Solution to problem 17 in Python
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# --- Day 17: Trick Shot ---
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# You finally decode the Elves' message. HI, the message says. You continue
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# searching for the sleigh keys.
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# Ahead of you is what appears to be a large ocean trench. Could the keys have
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# fallen into it? You'd better send a probe to investigate.
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# The probe launcher on your submarine can fire the probe with any integer
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# velocity in the x (forward) and y (upward, or downward if negative)
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# directions. For example, an initial x,y velocity like 0,10 would fire the
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# probe straight up, while an initial velocity like 10,-1 would fire the probe
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# forward at a slight downward angle.
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# The probe's x,y position starts at 0,0. Then, it will follow some trajectory
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# by moving in steps. On each step, these changes occur in the following order:
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# The probe's x position increases by its x velocity.
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# The probe's y position increases by its y velocity.
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# Due to drag, the probe's x velocity changes by 1 toward the value 0; that
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# is, it decreases by 1 if it is greater than 0, increases by 1 if it is less
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# than 0, or does not change if it is already 0.
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# Due to gravity, the probe's y velocity decreases by 1.
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# For the probe to successfully make it into the trench, the probe must be on
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# some trajectory that causes it to be within a target area after any step. The
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# submarine computer has already calculated this target area (your puzzle
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# input). For example:
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# target area: x=20..30, y=-10..-5
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# This target area means that you need to find initial x,y velocity values such
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# that after any step, the probe's x position is at least 20 and at most 30, and
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# the probe's y position is at least -10 and at most -5.
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# Given this target area, one initial velocity that causes the probe to be
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# within the target area after any step is 7,2:
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# .............#....#............
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# .......#..............#........
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# ...............................
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# S........................#.....
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# ...............................
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# ...............................
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# ...........................#...
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# ...............................
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# ....................TTTTTTTTTTT
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# ....................TTTTTTTTTTT
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# ....................TTTTTTTT#TT
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# ....................TTTTTTTTTTT
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# ....................TTTTTTTTTTT
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# ....................TTTTTTTTTTT
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# In this diagram, S is the probe's initial position, 0,0. The x coordinate
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# increases to the right, and the y coordinate increases upward. In the bottom
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# right, positions that are within the target area are shown as T. After each
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# step (until the target area is reached), the position of the probe is marked
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# with #. (The bottom-right # is both a position the probe reaches and a
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# position in the target area.)
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# Another initial velocity that causes the probe to be within the target area
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# after any step is 6,3:
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# ...............#..#............
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# ...........#........#..........
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# ...............................
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# ......#..............#.........
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# ...............................
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# ...............................
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# S....................#.........
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# ...............................
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# ...............................
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# ...............................
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# .....................#.........
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# ....................TTTTTTTTTTT
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# ....................TTTTTTTTTTT
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# ....................TTTTTTTTTTT
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# ....................TTTTTTTTTTT
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# ....................T#TTTTTTTTT
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# ....................TTTTTTTTTTT
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# Another one is 9,0:
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# S........#.....................
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# .................#.............
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# ...............................
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# ........................#......
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# ...............................
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# ....................TTTTTTTTTTT
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# ....................TTTTTTTTTT#
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# ....................TTTTTTTTTTT
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# ....................TTTTTTTTTTT
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# ....................TTTTTTTTTTT
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# ....................TTTTTTTTTTT
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# One initial velocity that doesn't cause the probe to be within the target area
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# after any step is 17,-4:
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# S..............................................................
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# ...............................................................
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# ...............................................................
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# ...............................................................
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# .................#.............................................
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# ....................TTTTTTTTTTT................................
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# ....................TTTTTTTTTTT................................
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# ....................TTTTTTTTTTT................................
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# ....................TTTTTTTTTTT................................
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# ....................TTTTTTTTTTT..#.............................
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# ....................TTTTTTTTTTT................................
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# ...............................................................
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# ...............................................................
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# ...............................................................
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# ...............................................................
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# ................................................#..............
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# ...............................................................
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# ...............................................................
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# ...............................................................
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# ...............................................................
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# ...............................................................
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# ...............................................................
