From 1c7035d43331fc4360e0285a880cd1b86ca79022 Mon Sep 17 00:00:00 2001
From: Andrew Ekstedt <andrew.ekstedt@gmail.com>
Date: Fri, 13 Dec 2024 05:41:12 +0000
Subject: [PATCH] day 13 cleanup

---
 day13/sol.py | 36 ++++++++++++++++++++++++++++--------
 1 file changed, 28 insertions(+), 8 deletions(-)

diff --git a/day13/sol.py b/day13/sol.py
index 3e81a73..7957da3 100644
--- a/day13/sol.py
+++ b/day13/sol.py
@@ -22,10 +22,14 @@ import numpy
 def solve(file):
     total = 0
     total2 = 0
-    for record in parse(file):
+    records = list(parse(file))
+    for record in records:
         #print(record)
         ax, ay, bx, by, px, py = record
 
+        # Part 1
+
+        # Solve the linear equation:
         # k_a ax + k_b * bx = px
         # k_a ay + k_b * by = py
         
@@ -38,34 +42,50 @@ def solve(file):
             print("yes", k1, k2)
             total += 3*k1 + k2
 
+    for record in records:
+        ax, ay, bx, by, px, py = record
 
-        m00 = ax
-        m01 = bx
-        m10 = ay
-        m11 = by
-        v1 = px+ 10000000000000
-        v2 = py+ 10000000000000
+        # Part 2
+        #
+        # Can't use numpy because the values are too large for floats
+        # So here's an ad-hoc solver
+
+        px += 10000000000000
+        py += 10000000000000
+
+        m00, m01 = ax, bx
+        m10, m11 = ay, by
+        v1 = px
+        v2 = py
         
+        # subtract c*eq1 from eq2 to cancel first coefficient
         c = F(m10,m00)
         m10 -= c*m00
         m11 -= c*m01
         v2  -= c*v1
 
+        # scale eq2
         c = F(1,m11)
         v2 *= c
         m11 *= c
 
+        # subtract c*eq2 from eq1 to cancel second coefficient
         c = F(m01,m11)
         m01 -= c*m11
         v1  -= c*v2
 
+        # scale eq1
         c = F(1,m00)
         v1  *= c
         m00 *= c
 
+        # we now have
+        # 1*k_a + 0     = v1
+        # 0     + 1*k_b = v2
+
         print(m00, m01, m10, m11, v1, v2)
         if v1.denominator == 1 and v2.denominator == 1 and v1 > 0 and v2 > 0:
-            #if v1*ax + v2*bx == px and v1*ay + v2*by == py:
+            if v1*ax + v2*bx == px and v1*ay + v2*by == py:
                 print("yes2", v1, v2)
                 total2 += 3*v1 + v2