Let's say that i have an array:
|A B C D
---------------
1 |2 8 6 3
2 |1 2 5 2
Where first row stand for "Goals Scored" and the second row for "Goals Lost". Columns stands for games/matches
I want to find the maximum total number of goals scored and lost in one match. In case above it would be 11 (C1 + C2).
I don't want to use
I spent few days trying functions like: MAX, ADDRESS, CELL, SUBTOTAL, SUM, MMULT, TRANSPOSE, etc. and even combined but i didn't get satisfying result.
The MAX function have to work:
Returns the maximum of a list of arguments, ignoring text entries.
Example:
MAX(B1:B3)
where cells B1, B2, B3 contain 1.1, 2.2, and apple returns 2.2.
Select cell A3 and set the formula to =A1+A2. Then click the square in the lower-right corner of the selected cell and drag to D3. This gives:
|A B C D
---------------
1 |2 8 6 3
2 |1 2 5 2
3 |3 10 11 5
Now =MAX(A3:D3) produces 11.
Related
I think the best way to show the problem is with an example. Column A is what i have now, and column B is what I would want.
A
B
1
1
1
1
2
2
2
2
5
3
5
3
5
3
8
4
8
4
9
5
9
5
14
6
14
6
17
7
17
7
17
7
Update: Based on your comment, use this formula
=ArrayFormula(IF(ISNUMBER(A1:A), VLOOKUP(A1:A, {UNIQUE(A1:A), ArrayFormula(RANK(UNIQUE(A1:A), UNIQUE(A1:A), 1))}, 2, 0), ""))
Previous answer: Have you already used the SORT formula?
Try =SORT(A1:A, 1, 1) in cell B1
Assuming your data starts at row 2 through row 10 column A. In B2 :
=arrayformula(1/COUNTIF($A$2:$A$10,$A$2:$A$10))
in C2
=sumproduct(($B$1:$B1)*($A$1:$A1<A2))+1
I have a tricky question about conditional sum in SAS. Actually, it is very complicated for me and therefore, I cannot explain it by words. Therefore I want to show an example:
A B
5 3
7 2
8 6
6 4
9 5
8 2
3 1
4 3
As you can see, I have a datasheet that has two columns. First of all, I calculated the conditional cumulative sum of column A ( I can do it by myself-So no need help for that step):
A B CA
5 3 5
7 2 12
8 6 18
6 4 8 ((12+8)-18)+6
9 5 17
8 2 18
3 1 10 (((17+8)-18)+3
4 3 14
So my condition value is 18. If the cumulative more than 18, then it equal 18 and next value if sum of the first value after 18 and exceeds amount over 18. ( As I said I can do it by myself )
So the tricky part is I have to calculate the cumulative sum of column B according to column A:
A B CA CB
5 3 5 3
7 2 12 5
8 6 18 9.5 (5+(6*((18-12)/8)))
6 4 8 5.5 ((5+6)-9.5)+4
9 5 17 10.5 (5.5+5)
8 2 18 10.75 (10.5+(2*((18-7)/8)))
3 1 10 2.75 ((10.5+2)-10.75)+1
4 3 14 5.75 (2.75+3)
As you can see from example the cumulative sum of column B is very specific. When column CA is equal to our condition value (18), then we calculate the proportion of the last value for getting our condition value (18) and then use this proportion for computing cumulative sum of column B.
Looks like when the sum of A reaches 18 or more you want to split the values of A and B between the current and the next record. One way is to remember the left over values for A and B and carry them forward in your new cumulative variables. Just make sure to output the observation before resetting those variables.
data want ;
set have ;
ca+a;
cb+b;
if ca >= 18 then do;
extra_a=ca - 18;
extra_b=b - b*((a - extra_a)/a) ;
ca=18;
cb=cb-extra_b ;
end;
output;
if ca=18 then do;
ca=extra_a;
cb=extra_b;
end;
drop extra_a extra_b ;
run;
I'm trying to solve a problem in SAS where I have quantities of customers across a range of groups, and the quantities I select need to be as even across the different categories as possible. This will be easier to explain with a small table, which is a simplification of a much larger problem I'm trying to solve.