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# ..............................................................#
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# The probe appears to pass through the target area, but is never within it
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# after any step. Instead, it continues down and to the right - only the first
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# few steps are shown.
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# If you're going to fire a highly scientific probe out of a super cool probe
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# launcher, you might as well do it with style. How high can you make the probe
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# go while still reaching the target area?
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# In the above example, using an initial velocity of 6,9 is the best you can do,
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# causing the probe to reach a maximum y position of 45. (Any higher initial y
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# velocity causes the probe to overshoot the target area entirely.)
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# Find the initial velocity that causes the probe to reach the highest y
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# position and still eventually be within the target area after any step. What
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# is the highest y position it reaches on this trajectory?
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with open("files/P17.txt") as f:
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target_area = [line for line in f.read().strip().split(": ")][1]
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x_min, x_max = target_area.split(",")[0].split("=")[1].split("..")
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y_min, y_max = target_area.split(", ")[1].split("=")[1].split("..")
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x_min, x_max, y_min, y_max = [int(i) for i in [x_min, x_max, y_min, y_max]]
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def hits(vx, vy):
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x = y = 0
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# Add a few sanity checks to ensure termination and one for performance
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while not (
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x > x_max or y < y_min or (vx == 0 and not x_min <= x <= x_max)
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):
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x += vx
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y += vy
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if x_min <= x <= x_max and y_min <= y <= y_max:
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return True
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vy -= 1
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vx = max(0, vx - 1)
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def part_1():
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valid_trajectories = [
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vy
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for vx in range(1, x_max + 1)
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for vy in range(y_min, 1 - y_min)
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if hits(vx, vy)
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]
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# Note that the height achieved for a given positive vy is given by
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# vy + (vy - 1) + ... + 1 = vy*(vy + 1)/2
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highest_y = max(vy * (vy + 1) // 2 for vy in valid_trajectories if vy > 0)
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print(f"The higest y position reached is {highest_y}")
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# --- Part Two ---
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# Maybe a fancy trick shot isn't the best idea; after all, you only have one
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# probe, so you had better not miss.
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# To get the best idea of what your options are for launching the probe, you
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# need to find every initial velocity that causes the probe to eventually be
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# within the target area after any step.
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# In the above example, there are 112 different initial velocity values that
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# meet these criteria:
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# 23,-10 25,-9 27,-5 29,-6 22,-6 21,-7 9,0 27,-7 24,-5
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# 25,-7 26,-6 25,-5 6,8 11,-2 20,-5 29,-10 6,3 28,-7
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# 8,0 30,-6 29,-8 20,-10 6,7 6,4 6,1 14,-4 21,-6
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# 26,-10 7,-1 7,7 8,-1 21,-9 6,2 20,-7 30,-10 14,-3
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# 20,-8 13,-2 7,3 28,-8 29,-9 15,-3 22,-5 26,-8 25,-8
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# 25,-6 15,-4 9,-2 15,-2 12,-2 28,-9 12,-3 24,-6 23,-7
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# 25,-10 7,8 11,-3 26,-7 7,1 23,-9 6,0 22,-10 27,-6
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# 8,1 22,-8 13,-4 7,6 28,-6 11,-4 12,-4 26,-9 7,4
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# 24,-10 23,-8 30,-8 7,0 9,-1 10,-1 26,-5 22,-9 6,5
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# 7,5 23,-6 28,-10 10,-2 11,-1 20,-9 14,-2 29,-7 13,-3
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# 23,-5 24,-8 27,-9 30,-7 28,-5 21,-10 7,9 6,6 21,-5
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# 27,-10 7,2 30,-9 21,-8 22,-7 24,-9 20,-6 6,9 29,-5
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# 8,-2 27,-8 30,-5 24,-7
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# How many distinct initial velocity values cause the probe to be within the
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# target area after any step?
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def part_2():
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valid_trajectories = [
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vy
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for vx in range(1, x_max + 1)
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for vy in range(y_min, 1 - y_min)
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if hits(vx, vy)
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]
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print(f"There are {len(valid_trajectories)} distinct values")
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if __name__ == "__main__":
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part_1()
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part_2()
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