Let g be an n × n grid. you start at a particular position, with zero velocity. at every time step you can modify your horizontal velocity by 1, or keep it the same. the same holds independently for vertical velocity. so if at a particular time you are at position x, y and already have velocity vx, vy, then at the next time step you will jump and land at position x + vx, y + vy, and you have the option of modifying each component of your velocity by ±1. at several (known) grid positions there are pits full of dragons that you want to avoid landing on. it is ok to jump over a dragon pit. you also shouldn’t jump off the grid. the goal is to arrive at a specified target position, with zero velocity, in as little time as possible. show how fast you can compute an optimal trajectory or decide that there is no way to reach the target.

hint: try this out in 1d instead of 2d. if you can solve that, you’ll be fine.

c a goverment agency or homeowner

okay, so i know we just goofed around in that chat, but ive been like genuinly depressed, like medically depressed for almost 4 years now. i had my first panic attack when i was 8. i woke my mum up and told her i felt like i was in a dream. like i was a goldfish in a bowl, looking at all these things going on around me and feeling . tiny. wort hless. and i now am now 17 y/o. i still feel those emotions daily. life used to go by so quick.like every day i would wake up and just like want to go back to bed cause i always felt like i was in the wrong place. i guess looking back, i was in the wrong state of mind. i took a expensive like nice trip to whyoming with my grandfather and ha ted it. like idk why. i would have loved it now, but i found myself writing in a journal everyday because i would forget what happened the day before, couldnt remember what i ate for like the previous meal. just my memory left me for the week i was there. worst feeling ive ever experienced.