diff --git a/src/Year_2021/P17.py b/src/Year_2021/P17.py new file mode 100644 index 0000000..0a24250 --- /dev/null +++ b/src/Year_2021/P17.py @@ -0,0 +1,219 @@ +# --- Day 17: Trick Shot --- + +# You finally decode the Elves' message. HI, the message says. You continue +# searching for the sleigh keys. + +# Ahead of you is what appears to be a large ocean trench. Could the keys have +# fallen into it? You'd better send a probe to investigate. + +# The probe launcher on your submarine can fire the probe with any integer +# velocity in the x (forward) and y (upward, or downward if negative) +# directions. For example, an initial x,y velocity like 0,10 would fire the +# probe straight up, while an initial velocity like 10,-1 would fire the probe +# forward at a slight downward angle. + +# The probe's x,y position starts at 0,0. Then, it will follow some trajectory +# by moving in steps. On each step, these changes occur in the following order: + +# The probe's x position increases by its x velocity. +# The probe's y position increases by its y velocity. +# Due to drag, the probe's x velocity changes by 1 toward the value 0; that +# is, it decreases by 1 if it is greater than 0, increases by 1 if it is less +# than 0, or does not change if it is already 0. +# Due to gravity, the probe's y velocity decreases by 1. + +# For the probe to successfully make it into the trench, the probe must be on +# some trajectory that causes it to be within a target area after any step. The +# submarine computer has already calculated this target area (your puzzle +# input). For example: + +# target area: x=20..30, y=-10..-5 + +# This target area means that you need to find initial x,y velocity values such +# that after any step, the probe's x position is at least 20 and at most 30, and +# the probe's y position is at least -10 and at most -5. + +# Given this target area, one initial velocity that causes the probe to be +# within the target area after any step is 7,2: + +# .............#....#............ +# .......#..............#........ +# ............................... +# S........................#..... +# ............................... +# ............................... +# ...........................#... +# ............................... +# ....................TTTTTTTTTTT +# ....................TTTTTTTTTTT +# ....................TTTTTTTT#TT +# ....................TTTTTTTTTTT +# ....................TTTTTTTTTTT +# ....................TTTTTTTTTTT + +# In this diagram, S is the probe's initial position, 0,0. The x coordinate +# increases to the right, and the y coordinate increases upward. In the bottom +# right, positions that are within the target area are shown as T. After each +# step (until the target area is reached), the position of the probe is marked +# with #. (The bottom-right # is both a position the probe reaches and a +# position in the target area.) + +# Another initial velocity that causes the probe to be within the target area +# after any step is 6,3: + +# ...............#..#............ +# ...........#........#.......... +# ............................... +# ......#..............#......... +# ............................... +# ............................... +# S....................#......... +# ............................... +# ............................... +# ............................... +# .....................#......... +# ....................TTTTTTTTTTT +# ....................TTTTTTTTTTT +# ....................TTTTTTTTTTT +# ....................TTTTTTTTTTT +# ....................T#TTTTTTTTT +# ....................TTTTTTTTTTT + +# Another one is 9,0: + +# S........#..................... +# .................#............. +# ............................... +# ........................#...... +# ............................... +# ....................TTTTTTTTTTT +# ....................TTTTTTTTTT# +# ....................TTTTTTTTTTT +# ....................TTTTTTTTTTT +# ....................TTTTTTTTTTT +# ....................TTTTTTTTTTT + +# One initial velocity that doesn't cause the probe to be within the target area +# after any step is 17,-4: + +# S.............................................................. +# ............................................................... +# ............................................................... +# ............................................................... +# .................#............................................. +# ....................TTTTTTTTTTT................................ +# ....................TTTTTTTTTTT................................ +# ....................TTTTTTTTTTT................................ +# ....................TTTTTTTTTTT................................ +# ....................TTTTTTTTTTT..#............................. +# ....................TTTTTTTTTTT................................ +# ............................................................... +# ............................................................... +# ............................................................... +# ............................................................... +# ................................................#.............. +# ............................................................... +# ............................................................... +# ............................................................... +# ............................................................... +# ............................................................... +# ............................................................... +# ..............................................................# + +# The probe appears to pass through the target area, but is never within it +# after any step. Instead, it continues down and to the right - only the first +# few steps are shown. + +# If you're going to fire a highly scientific probe out of a super cool probe +# launcher, you might as well do it with style. How high can you make the probe +# go while still reaching the target area? + +# In the above example, using an initial velocity of 6,9 is the best you can do, +# causing the probe to reach a maximum y position of 45. (Any higher initial y +# velocity causes the probe to overshoot the target area entirely.) + +# Find the initial velocity that causes the probe to reach the highest y +# position and still eventually be within the target area after any step. What +# is the highest y position it reaches on this trajectory? + +with open("files/P17.txt") as f: + target_area = [line for line in f.read().strip().split(": ")][1] +x_min, x_max = target_area.split(",")[0].split("=")[1].split("..") +y_min, y_max = target_area.split(", ")[1].split("=")[1].split("..") + +x_min, x_max, y_min, y_max = [int(i) for i in [x_min, x_max, y_min, y_max]] + + +def hits(vx, vy): + x = y = 0 + # Add a few sanity checks to ensure termination and one for performance + while not ( + x > x_max or y < y_min or (vx == 0 and not x_min <= x <= x_max) + ): + x += vx + y += vy + if x_min <= x <= x_max and y_min <= y <= y_max: + return True + vy -= 1 + vx = max(0, vx - 1) + + +def part_1(): + valid_trajectories = [ + vy + for vx in range(1, x_max + 1) + for vy in range(y_min, 1 - y_min) + if hits(vx, vy) + ] + + # Note that the height achieved for a given positive vy is given by + # vy + (vy - 1) + ... + 1 = vy*(vy + 1)/2 + highest_y = max(vy * (vy + 1) // 2 for vy in valid_trajectories if vy > 0) + + print(f"The higest y position reached is {highest_y}") + + +# --- Part Two --- + +# Maybe a fancy trick shot isn't the best idea; after all, you only have one +# probe, so you had better not miss. + +# To get the best idea of what your options are for launching the probe, you +# need to find every initial velocity that causes the probe to eventually be +# within the target area after any step. + +# In the above example, there are 112 different initial velocity values that +# meet these criteria: + +# 23,-10 25,-9 27,-5 29,-6 22,-6 21,-7 9,0 27,-7 24,-5 +# 25,-7 26,-6 25,-5 6,8 11,-2 20,-5 29,-10 6,3 28,-7 +# 8,0 30,-6 29,-8 20,-10 6,7 6,4 6,1 14,-4 21,-6 +# 26,-10 7,-1 7,7 8,-1 21,-9 6,2 20,-7 30,-10 14,-3 +# 20,-8 13,-2 7,3 28,-8 29,-9 15,-3 22,-5 26,-8 25,-8 +# 25,-6 15,-4 9,-2 15,-2 12,-2 28,-9 12,-3 24,-6 23,-7 +# 25,-10 7,8 11,-3 26,-7 7,1 23,-9 6,0 22,-10 27,-6 +# 8,1 22,-8 13,-4 7,6 28,-6 11,-4 12,-4 26,-9 7,4 +# 24,-10 23,-8 30,-8 7,0 9,-1 10,-1 26,-5 22,-9 6,5 +# 7,5 23,-6 28,-10 10,-2 11,-1 20,-9 14,-2 29,-7 13,-3 +# 23,-5 24,-8 27,-9 30,-7 28,-5 21,-10 7,9 6,6 21,-5 +# 27,-10 7,2 30,-9 21,-8 22,-7 24,-9 20,-6 6,9 29,-5 +# 8,-2 27,-8 30,-5 24,-7 + +# How many distinct initial velocity values cause the probe to be within the +# target area after any step? + + +def part_2(): + valid_trajectories = [ + vy + for vx in range(1, x_max + 1) + for vy in range(y_min, 1 - y_min) + if hits(vx, vy) + ] + + print(f"There are {len(valid_trajectories)} distinct values") + + +if __name__ == "__main__": + part_1() + part_2()