Solve 2024:13 p1-2 "Claw Contraption"

Initial version of the code tried to solve pt 1
using BFS, which took way too long even for the
test data.

After some fiddling with algebra with pen and paper,
I realized this 2 formulaes (using first example):

94 * b1 + 22 * b2 == 840
34 * b1 + 67 * b2 == 540

*b1 = button A presses
*b2 = button B presses

... could be rewritten to this single expression:

(94 + 34) * b1 + (22 + 67) * b2 = 840 * 540

I failed to remember the algebra for solving x than
y though, that I had to learn from the subreddit.
In the code, this is the ratio part.

Also, this solution using fractions is SICK.
https://www.reddit.com/r/adventofcode/comments/1hd4wda/comment/m1tz3nf/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

2024-python/output/day_12.py

@@ -25,11 +25,13 @@ def solve(data):
                 areas += 1
                 y, x = rc
                 for dy, dx in D:
-                    if (0 <= y + dy < H and 0 <= x + dx <W) and grid[y + dy][x + dx] == col:
+                    if (0 <= y + dy < H and 0 <= x + dx < W) and grid[y + dy][
+                        x + dx
+                    ] == col:
                         q.append((y + dy, x + dx))
                     else:
                         perimeters += 1
-            p1 += areas*perimeters
+            p1 += areas * perimeters
     p2 = None
     return p1, p2
 

2024-python/output/day_13.py

@@ -0,0 +1,36 @@
+from output import ints
+
+
+def solve(data):
+    offset = 10_000_000_000_000
+    machines = data.split("\n\n")
+    p1 = ratio(machines)
+    p2 = ratio(machines, offset)
+    return p1, p2
+
+
+def ratio(machines, offset=0):
+    cost = 0
+    for mid, config in enumerate(machines):
+        a_x, a_y, b_x, b_y, goal_x, goal_y = ints(config)
+
+        goal_x, goal_y = goal_x + offset, goal_y + offset
+
+        ratio = (goal_x * a_y - goal_y * a_x) / (goal_y * b_x - goal_x * b_y)
+        a_presses = round(goal_x / (b_x * ratio + a_x))
+        b_presses = round(a_presses * ratio)
+
+        a_presses, b_presses = int(a_presses), int(b_presses)
+        if (a_x + a_y) * a_presses + (b_x + b_y) * b_presses == goal_x + goal_y:
+            cost += 3 * a_presses + b_presses
+    return cost
+
+
+if __name__ == "__main__":
+    with open("./input/13.txt", "r") as f:
+        inp = f.read().strip()
+
+    p1, p2 = solve(inp)
+
+    print(p1)
+    print(p2)