Here is the table:
Customer Category | Revenue band | Churn Band | # Customers
A 1 1 4895
A 1 2 383
A 1 3 222
A 2 1 28
A 2 2 2828
A 2 3 232
B 1 1 4454
B 1 2 545
B 1 3 454
B 2 1 4534
B 2 2 434
B 2 3 454
Suppose I need to select 3000 customers from category A, and 3000 customers from category B. From the second category, within each A and B, I need to select an equal amount from 1 and 2. If possible, I need to select a proportional amount across each 1, 2, and 3 subcategories. Is there an elegant solution to this problem? I'm relatively new to SAS and so far I've investigated OPTMODEL, but the examples are either too simple or too advanced to be much use to me yet.
Edit: I've thought about using survey select. I can use this to select equal sizes across the Revenue Bands 1, 2, and 3. However where I'm lacking customers in the individual churn bands, surveyselect may not select the maximum number of customers available where those numbers are low, and I'm back to manually selecting customers.
There are still some ambiguities in the problem statement, but I hope that the PROC OPTMODEL code below is a good start for you. I tried to add examples of many different features, so that you can toy around with the model and hopefully get closer to what you actually need.
Of the many things you could optimize, I am minimizing the maximum violation from your "If possible" goal, e.g.:
min MaxMismatch = MaxChurnMismatch;
I was able to model your constraints as a Linear Program, which means that it should scale very well. You probably have other constraints you did not mention, but that would probably beyond the scope of this site.
With the data you posted, you can see from the output of the print statements that the optimal penalty corresponds to choosing 1500 customers from A,1,1, where the ideal would be 1736. This is more expensive than ignoring the customers from several groups:
[1] ChooseByCat
A 3000
B 3000
[1] [2] [3] Choose IdealProportion
A 1 1 1500 1736.670
A 1 2 0 135.882
A 1 3 0 78.762
A 2 1 28 9.934
A 2 2 1240 1003.330
A 2 3 232 82.310
B 1 1 1500 1580.210
B 1 2 0 193.358
B 1 3 0 161.072
B 2 1 1500 1608.593
B 2 2 0 153.976
B 2 3 0 161.072
Proportion MaxChurnMisMatch
0.35478 236.67
That is probably not the ideal solution, but figuring how to model exactly your requirements would not be as useful for this site. You can contact me offline if that is relevant.
I've added quotes from your problem statement as comments in the code below.
Have fun!
data custCounts;
input cat $ rev churn n;
datalines;
A 1 1 4895
A 1 2 383
A 1 3 222
A 2 1 28
A 2 2 2828
A 2 3 232
B 1 1 4454
B 1 2 545
B 1 3 454
B 2 1 4534
B 2 2 434
B 2 3 454
;
proc optmodel printlevel = 0;
set CATxREVxCHURN init {} inter {<'A',1,1>};
set CAT = setof{<c,r,ch> in CATxREVxCHURN} c;
num n{CATxREVxCHURN};
read data custCounts into CATxREVxCHURN=[cat rev churn] n;
put n[*]=;
var Choose{<c,r,ch> in CATxREVxCHURN} >= 0 <= n[c,r,ch]
, MaxChurnMisMatch >= 0, Proportion >= 0 <= 1
;
/* From OP:
Suppose I need to select 3000 customers from category A,
and 3000 customers from category B. */
num goal = 3000;
/* See "implicit slice" for the parenthesis notation, i.e. (c) below. */
impvar ChooseByCat{c in CAT} =
sum{<(c),r,ch> in CATxREVxCHURN} Choose[c,r,ch];
con MatchCatGoal{c in CAT}:
ChooseByCat[c] = goal;
/* From OP:
From the second category, within each A and B,
I need to select an equal amount from 1 and 2 */
con MatchRevenueGroupsWithinCat{c in CAT}:
sum{<(c),(1),ch> in CATxREVxCHURN} Choose[c,1,ch]
= sum{<(c),(2),ch> in CATxREVxCHURN} Choose[c,2,ch]
;
/* From OP:
If possible, I need to select a proportional amount
across each 1, 2, and 3 subcategories. */
con MatchBandProportion{<c,r,ch> in CATxREVxCHURN, sign in / 1 -1 /}:
MaxChurnMismatch >= sign * ( Choose[c,r,ch] - Proportion * n[c,r,ch] );
min MaxMismatch = MaxChurnMismatch;
solve;
print ChooseByCat;
impvar IdealProportion{<c,r,ch> in CATxREVxCHURN} = Proportion * n[c,r,ch];
print Choose IdealProportion;
print Proportion MaxChurnMismatch;
quit;
Combinational Circuit design question.
