Did it with mostly brute force as well.
Broke it up into brute force in the x-range to find all valid velocities and the valid time steps for which (in the x coordinate) it would be in the target area.
Then used those time stamps to limit the scope of the y-velocities.
Still brute force tested y, but I really wanted to just use s=vt+a(t^2)/2 to calculate v for the valid y + x time spans. But I wasn’t getting it to work out. So, I’ll revisit in the morning.
My notes may interest folks, but my soln for part2 involved expanding some bounds until I got it right :/ https://github.com/benknoble/advent2021/blob/main/day17/solution.rkt
<https://github.com/lojic/LearningRacket/blob/master/advent-of-code–2021/solutions/day17/day17.rkt|Day 17>
I tried something a little different this afternoon. I traverse the Y direction and build a hash table of “time step -> list of initial VY’s that end up in the target area at that time step”.
Then traverse in X, and for every time step where X is in the range, pair up with all the VYs for that time step from the hash table.
Optimizations aside from the hash table include are mostly about recognizing that going up can be ignored. Only go down and - for going up - realize that for some initial VY, you’ll be back at y=0 again at step vy*2+1 with vy=-vy-1, so a whole lot of loop iterating can be skipped.
I still think this could be a simple physics problem, but I couldn’t rectify vx eventually stopping in the equations.
(require plot)
(define (plot-trajectory dx dy)
(let ([ pts (trajectory dx dy) ])
(plot (list (rectangles (list (vector (ivl 206 250) (ivl -57 -105))))
(points pts))
#:x-min -1
#:x-max 300
#:y-min -150
#:y-max 100)))
(plot-trajectory 21 12)
I love how I can just hit <F5> in Emacs, and see the plot in the repl window!