I came to this a bit late, partly because I was singing Advent & Christmas
Carols!
There was a spiral constructor that around in an old script; it serves
its purpose! Best to call it with an odd argument, so that it ends
nicely on
an odd square lower right corner. It's slower and fatter than Raul's verb.
Using the "spiral" function merely to study the part 1 question, I came
up with
a fairly algorithmic answer rather than seeking the coordinates of the
required
point, see "steps" below, so its time and space are small.
I _did_ use spiral for part 2, rather than seek a formula. Called
"part2",
it's listed below. The optional left argument specifies the size of the
spiral
whose maximum entry we hope exceeds the search value.
It's quite fast and slim.
Mike
ring =: <.@>:@-:@>.@%: NB. which "ring"?
ring 1 12 23 1024
1 3 3 17
NB. yval is a misnomer - I assumed the value was on
NB. a vertical side, and this is the displacement
NB. from the row containing 1
yval =: (] (] |@- (+:@]) | (- *:@>:@+:)) <:@ring)
NB. Manhattan distance...
steps =: yval <:@+ ring
NB. steps 312051 NB. my problem...
NB. 430
NB. for pedestrian spirallers
NB. with default lhs, rhs is an appropriate odd
NB. square root of a bottom right-hand corner
spiral =: 3 : 0
(1 1$1) spiral y
:
n2 =. *: n =. y
old =. x
new =. (>: i. n2 ) -. , old
rotate=. |."1 @ |:
if. * # new do.
for. i. 4 do.
old =. rotate old,. |. (nadd =. #old) {. new
new =. nadd }. new
end.
old spiral n
else. old
end.
)
NB. part 2 - I assumed (or perhaps knew) that spiral ending in
NB. position 121 would suffice
part2 =: 3 : 0
11 part2 y
:
v =. y
s =. spiral x NB. spiral matrix
NB. coordinates relative to the centre, 1
c =. (}. -~"1 {.) (1, >:i.*:x) (#@] #. inv (i.~,))s
NB. 8 coordinate offsets for any neighbour are coords of second ring
m =. }.9{. c NB. assumes at least two rings!
NB. indices of every set of 8 neighbours
NB. - wrong for outside ring, but who cares?
n =. (<:*:x) <. c i. c +"1 / m
NB. initialise "memory"
vals =. 1{.~ *:x
for_i. }. i.*:x do. NB. just loop through positions 2 3 ... !
ni =. i{n
add =. +/ vals{~ ni
vals =. add i} vals
if. add > y do.
ii =. i
break. end.
end.
ii; (ring ii); add NB. add is the required entry value
)
NB. 10 part2 312051
NB. ┌──┬─┬──────┐
NB. │60│5│312453│
NB. └──┴─┴──────┘
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