measure column)
A "business object" (which is a mine field actually) can have multiple devices, is located in a single location (Gazetteer) and ocuppies X square meters.
So in order to know which device categories there are, I created a fact per each device in hazard like this:
+--------------+---------------------+-----------------------+-----------+
| gazetteer_id | device_dimension_id | hazard_id | area_m2 |
+--------------+---------------------+-----------------------+-----------+
| 123 | 321 | 0a0a-502c-11aa1331e98 | 6000 |
+--------------+---------------------+-----------------------+-----------+
| 123 | 654 | 0a0a-502c-11aa1331e98 | 6000 |
+--------------+---------------------+-----------------------+-----------+
| 123 | 987 | 0a0a-502c-11aa1331e98 | 6000 |
+--------------+---------------------+-----------------------+-----------+
I defined a measure "number of hazards" as distinct-count of hazard_id.
I also defined a "total area occupied" measure as a sum of area_m2.
Now I can use the dimension gazetteer and device and know how many hazards there are with given dimension members.
But the problem is the area_m2: because it is defined as a sum, it gives a value n-times higher than the actual area, where n is th number of devices of the hazard object. For example, with the data above would give 18000m2.
How would you solve this problem?
I am using the Pentaho stack.
Thanks in advance
[moved from comment]
If a hazard-id is a minefield, and you're looking at mines-by-region(gazetter) & size-of-minefields-by-gazetteer, maybe you could make a Hazard dimension, which holds the area of the Hazard; or possibly make a Null-device entry in the DeviceDimension table, and only the Null-device entry gets the area_m2 set, the real devices get area_m2=0.
If you need to answer queries like: total area of minefields containing device 321, the second approach isn't going to easily answer these questions, which suggests that making a Hazard dimension might be a better approach.
I would also consider adding a device-count fact, which could have the num devices of each type per hazard.
I have to make a control in ASP.NET that allows me to create a matrix. I have a list of strings (obtained from a method) that will be the rows (each string is one row), and I have another list of strings (obtained from other method) that will be the columns (each string is one column). After that, depending on the row-cloumn cross I have to put an image in that position, something like this:
x | y | z
a | OK | OK | BAD|
------------------
b | OK |BAD | OK |
------------------
c |BAD |BAD | BAD|
How can I achieve this? Thanks a lot in advance!
You can use nested Repeaters.
The outer repeater for rows, the inner one for columns/cells.