From 37f1ac7c030d6a7e24f9df0dbd80254d075cf14c Mon Sep 17 00:00:00 2001
From: Fedor Lyanguzov <Fedor-Lyanguzov@users.noreply.github.com>
Date: Sat, 14 Dec 2024 16:22:20 +0300
Subject: [PATCH] 13.2 python cramers rule

---
 13/13.py | 62 ++++++++------------------------------------------------
 1 file changed, 9 insertions(+), 53 deletions(-)

diff --git a/13/13.py b/13/13.py
index 60a4929..c9f84d2 100644
--- a/13/13.py
+++ b/13/13.py
@@ -8,23 +8,6 @@ Prize: X=(\d+), Y=(\d+)
 
 
 data = open("input.txt").read().strip().split("\n\n")
-data = '''
-Button A: X+94, Y+34
-Button B: X+22, Y+67
-Prize: X=8400, Y=5400
-
-Button A: X+26, Y+66
-Button B: X+67, Y+21
-Prize: X=12748, Y=12176
-
-Button A: X+17, Y+86
-Button B: X+84, Y+37
-Prize: X=7870, Y=6450
-
-Button A: X+69, Y+23
-Button B: X+27, Y+71
-Prize: X=18641, Y=10279
-'''.strip().split("\n\n")
 
 data = [tuple(map(int, pattern.match(x).groups())) for x in data]
 
@@ -43,7 +26,6 @@ def f(data):
                     if ya*i+yb*j==yt:
                         s2.add((i, j))
         if s1&s2:
-            print("@0", n, s1&s2)
             s += tok(min(s1&s2, key=tok))
     return s
 
@@ -51,41 +33,15 @@ def f(data):
 def f2(data):
     s = 0
     for i, (xa, ya, xb, yb, xt, yt) in enumerate(data):
-        print(f'@1 {i} {xa=}, {ya=}, {xb=}, {yb=}, {xt=}, {yt=}')
-        #xt += 10_000_000_000_000
-        #yt += 10000000000000
-        b = 0
-        a = 0
-        al = 0
-        ar = max(xt//xa+1, yt//ya+1)
-        while ar-al>1:
-            am = (ar+al)//2
-            bl = 0
-            br = max(xt//xb+1, yt//yb+1)
-            f = False
-            while br-bl>1:
-                bm = (bl+br)//2
-                if xa*am+xb*bm>xt and ya*am+yb*bm>xt:
-                    br = bm
-                elif xa*am+xb*bm<xt and ya*am+yb*bm<xt:
-                    bl = bm
-                elif xa*am+xb*bm==xt and ya*am+yb*bm==xt:
-                    f = True
-                    b = bm
-                    break
-                else:
-                    break
-            print(al, ar)
-            if f:
-                a = am
-                ar = am
-            else:
-                if a>3*br:
-                    al = am
-                else:
-                    ar = am
-        print('@end', a, b, a*3+b)
-        s += a*3+b
+        xt += 10_000_000_000_000
+        yt += 10000000000000
+        d = xa*yb - xb*ya
+        da = xt*yb - xb*yt
+        db = xa*yt - xt*ya
+        if da%d==db%d==0:
+            a = da//d
+            b = db//d
+            s += a*3+b
     return s
 print(f(data))
 print(f2(data))