No pruning required! Recursively count neighbours of each vertex in the directed graph until you get to your target vertex (count 1) or the end of the road (count 0) with memoisation. See alt text

Yes part 2 is actually solvable by hand with a print out! Perhaps this hard problem has a ‘thermal exhaust port’…

I cheated with memoise 😉 - However the R solution from @thoughtfulnz.bsky.social is much more elegant.

Speeds up 20-fold by only checking locations with paper rolls

#Part2
x1 <- x
x2 <- x-x
repeat{
p <- which(x1==1, arr.ind = T)
for(i in 1:nrow(p)){
x2[p[i,,drop=F]]=as.numeric(sum(x1[(p[i,1]-1):(p[i,1]+1),(p[i,2]-1):(p[i,2]+1)])>4)}
if(sum(x1)==sum(x2)){break()}
x1 <- x2
x2 <- x2-x2}
sum(x)-sum(x1)

#Part1
input_d4 |> read_lines()|> str_split("",simplify=T)
x <- x=="@"
x=cbind(rep(0,nrow(x)),x,rep(0,nrow(x)))
x=rbind(rep(0,ncol(x)),x,rep(0,ncol(x)))
p <- which(x==1, arr.ind = T)
tot <- 0
for(i in 1:nrow(p)){
tot <- tot+(sum(x[(p[i,1]-1):(p[i,1]+1),(p[i,2]-1):(p[i,2]+1)])<5)}
tot

A brief history of the discovery of the immunoglobulins and the origin of the modern immunoglobulin nomenclature

onlinelibrary.wiley.com/doi/epdf/10....

After 14 days in ICU eGFR or eCrCl will over estimate true GFR more than TWO-fold yet they are still often quoted as guides to drug dosing!

As intravenous fluids are rapidly lost to the interstitial space any affect on cardiac output and GFR will be very transient…

However creatinine concentration decrease reduces its excretion for any fixed GFR causing loss of steady state and rapid accumulation of creatinine in the expanded volume until concentration is normalized and steady state is regained. This can be easily modeled and takes a few hours at most.

Also our good friend the Canadian Intensivist!!

I’m no expert in this area but this is a good start I think: www.kireports.org/article/S246...

What about hyponatraemia in chronic dialysis patients? - common and impactful - mostly but not exclusively due to fluid overload??

Incredibly valuable approach. I’m interested in ordinal longitudinal outcomes based on an organ failure score - ie where there might be more than one way to achieve the same level. Can this approach be applied to this type of ordinal outcome variable?

My approach was by no means perfect but see journals.lww.com/anesthesia-a...

So what you need to model is an interaction term between age and eGFR with eGFR fitted to a spline (ie rcs). If you use creatinine then you would do the same but an interaction with sex would also be needed!