Day 1: Historian Hysteria : code takeaways
- P1: sort lists -> pairwise distance
- P2: freq maps -> val * freq * freq
Day 2: Red-Nosed Reports : code takeaways
- P1: Kernel Convolution,
- P2: + Solution via Differences
Raw : 1 2 1 3
Diffs: * 1 -1 2 *
Sum : 0 1
Raw : 1 2 6 5
Diffs: * 1 4 -1 *
Sum : 5 3
Raw : 1 2 6 7
Diffs: * 1 4 1 *
Sum : 5 5
Raw : 9 1 2
Diffs: * -8 1 *
Sum : x -7
NOTE: recursive solution over raw input with forking on ‘bad transition’: simpler code (just wanted to do it via the diffs)
Day 3: Mull It Over : code takeaways
- P1: pattern match & extract
- P2: + split out "do" segments
regex: mul\((\d+),(\d+)\)
Day 4: Ceres Search : code takeaways
- P1: pattern match, mult directions (did a very non-performant state machine parser ... must be allocations; will check)
- P2: 'wider' pattern; convert to 1D using fixed width rows, recursively run regex using start offsets (to allow pattern overlaps)
rc
00 10 20 30
01 11 21 31
02 12 22 32
03 13 23 33
00
01 10
02 11 20
across,row : [+1, 0] new start: 00 [0, +1] 0_MAX
down, cal : [0, +1] new start: 00 [+1, 0] MAX_0
up-rt, diag: [+1, -1] new start: 00 [0, +1] 0_MAX [+1, 0] MAX_MAX
Day 5: Print Queue : ----
- P1: checks against partial order
a < b
a < d
c < x
d < f
l < b
l b <--- awkward to represent without a graph
[a{b[df]}]
[cx]
l -- b -- d -- f
a --<
a
c -- x
| id | < | > | ~ |
|---|---|---|---|
| a | b,d | ||
| b | a,l | ||
| d | f | a | |
| c | x | ||
| x | c | ||
| f | d | ||
| l | b |
Day 6: Guard Gallivant : ----
- P1: agent simulation (optional tensor multiplication)
- range and segment calculations as simple start
Simulation while checking for location + direction repetition (3D statespace)
For speed (if dealing with many positions) one could pre-calculate "trap regions"
e.g.
T is a trap region: {<,T,T,>} # . .
V,^ T # .
T . .
T . .
_____
As having state V || ^ in any of those positions will lead to confinement to the region.
Notes:
- Not all lead-ins to a Trap are necessarily hit (may be separate head and repetition areas)
- We can also look at valid transitions into a Trap region
- e.g. In the above, at some distance the below are trap lead-in states:
T is a trap region: {<,T,T,>} # . V
V,^ T # V
T < (<,V)
T < (<,V)
_____
This can also be represented as Matrix Multiplication. Specifically a 4D “binary tensor” (binary for populate-able values .. we can do whatever with non-populate-able values) (I’m not seeing any nice algebra, that’s not just a hidden dimension, that allows for a 3D Tensor. - e.g. no id element in direction group)
but… still you could have a 4d element rep, but that’ just a hidden tensor dimension in this case < V ^ >
Could make a bunch of redundant elements to force a group, but awkward
(x,_) * (_,_x) = (x,_x)
(x,_) * (_,_y) = (_,_y)
Implementation-wise: a different matrix for each directional state with transitions …
1D (2dirs) maze version (3D Tensor):
<,> : dimensions represents reversal iff that direction
... note this may be "non-linear" ... as it's value dependent ...?
1: represents same direction
< [. . . . # . . . .] > [. . . . # . . . .]
[. > 1 x [. x
. 1 x . 1 x
. 1 x . 1 x
. x . 1 < x
# x x x x x x x x x # x x x x x x x x x
. x > 1 . x
. x 1 . x 1
. x 1 . x 1
.] x .] x 1 <
<
{
{R,1,0,0,0,0,0,0,0},
{0,0,1,0,0,0,0,0,0},
{0,0,0,1,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,R,1,0,0},
{0,0,0,0,0,0,0,1,0},
{0,0,0,0,0,0,0,0,1},
{0,0,0,0,0,0,0,0,0}
}
if we needed to calculate paths for many positions then we could pre calculate n-steps via matrix multiplications. — given sparsity it may not be so bad …
If we save the matrix at each step (a vector of 4D points) then as soon as we see a repetition (across steps) then that
Alt: Implementing binary tensory multiplication with portable SIMD would be fun, but not the right task for right now. And, regardless, from a perf standpoint this would be a sparse tensor anyway and we'd be unlikely to want to implement it with full tensor multiplicattion. (Not that we're too worried about such things, but still notable, lol.) One alternative would be to just record obstacles' positions and then from those calculate 'lead' and 'follow' segments. These segments just being a range of positions. [Slight mucking in defining a 2D range; but since only axis directions it wouldn't be too pokey.]
What's our max problem scope then: n obstacles -> max 4n (lead,follow) segments. Each segment 'indexed' by a pair of ranges [actually one range and a coordinate, since only axial translation], with segments posesing overlapping indices. Oh, and a direction, ofc (so each 'segment' gets a dir associatted with it, even though lead-follow dir pairs are fixed).
So:
- scan input for dimensions & obstacle positions, give each position an arbitrary id, then calculate 4 segment pairs for each (@xy -> (0.max(obstaclish)..x),(x+1..xmax.min(obstaclisih)) @y (0.max(obstacliesh)..y),(y+1..ymax.min(obstacleish)@x)
- now, for each segment search for overlap to create a map of segment ownership
- search segment map for cycles and pull positions back out ... not very exciting, but probably performant, and would allow branching parallelism with a shared hashmap or the like (if problems were large enough -- overhead of multi threading may outstrip the time taken to solve the problem as is.) Edit: boundaries are not obstacles; sequence also ends if unit exits past a boundary.