A
____
| |
F | | B
| |
____
| G |
E | | C
| |
____
D
Suppose this is a LED display. It would take input of 4 bit
(0000)-(1111) and display the Hex of it. For example
if (1100) come in it would display C by turning on AFED and turning off BCG.
If (1010) comes in it would display A by turning on ABCEFG
and turn off D.
These display will all be Capital letters so there is no visual
difference between 0 and D and 8 and B.
Develop a truth table and an optimized expression using Karnaugh Maps.
I'm not exactly sure how to begin. For the truth table would I be using (w,x,y,z) as input variable or just the ABCDEFG variable since it's the one turning on and off?
input (1010)-->A--> ABCEFG~D (~ stand for NOT)
input (1011)-->B--> ABCDEFG
input (1100)-->C--> ADEF~B~C~G
So would I do for all hex 0-F then that would give me the min. term canonical then use Karnaugh Map to optimize it? Any help would be grateful!
1) Map your lights to bits:
ABCDEFG, so truth table will be:
ABCDEFG
input (1010)-->A-->1110110
and so on.
You will have big table (with 16 rows).
2) Then follow sample on wikipedia for every output light.
You need to do 7 of these: Each for one segment in the 7-segment display.
This figure is for illustration only. It doesn't necessarily map to any segment in your problem.
cd=00 01 11 10 <-- where abcd = 0000 for 0 : put '1' if the light is on
ab= 00 1 1 1 1 = 0001 for 1 : put '0' if it's off for
ab= 01 1 1 1 0 = 0010 for 2 ... the given segment
ab= 11 0 1 1 1
ab= 10 1 1 1 0 = 1111 for f
^^^^ = d=1 region
^^^^ = c==1 region
The two middle rows represent "b==1" region and the two last rows are a==1 region.
From that map find maximum size rectangles (that are of size [1,2 or 4] x [1, 2 or 4]); that can be overlapping. The middle 2x4 region is coded as 'd'. The top row is '~a~b'. The top left 2x2 square is '~a~c'. A bottom left square that wraps from row 4 to row 1 is '~b~c'. Finally the small 2x1 region that covers position x=4, y=3 is 'abc'.
This function would thus be 'd + ~a~b + ~a~c + ~b~c + abc'. If there are no redundant squares (that are completely covered by other squares), then this formula should be optimal canonical form. (not counting XOR operation). Repeat for 7 times for the real data!
Any selection/permutation of the variables should give the same logical circuit, whether you use abcd or dcba or acbd etc.
I am working on a project where I need to create a boundary around a group of rectangles.
Let's use this picture as an example of what I want to accomplish.
EDIT: Couldn't get the image tag to work properly, so here is the full link:
http://www.flickr.com/photos/21093416#N04/3029621742/
We have rectangles A and C who are linked by a special link rectangle B. You could think of this as two nodes in a graph (A,C) and the edge between them (B). That means the rectangles have pointers to each other in the following manner: A->B, A<-B->C, C->B
Each rectangle has four vertices stored in an array where index 0 is bottom left, and index 3 is bottom right.
I want to "traverse" this linked structure and calculate the vertices making up the boundary (red line) around it. I already have some small ideas around how to accomplish this, but want to know if some of you more mathematically inclined have some neat tricks up your sleeves.
The reason I post this here is just that someone might have solved a similar problem before, and have some ideas I could use. I don't expect anyone to sit down and think this through long and hard. I'm going to work on a solution in parallell as I wait for answers.
Any input is greatly appreciated.
