Solution to problem 10 in Python

src/Year_2023/Day10.py

@@ -134,53 +134,235 @@
 # it take to get from the starting position to the point farthest from the
 # starting position?
 
+import re
+
 with open("files/P10.txt") as f:
-    p = [row for row in f.read().strip().split("\n")]
+    grid = [row for row in f.read().strip().split("\n")]
 
+U, D, L, R = (-1, 0), (1, 0), (0, -1), (0, 1)
+directions = {
+    "|": (U, D),
+    "-": (L, R),
+    "L": (U, R),
+    "J": (U, L),
+    "7": (D, L),
+    "F": (D, R),
+    ".": (),
+}
 
-def bfs(grid, directions, connections):
-    start = [pos for pos, c in grid.items() if c == "S"][0]
-    queue, seen = [(0, start)], set()
-    while queue:
-        count, (x, y) = queue.pop(0)
-        seen.add((x, y))
-        for dx, dy in directions[grid[x, y]]:
-            new_x, new_y = x + dx, y + dy
-            if (new_x, new_y) not in grid or (new_x, new_y) in seen:
-                continue
-            if grid[new_x, new_y] not in connections[dx, dy]:
-                continue
-            queue.append((count + 1, (new_x, new_y)))
-    return count, seen
+s_values = set(directions) - {"."}
+
+# where is "S" located?
+ss = [
+    (r, c)
+    for r, row in enumerate(grid)
+    for c, ch in enumerate(row)
+    if ch == "S"
+]
+# must be unique
+assert len(ss) == 1
+sr, sc = ss[0]
+
+# if we are in the first row, we can't go up or if the above row does not let us
+# go down
+if sr == 0 or D not in directions[grid[sr - 1][sc]]:
+    # s is not on top of a pipe that point upwards
+    s_values -= set("|LJ")
+
+# if we are in the last row, we can't go down or we can't go up from the char
+# below us
+if sr == len(grid) - 1 or U not in directions[grid[sr + 1][sc]]:
+    # s is not on top of a pipe that point downwards
+    s_values -= set("|7F")
+
+# if we are in the first column, we can´t go left or if the pipe towards left
+# does not go right
+if sc == 0 or R not in directions[grid[sr][sc - 1]]:
+    s_values -= set("-J7")
+
+# if we are in the last column, we can't go to the right or if the pipe towards
+# right does not go left
+if sc == len(grid[0]) - 1 or L not in directions[grid[sr][sc + 1]]:
+    s_values -= set("-LF")
+
+# only one value is possible
+assert len(s_values) == 1
+[S] = s_values
+
+# replace grid value of S with its true value
+grid = [row.replace("S", S) for row in grid]
 
 
 def part1():
-    N, S, W, E = (0, -1), (0, 1), (-1, 0), (1, 0)
-    directions = {
-        "S": [N, S, W, E],
-        "|": [N, S],
-        "-": [E, W],
-        "L": [N, E],
-        "J": [N, W],
-        "7": [S, W],
-        "F": [S, E],
-    }
-    connections = {
-        N: {"|", "7", "F"},
-        S: {"|", "L", "J"},
-        E: {"-", "J", "7"},
-        W: {"-", "L", "F"},
-    }
-    grid = {
-        (x, y): c
-        for y, row in enumerate(p)
-        for x, c in enumerate(row)
-        if c != "."
-    }
-    total, _ = bfs(grid, directions, connections)
+    # we will traverse our pipe to find the path length divided by 2, because we
+    # need to find the furthest point from the starting position
+    prev_r = sr
+    prev_c = sc
 