Day 7: Bridge Repair : ----
- P1: combinatorial
operators: * +
190 == 10 _ 19
21037 != 9 _ 7 _ 18 _ 13
292 == 11 _ 6 _ 16 _ 20
n elements -> n-1 operators -> (n-1)^2 options
If we wanted to avoid brute force:
- we could look for multiplication sets that bound first
- shrink to sequencs of mults that are within bounds
- then test addition We could do this recursively -- pulling back from bound edges.
We could also just start with all * and then, in parallel and recursively, replace a * by a + at each step
This allows immediate rejections if UNDER bounds
(and vice versa if starting from bottom)
Rejecting whole branch if UNDER bounds at any node.
0 * * * *
1 +
1 +
1 +
1 +
Naive + Blind parallelization would result in a lot of redundant work.
(Note: I'm NOT certain memoization would be helpful given how cheap the operations are.)
¿Nice way to coordinate branching to prevent redundant descent?
e.g.
wasteful:
0 * * * *
1a +
2a. + + <---- same
2a...
1b +
2b. + + <---- same
2b...
1...
Solution: only descend to one side -
(yes: this is esentialy factorial multiplication :)
Now, if we want non-cooperative parallelism. we don't introduce redundancy
0 | * * * * |
1a | + |
1b | + |
2b | + + |
1c | + |
2c. | + + |
2c: | + + |
1d | + |
2d. | + + |
2d: | + + |
2d; | + + |
We can still kill a branch if it's UNDER bounds at any point.
It's not optimal in terms of bounds detection, but it should be correct.
I'm not sure whether we'd get much advantage from doing relative product comparison -- which would allow more early branch kills.
If the number of operations were large enough it would benefit. (But they seem relatively short from a quick peak at input.)
Other optimizations:
- we're doing a lot of semi-small problems
- of course we can parallelize each one (really eating up any parallelization utility of the above solution approach actually 🤷)
- chances of precise repetition of subsequences seems low (but we could store all possible values)
- we could ... round and bound ... allowing reuse of pruning information broadly ... not sure if worth, but doable
Caution:
- need to check max requested value and what it fits in -- (I think they all fit in u64)
- if u64 holds desired value, then any pair will be within u128 ... but it would require pair-wise bounds checking... I suppose that's fine
- could also do saturating mul or 'erring -- I imagine using u128 would be faster, but have never compared
Day 8: Resonant Collinearity : ----
- P1: tuples of distances at each point, marking section that have the 2x:x ratio for certain indices ("insideness" my also need to be checked)
- (perf: just calculate "anti-node distances" and check for inclusion & overlap)
Questions: - distance is Manhattan, I think
- the problems explicitly says there are "for any pair ... there are two [special locations], one on either side of them" ... but this is untrue generally. Ignoring discretrization there would be four: two inside and two outside. (where special is "in - line" an with "2:1" distance)
- if we have to check "insideness" then this isn't just the trivial distance marking and reading
- NOTE: because of discreteization: there will only be inside nodes if there
- solution (if needed): the outside distances will always be larger than the inside distances, so we can just calculate those
Perf.: we can also just calculate the distances where "anti-nodes" can exist from the raw list of elements and then just test for inclusion and overlap -- will be faster.
No inner "anti-nodes":
(no 2:1 ratios)
- (perf: just calculate "anti-node distances" and check for inclusion & overlap)
# 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 #
Inner "anti-nodes":
d = x + 2x
i.e. d ∈ {3n} (1/3 of distances)
(3) |# 1 2 3|
|3 2 1 #|
* *
(6) |# 1 2 3 4 5 6|
|6 5 4 3 2 1 #|
* *
(9) |# 1 2 3 4 5 6 7 8 9|
|9 8 7 6 5 4 3 2 1 #|
* *
(12) |# 1 2 3 4 5 6 7 8 9 0 1 2|
|2 1 0 9 8 7 6 5 4 3 2 1 #|
* *
Outer "anti-nodes":
d = x + x
i.e. d ∈ {n} (all distances)
NOTE: there will be no further "anti-nodes" due to the share distance offset of all further locations
(1) 1 |# 1|
2 |1 #|
*
(2) 2 1 |# 1 2|
4 3 |2 1 #|
*
(3) 3 2 1 |# 1 2 3|
6 5 4 |3 2 1 #|
*
(4) 4 3 2 1 |# 1 2 3 4|
8 7 6 5 |4 3 2 1 #|
*
Day 9: Disk Fragmenter : ----
- P1: just ... count free indices, then count as you fill (seems strangely easy)
raw : 2333133121414131402
data : 2 3 1 3 2 4 4 3 4 2
empty: 3 3 3 1 1 1 1 1 0
id : 0 1 2 3 4 5 6 7 8 9
data : 2 3 1 3 2 4 4 3 4 2
empty: 3 3 3 1 1 1 1 1 0
raw : 2333133121414131402
start: 0258...
ranges: (..2)(2..5)(5..8)(8..11)(11..12)(12..13), etc.)
ranges: (2..5) (8..11) (12..13), etc.)
We can just ... linearly drain files until empty is filled. Ids are just a matter of keeping track of indices and values
We can directly calculate. Things seem small enough that it may be simplest to just simulate -- calculating the transfer, but populating an actually array and mapping over its enumeration.