Day 13 (more glamor)

day13/part2.py

@@ -1,20 +1,19 @@
-import math
+from math import gcd
+
 
 def lcm(a, b):
-    return abs(a*b) // math.gcd(a, b)
+    return abs(a*b) // gcd(a, b)
 
 
-# an+b=xn+y -> n=(y-b)/(a-x)
+# f(n)=an+b and f(m)=xm+y
-# -> cn+d
+# Intersection of 2 sequences -> ck+d
 def merge(a, b, x, y):
-    d1 = b
+    while b != y:
-    d2 = y
+        if b < y:
-    while d1 != d2:
+            b += a * ((y-b-1) // a + 1)
-        if d1 < d2:
-            d1 += a * ((d2-d1-1) // a + 1)
         else:
-            d2 += x * ((d1-d2-1) // x + 1)
+            y += x * ((b-y-1) // x + 1)
-    d = d1
+    d = b
     c = lcm(a, x)
     return c, d
 
@@ -26,5 +25,4 @@ current = (1, 0)
 for bus in busses:
     current = merge(*current, *bus)
 
-
 print(current[1])