+    # we pick a random direction, first one for example
+    dr, dc = directions[grid[sr][sc]][0]
+
+    next_r = prev_r + dr
+    next_c = prev_c + dc
+
+    # # we count the start position
+    seen = {(sr, sc)}
+
+    while (next_r, next_c) != (sr, sc):
+        seen.add((next_r, next_c))
+        # for each direction we can take in the pipe for the next position
+        for dr, dc in directions[grid[next_r][next_c]]:
+            if (next_r + dr, next_c + dc) != (prev_r, prev_c):
+                # set previous to our current position
+                prev_r = next_r
+                prev_c = next_c
+                # moves to our next position
+                next_r += dr
+                next_c += dc
+                # we are done!
+                break
+
+    total = len(seen) // 2
     print(f"You need {total} steps")
+    # for part 2
+    return grid, seen
+
+
+# --- Part Two ---
+
+# You quickly reach the farthest point of the loop, but the animal never
+# emerges. Maybe its nest is within the area enclosed by the loop?
+
+# To determine whether it's even worth taking the time to search for such a
+# nest, you should calculate how many tiles are contained within the loop. For
+# example:
+
+# ...........
+# .S-------7.
+# .|F-----7|.
+# .||.....||.
+# .||.....||.
+# .|L-7.F-J|.
+# .|..|.|..|.
+# .L--J.L--J.
+# ...........
+
+# The above loop encloses merely four tiles - the two pairs of . in the
+# southwest and southeast (marked I below). The middle . tiles (marked O below)
+# are not in the loop. Here is the same loop again with those regions marked:
+
+# ...........
+# .S-------7.
+# .|F-----7|.
+# .||OOOOO||.
+# .||OOOOO||.
+# .|L-7OF-J|.
+# .|II|O|II|.
+# .L--JOL--J.
+# .....O.....
+
+# In fact, there doesn't even need to be a full tile path to the outside for
+# tiles to count as outside the loop - squeezing between pipes is also allowed!
+# Here, I is still within the loop and O is still outside the loop:
+
+# ..........
+# .S------7.
+# .|F----7|.
+# .||OOOO||.
+# .||OOOO||.
+# .|L-7F-J|.
+# .|II||II|.
+# .L--JL--J.
+# ..........
+
+# In both of the above examples, 4 tiles are enclosed by the loop.
+
+# Here's a larger example:
+
+# .F----7F7F7F7F-7....
+# .|F--7||||||||FJ....
+# .||.FJ||||||||L7....
+# FJL7L7LJLJ||LJ.L-7..
+# L--J.L7...LJS7F-7L7.
+# ....F-J..F7FJ|L7L7L7
+# ....L7.F7||L7|.L7L7|
+# .....|FJLJ|FJ|F7|.LJ
+# ....FJL-7.||.||||...
+# ....L---J.LJ.LJLJ...
+
+# The above sketch has many random bits of ground, some of which are in the
+# loop (I) and some of which are outside it (O):
+
+# OF----7F7F7F7F-7OOOO
+# O|F--7||||||||FJOOOO
+# O||OFJ||||||||L7OOOO
+# FJL7L7LJLJ||LJIL-7OO
+# L--JOL7IIILJS7F-7L7O
+# OOOOF-JIIF7FJ|L7L7L7
+# OOOOL7IF7||L7|IL7L7|
+# OOOOO|FJLJ|FJ|F7|OLJ
+# OOOOFJL-7O||O||||OOO
+# OOOOL---JOLJOLJLJOOO
+
+# In this larger example, 8 tiles are enclosed by the loop.
+
+# Any tile that isn't part of the main loop can count as being enclosed by the
+# loop. Here's another example with many bits of junk pipe lying around that
+# aren't connected to the main loop at all:
+
+# FF7FSF7F7F7F7F7F---7
+# L|LJ||||||||||||F--J
+# FL-7LJLJ||||||LJL-77
+# F--JF--7||LJLJ7F7FJ-
+# L---JF-JLJ.||-FJLJJ7
+# |F|F-JF---7F7-L7L|7|
+# |FFJF7L7F-JF7|JL---7
+# 7-L-JL7||F7|L7F-7F7|
+# L.L7LFJ|||||FJL7||LJ
+# L7JLJL-JLJLJL--JLJ.L
+
+# Here are just the tiles that are enclosed by the loop marked with I:
+
+# FF7FSF7F7F7F7F7F---7
+# L|LJ||||||||||||F--J
+# FL-7LJLJ||||||LJL-77
+# F--JF--7||LJLJIF7FJ-
+# L---JF-JLJIIIIFJLJJ7
+# |F|F-JF---7IIIL7L|7|
+# |FFJF7L7F-JF7IIL---7
+# 7-L-JL7||F7|L7F-7F7|
+# L.L7LFJ|||||FJL7||LJ
+# L7JLJL-JLJLJL--JLJ.L
+
+# In this last example, 10 tiles are enclosed by the loop.
+
+# Figure out whether you have time to search for the nest by calculating the
+# area within the loop. How many tiles are enclosed by the loop?
+
+
+def part2(grid, seen):
+    # get rid of all garbage pipes
+    grid = [
+        "".join(ch if (r, c) in seen else "." for c, ch in enumerate(row))
+        for r, row in enumerate(grid)
+    ]
+
+    inside = set()
+    for r, row in enumerate(grid):
+        # ignore pipes that face up or down on both ends because they don't matter
+        row = re.sub("L-*J|F-*7", lambda match: "." * len(match.group()), row)
+        within = False
+        # toggle on left
+        for c, ch in enumerate(row):
+            if ch in "|FL":
+                within = not within
+            if within:
+                inside.add((r, c))
+
+    total = len(inside - seen)
+    print(f"There are {total} tiles enclosed by the loop")
 
 
 if __name__ == "__main__":
-    part1()
+    g, sol1 = part1()
+    part2(g, sol1)