Solution to problem 17 in Python

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()