Solve 2020 day 13 CRT jojo

2020/d13.py

@@ -0,0 +1,39 @@
+from lib import get_data, str_to_ints, mod_inverse
+from functools import reduce
+
+data = get_data(__file__)
+lines = data.splitlines()
+
+earliest = int(lines[0])
+times = str_to_ints(lines[1])
+
+mintime = 10**21
+id = None
+
+for time in times:
+    mintimecur = (earliest // time) * time + time
+    if mintimecur < mintime:
+        mintime = mintimecur
+        id = time
+
+
+assert id is not None
+print((mintime - earliest) * id)
+
+fields = lines[1].split(",")
+
+buses = []
+for offset, busid in enumerate(fields):
+    if busid == "x":
+        continue
+    period = int(busid)
+    buses.append((period, -offset % period))
+
+
+total = 0
+product = reduce(lambda a, b: a * b, map(lambda x: x[0], buses))
+for period, offset in buses:
+    p = product // period
+    total += offset * mod_inverse(p, period) * p
+
+print(total % product)

README.md

@@ -148,7 +148,8 @@ Solutions and utility script for Advent of Code challenges in Python.
 - Day 10: 34:27 (so weak)
 - Day 11: 21:05 (hmmm, I rally have to analyze why I am so slow)
 - Day 12: 21:52 (just slow again for an easy problem)
-- Day 13:
+- Day 13: 18:00 (I don't really understand the CRT to be honest)
+- Day 14:
 
 
 ## AoC 2022

lib.py

@@ -280,3 +280,18 @@ def get_data(filename):
         assert os.path.isfile(txt_file), "Could not download AoC file"
         with open(txt_file) as f:
             return f.read()
+
+
+def mod_inverse(a, m):
+    def egcd(a, b):
+        if a == 0:
+            return b, 0, 1
+        else:
+            g, y, x = egcd(b % a, a)
+            return g, x - (b // a) * y, y
+
+    g, x, _ = egcd(a, m)
+    if g != 1:
+        raise Exception('Modular inverse does not exist')
+    else:
+        return x % m