Forum Discussion
LAMBDA Halloween Challenge
Finally, I have a solution!
This time I used a Lambda function to add 1 to the previous index (stored in base n) but before returning the value, I scanned the digits and copied the larger digit across.
WorksheetFormula = LET( count, COUNTA(Items), initialise, REPT("0",pick), indices, VSTACK( initialise, SCAN(initialise, SEQUENCE(combinations-1), NextCombinationλ(count,pick)) ), INDEX(Items, 1 + Explodeλ(indices)) )where
NextCombinationλ = LAMBDA(n,p, LAMBDA(initial,s, LET( place, n^SEQUENCE(1,p,p-1,-1), increment, 1 + SUM(place * Explodeλ(initial)), converted, BASE(increment,n,p), vector, Explodeλ(converted), modified, SCAN( , vector, Maxλ), CONCAT(modified) ) ) );supported by
Explodeλ = LAMBDA(term, MID(term, SEQUENCE(1,pick), 1)); Maxλ = LAMBDA(u, v, Max(u,v));I have just performed the calculation for 8 picks taken for 9 items in 300ms. Ther are 12,870 combinations and the permutations would have been over 43M!
PeterBartholomew1 Ok now for my questions to Peter...
you have a line:
SCAN(initialise, SEQUENCE(), NextCombinationλ(count,pick))
then in Next Combination you have:
= LAMBDA(n,p,
LAMBDA(initial,s,
so does the (count,pick) of the lambda caller get assigned to the outer Lambda into n,p and then the SCAN variables get passed to the inner Lambda as initial, s ????
This is a very interesting structure to me that I haven't seen/played with.
If i understand correctly your 'place' and 'increment' variables are basically reconstructing the DECIMAL value? or is there something more?
I'm really perplexed my your Max lambda using MAX() as it appears those are (potentially) ascii characters at that point. did you try it when you exceed 9?
Thank you both, the exercise and diving into the solutions has been very educational.
Yes, you are correct that I used 'place' and 'increment' in lieu of DECIMAL. Sadly, I had not come across DECIMAL though I assume it was introduced at the same time as BASE! 😞
The function definition
NextCombinationλ
= LAMBDA(n,p, LAMBDA(initial,s,
LET(
increment, 1 + DECIMAL(initial,n),
converted, BASE(increment,n,p),
vector, Explodeλ(converted),
modified, SCAN( , vector, Maxλ),
CONCAT(modified)
)
));
now reads somewhat better. Your understanding of the parameter strings for 'NextCombinationλ' is also correct. It would be possible to take the process further and provide each of the parameters individually, expressing the function in its 'Curried' form. Such a form takes the parameters one at a time from left to right. The function is only evaluated when the final parameter value is provided. In this case, I wanted to provide 'n' and 'p' explicitly within a parameter string but allow the function to accept the remaining parameters from the Lambda helper function.
At the time I was developing the formula, I did not think going beyond 9 items was going to be a practicality, so I did not consider the possibility that 'A' and 'B' were going to appear as 'digits'! I guess redefining
Maxλ = LAMBDA(u, v, IF(u>v, u, v));
would be a start. My search for 'readability' above all, has taken me down a path of long variable names, avoiding nested formulas, and placing each statement on a new line. I even asked for an option to use ':=' as an assignment operator in place of alternate comma separators.
The penalty is that my formulas are somewhat idiosyncratic and sometimes the natural language readability can mask the underlying syntax.
- ah thank you. it is good to know how the lambda callers nest that way.
Now i think our codes are essentially identical except i believe in your main lines 4-8 could be reduced to just:
indices, SCAN( ,SEQUENCE(....
as the 0000 value will be created by default (at least it appeared to work for me).