Using the example, where rectangles are perpendicular to each other and can therefore be presented by four values (two x coordinates and two y coordinates):
1 2 3 4 5 6
1 +---+---+
| |
2 + A +---+---+
| | B |
3 + + +---+---+
| | | | |
4 +---+---+---+---+ +
| |
5 + C +
| |
6 +---+---+
1) collect all the x coordinates (both left and right) into a list, then sort it and remove duplicates
1 3 4 5 6
2) collect all the y coordinates (both top and bottom) into a list, then sort it and remove duplicates
1 2 3 4 6
3) create a 2D array by number of gaps between the unique x coordinates * number of gaps between the unique y coordinates. It only needs to be one bit per cell, so in c++ a vector<bool> with likely give you a very memory-efficient version of this
4 * 4
4) paint all the rectangles into this grid
1 3 4 5 6
1 +---+
| 1 | 0 0 0
2 +---+---+---+
| 1 | 1 | 1 | 0
3 +---+---+---+---+
| 1 | 1 | 1 | 1 |
4 +---+---+---+---+
0 0 | 1 | 1 |
6 +---+---+
5) for each cell in the grid, for each edge, if the cell beside it in that cardinal direction is not painted, draw the boundary line for that edge
In the question, the rectangles are described as being four vectors where each represents a corner. If each rectangle can be at arbitrary and different rotation from others, then the approach I've outlined above won't work. The problem of finding the path around a complex polygon is regularly solved by vector graphics rasterizers, and a good approach to solving the problem is using a library such as Cairo to do the work for you!
The generalized solution to this problem is to implement boolean operations in terms of a scanline. You can find a brief discussion here to get you started. From the text:
"The basis of the boolean algorithms is scanlines. For the basic principles the book: Computational Geometry an Introduction by Franco P. Preparata and Michael Ian Shamos is very good."
I own this book, though it's at the office now, so I can't look up the page numbers you should read, though chapter 8, on the geometry of rectangles is probably the best starting point.
Calculate the sum of the boundaries of all 3 rectangles seperately
calculate the overlapping rectangle of A and B, and subtract it from the sum
Do the same for the overlapping rectangle of B and C
(to get the overlapping rectangle from A and B take the middle 2 X positions, together with the middle 2 Y positions)
Example (x1,y1) - (x2,y2):
Rectangle A: (1,1) - (3,4)
Rectangle B: (3,2) - (5,4)
Rectangle C: (4,3) - (6,6)
Calculation:
10 + 8 + 10 = 28
X coords ordered = 1,3,3,5 middle two are 3 and 3
Y coords ordered = 1,2,4,4 middle two are 2 and 4
so: (3,2) - (3,4) : boundery = 4
X coords ordered = 3,4,5,6 middle two are 4 and 5
Y coords ordered = 2,3,4,6 middle two are 3 and 4
so: (4,3) - (5,4) : boundery = 4
28 - 4 - 4 = 20
This is my example visualized:
1 2 3 4 5 6
1 +---+---+
| |
2 + A +---+---+
| | B |
3 + + +---+---+
| | | | |
4 +---+---+---+---+ +
| |
5 + C +
| |
6 +---+---+
A simple trick should be:
Create a region from the first rectangle
Add the other rectangles to the region
Get the boundary of the region (somehow? :P)
After some thinking I might end up doing something like this:
Pseudo code:
LinkRectsConnectedTo(Rectangle rectangle,Edge startEdge) // Edge can be West,North,East,South
for each edge in rectangle starting with the edge facing last rectangle
add vertices in the edge to the final boundary polygon
if edge is connected to another rectangle
if edge not equals startEdge
recursively call LinkRectsConnectedTo(rectangle,startEdge)
Obvisouly this pseudo code would have to be refined a bit and might not cover all cases, but I think I might have solved my own problem.
I haven't thought this out completely, but I wonder if you couldn't do something like:
Make a list of all the edges.
Get all the edges where P1.X = P2.X
In that list, get the pairs where X are equal
For each pair, replace with one or two edges for the parts where they DON'T overlap
Do something clever to get the edges in the right order
Will your rectangles always be horizontally aligned, if not you'd need to do the same thing but for Y too?
And are they always guaranteed to be touching? If not the algorithm wouldn't be broken, but the 'right order' wouldn't be definable.