You can represent sets as bit vectors and then use bit operators "equal" or "AND" to test which sets get matched. Using bit vectors as set representation will solve problem of ordering and duplicate values automatically as position of each value in the bit vector is fixed and each bit will be "set" only once, regardless of how many times the value appears in the column that defines the set.
Simple to use bit vector representation in Excel including operators OR, AND, NOT is listed here: http://chandoo.org/wp/2011/07/29/bitwise-operations-in-excel/#comment-207723
For example following function
=POWER(10;0)*MIN(COUNTIF($B$3:$B$12;"T1");1)+POWER(10;1)*MIN(COUNTIF($B$3:$B$12;"T2");1)+POWER(10;2)*MIN(COUNTIF($B$3:$B$12;"S");1)+POWER(10;3)*MIN(COUNTIF($B$3:$B$12;"PL");1)+POWER(10;4)*MIN(COUNTIF($B$3:$B$12;"CC");1)+POWER(10;5)*MIN(COUNTIF($B$3:$B$12;"GC");1)
Converts values in the range $B$3
->$B$12
into a bit vector representation having bits 0..5
defined so that the bit is set if the value in any column in the range is equal to:
- bit 0 =
T1
- bit 1 =
T2
- bit 2 =
S
- bit 3 =
PL
- bit 4 =
CC
- bit 5 =
GC
You can add more bits with other values easily by following the same copy/paste pattern.
So to check if certain column matches certain scenario, just compare the bit vectors. Use expression like IF(x=y;"warn2";IF(..))
and substitute bit vector of the column for x
and bit vector of the warn2
scenario for y
.
If partial matching is needed, you can use the bitwise AND operator as defined in the above article.
This solution as opposed to a VBA-based solution will require some copy/pasting discipline, e.g. when new trial column or new scenario will be added few expressions will have to be copy/pasted and few will have to be updated.
VBA-based solution might solve this maintenance problem automatically for you by using auto-detected CurrentRegions, all necessary logic hidden behind one macro-click.
EDIT: The bit vectors concept applied to the new soccer teams dataset
As it is ambiguous what will be the exact team setup on a given day as one player may be assigned different positions, I have simplified the problem in such a way that instead of "present" or "absent" I expect the table to contain player's position. It should not be a problem to achieve as if you know what positions the player can play then instead of absent,present
you can define the set of valid values to be (empty or anything else),Midfielder,Centre midfield,Wide
for players 14,17,18. List of valid available values can be configured for each cell using the "Data validation" rules. The abstract role Midfielder
stands for "this player can play a midfielder, exact position is not known yet".
To represent positions I use bit vector calculated with this formula
=POWER(10;6)*MIN(COUNTIF(D2:ZZ2;"Goalkeeper");1)+POWER(10;5)*MIN(COUNTIF(D2:ZZ2;"Centre back");1)+POWER(10;4)*MIN(COUNTIF(D2:ZZ2;"Wing");1)+POWER(10;3)*MIN(COUNTIF(D2:ZZ2;"Centre midfield");1)+POWER(10;2)*MIN(COUNTIF(D2:ZZ2;"Wide");1)+POWER(10;1)*MIN(COUNTIF(D2:ZZ2;"Centre forward");1)+POWER(10;0)*MIN(COUNTIF(D2:ZZ2;"Winger");1)
the formula calculates bit vector from a range D2:ZZ2
in such a way so that each position in the range is counted only once and in final vector each position has a fixed place. It is useful to set number format of the vector to custom numeric format 0000000
. For example a row containing Wide,Winger,Goalkeeper
in any order with any number of repeats will evaluate to vector 1000101
where the left-most bit 6 stands for Goalkeeper
and 2nd from the right goes bit 2 standing for Wide
. The most comfortable situation is the one with bit vector evaluating to 1111111
. The only purpose of this bit vector is to detect the comfortable situation
For matching scenarios to team setups I use another vector composed of 4 digits with this meaning:
- leftmost digit 3 - number of goalies (at most 1 counts)
- digit 2 - number of defenders (at most 2 counts)
- digit 1 - number of midfielders (at most 2 counts)
- rightmost digit 0 - number of forwards (at most 2 counts)
The formula to calculate this vector for range
D2:ZZ2
looks like this
=POWER(10;3)*MIN(COUNTIF(D2:ZZ2;"Goalkeeper");1)+POWER(10;2)*MIN(COUNTIF(D2:ZZ2;"Defender")+COUNTIF(D2:ZZ2;"Centre back")+COUNTIF(D2:ZZ2;"Wing");2)+POWER(10;1)*MIN(COUNTIF(D2:ZZ2;"Midfielder")+COUNTIF(D2:ZZ2;"Centre midfield")+COUNTIF(D2:ZZ2;"Wide");2)+POWER(10;0)*MIN(COUNTIF(D2:ZZ2;"Forward")+COUNTIF(D2:ZZ2;"Centre forward")+COUNTIF(D2:ZZ2;"Winger");2)
It is useful to set number format of the vector to custom numeric format 0000
. This same formula can calculate the 4-digit vector for team setup and for scenario.
Besides position names it can count also abstract position names like Defender
.
For example in a row containing Centre back,Centre back,Goalkeeper,Goalkeeper,Goalkeeper,Defender,Defender,Midfielder,Midfielder,Winger
the vector looks like 1221
.
There are (1+1)*(2+1)*(2+1)*(2+1) = 54
different possible scenarios. I assume each of them is listed in the constraints
sheet. You should be able to generate them all in python quite easily.
There are 2 sheets constraints
with scenarios and events
with days and team setups. The lookup formula that takes the vector calculated for a team setup in row #2 and searches the constraints
sheet for a row with exactly the same vector and returns the value from the value column looks like this
=IFERROR(VLOOKUP($A2;constraints!$A:$B;2;FALSE);"?")
- $A2 - contains the 4-digit vector formula for the team setup
- constraints!$A - column in the sheet with scenarios containing the 4-digit vector formula for the scenario
- constraints!$B - column in the sheet with scenarios containing the scenario name - the thing you are looking for
- 2 - index of column constraints!$B
- FALSE - means the lookup column does not have to be sorted
- ? - fallback value if no matching scenario was found (should not occur)
The Google docs link above contains the formulas, example 3 days and example 11 scenarios.
If there's something unclear let me know and I'll improve the answer as the Google docs link will vanish some day