[Advent of Code 2021] Day 5 | Hydrothermal Venture

Part 1

You come across a field of hydrothermal vents on the ocean floor! These vents constantly produce large, opaque clouds, so it would be best to avoid them if possible.

They tend to form in lines; the submarine helpfully produces a list of nearby lines of vents (your puzzle input) for you to review. For example:

0,9 -> 5,9
8,0 -> 0,8
9,4 -> 3,4
2,2 -> 2,1
7,0 -> 7,4
6,4 -> 2,0
0,9 -> 2,9
3,4 -> 1,4
0,0 -> 8,8
5,5 -> 8,2

Each line of vents is given as a line segment in the format x1,y1 -> x2,y2 where x1,y1 are the coordinates of one end the line segment and x2,y2 are the coordinates of the other end. These line segments include the points at both ends. In other words:

• An entry like 1,1 -> 1,3 covers points 1,1, 1,2, and 1,3.
• An entry like 9,7 -> 7,7 covers points 9,7, 8,7, and 7,7.

For now, only consider horizontal and vertical lines: lines where either x1 = x2 or y1 = y2.

So, the horizontal and vertical lines from the above list would produce the following diagram:

.......1..
..1....1..
..1....1..
.......1..
.112111211
..........
..........
..........
..........
222111....

In this diagram, the top left corner is 0,0 and the bottom right corner is 9,9. Each position is shown as the number of lines which cover that point or . if no line covers that point. The top-left pair of 1s, for example, comes from 2,2 -> 2,1; the very bottom row is formed by the overlapping lines 0,9 -> 5,9 and 0,9 -> 2,9.

To avoid the most dangerous areas, you need to determine the number of points where at least two lines overlap. In the above example, this is anywhere in the diagram with a 2 or larger - a total of _5_ points.

Consider only horizontal and vertical lines. At how many points do at least two lines overlap?

Proposed solution: iterate through the input and maintain a mapping between points and frequencies – only considering horizontal and vertical lines

Time complexity: O(n) where n is the length of all the input lines

Space complexity: O(n)

#!/usr/bin/env python3
import sys

if len(sys.argv) != 2:
    print("Usage: {} <input file>".format(sys.argv[0]))
    sys.exit(1)

field = {}
file_input = open(sys.argv[1], "r").read().strip().split("\n")

def delta(p1, p2):
    if p1 > p2:
        return -1
    return int(p1 != p2)

for line in file_input:
    start, end = line.split(" -> ")
    x1, y1 = list(map(lambda x: int(x), start.split(",")))
    x2, y2 = list(map(lambda x: int(x), end.split(",")))
    delta_x, delta_y = delta(x1, x2), delta(y1, y2)
    x, y = x1, y1
    if delta_y == 0 and delta_x != 0:
        while x != x2:
            field[x,y] = field.get((x,y),0) + 1
            x += delta_x
        field[x,y] = field.get((x,y),0) + 1
    if delta_x == 0 and delta_y != 0:
        while y != y2:
            field[x,y] = field.get((x,y),0) + 1
            y += delta_y
        field[x,y] = field.get((x,y),0) + 1

num_points = sum(list(map(lambda x: x >= 2, field.values())))
print("Dangerous Points: " + str(num_points))

Not much to this. Parse each line to get the start and end coordinates for each. Iterate through only vertical/horizontal lines and track frequency of each coordinate in a map. Finally, count the number of points that are frequented by 2 or more lines.

❯ python3 solution5.py input5
Dangerous Points: 6666

Part 2

Unfortunately, considering only horizontal and vertical lines doesn't give you the full picture; you need to also consider diagonal lines.

Because of the limits of the hydrothermal vent mapping system, the lines in your list will only ever be horizontal, vertical, or a diagonal line at exactly 45 degrees. In other words:

• An entry like 1,1 -> 3,3 covers points 1,1, 2,2, and 3,3.
• An entry like 9,7 -> 7,9 covers points 9,7, 8,8, and 7,9.

Considering all lines from the above example would now produce the following diagram:

1.1....11.
.111...2..
..2.1.111.
...1.2.2..
.112313211
...1.2....
..1...1...
.1.....1..
1.......1.
222111....

You still need to determine the number of points where at least two lines overlap. In the above example, this is still anywhere in the diagram with a 2 or larger - now a total of _12_ points.

Consider all of the lines. At how many points do at least two lines overlap?

Proposed solution: same solution but now addressing diagonal lines

Time complexity: O(n)

Space complexity: O(n)

#!/usr/bin/env python3
import sys

if len(sys.argv) != 2:
    print("Usage: {} <input file>".format(sys.argv[0]))
    sys.exit(1)

field = {}
file_input = open(sys.argv[1], "r").read().strip().split("\n")

def delta(p1, p2):
    if p1 > p2:
        return -1
    return int(p1 != p2)

for line in file_input:
    start, end = line.split(" -> ")
    x1, y1 = list(map(lambda x: int(x), start.split(",")))
    x2, y2 = list(map(lambda x: int(x), end.split(",")))
    delta_x, delta_y = delta(x1, x2), delta(y1, y2)
    x, y = x1, y1
    while x != x2 or y != y2:
        field[x,y] = field.get((x,y),0) + 1
        x += delta_x
        y += delta_y
    field[x,y] = field.get((x,y),0) + 1

num_points = sum(list(map(lambda x: x >= 2, field.values())))
print("Dangerous Points: " + str(num_points))

This is the same solution except now we keep track of the change in x and y since diagonal lines have non-zero values for both.

❯ python3 solution5.py input5
Dangerous Points: 19081