Solve 2019 day 22

2019/d22.py

@@ -4,6 +4,7 @@ from math import gcd
 data = get_data(__file__)
 deck = list(range(10007))
 
+# part 1
 for line in data.splitlines():
     if "new stack" in line:
         deck = list(reversed(deck))
@@ -24,30 +25,94 @@ for line in data.splitlines():
 
 print(deck.index(2019))
 
-# idea: just follow the index of the target card
-len = 119315717514047
 len = 10007
-index = 2019
+orig_index = 2019
 
-
-for i in range(101741582076661):
-    for line in data.splitlines():
+# figure out how to reverse...
+index = orig_index
+for line in data.splitlines():
     if "new stack" in line:
-            index = len - (index + 1)
+        new_index = len - (index + 1)
+        rev_index = -(new_index - len + 1)
+        assert rev_index == index
+        index = new_index
     elif "cut" in line:
         cut, = str_to_ints(line)
         cut = (len + cut) % len
         if index >= cut:
-                index = index - cut
+            new_index = index - cut
         else:
-                index = (len - cut) + index
+            new_index = (len - cut) + index
+        rev_index = (new_index + cut) % len
+        assert rev_index == index
+        index = new_index
+        # calculate index from new_index and store in rev_index
     elif "increment" in line:
         n, = str_to_ints(line)
         assert gcd(n, len) == 1
         new_index = (n * index) % len
         m = mod_inverse(n, len)
-            assert (new_index * m) % len == index
+        rev_index = (new_index * m) % len
+        assert rev_index == index
         index = new_index
-    break
 
-print(index)
+assert index == deck.index(2019)
+
+# check that reverse approach works
+for line in reversed(data.splitlines()):
+    if "new stack" in line:
+        index = -(index - len + 1)
+    elif "cut" in line:
+        cut, = str_to_ints(line)
+        cut = (len + cut) % len
+        index = (index + cut) % len
+    elif "increment" in line:
+        n, = str_to_ints(line)
+        assert gcd(n, len) == 1
+        m = mod_inverse(n, len)
+        index = (index * m) % len
+assert index == orig_index
+
+lines = list(reversed(data.splitlines()))
+
+# new length of deck
+len = 119315717514047
+
+# get expression for one loop using sympy
+from sympy import symbols, simplify
+index = symbols("index")
+expr = index
+for line in lines:
+    if "new stack" in line:
+        # index = -(index - len + 1)
+        expr = -(expr - len + 1)
+    elif "cut" in line:
+        cut, = str_to_ints(line)
+        cut = (len + cut) % len
+        # index = (index + cut) % len
+        expr = (expr + cut)
+    elif "increment" in line:
+        n, = str_to_ints(line)
+        assert gcd(n, len) == 1
+        m = mod_inverse(n, len)
+        # index = (index * m) % len
+        expr = (expr * m)
+
+# we can see that expression is in the form (a - b * i) % m
+expr = simplify(expr % len)
+coeff_dict = expr.args[0].as_coefficients_dict()
+a = coeff_dict[1]
+b = -coeff_dict[index]
+
+# math
+n_shuffles = 101741582076661
+r0 = 2020
+m = len
+p = (-b) % m
+p_t = pow(p, n_shuffles, m)
+inv_b1 = mod_inverse(b + 1, m)
+term1 = (p_t * r0) % m
+term2 = (a * (1 - p_t) * inv_b1) % m
+r_t = (term1 + term2) % m
+print(r_t)
+

README.md

@@ -106,13 +106,13 @@ Solutions and utility script for Advent of Code challenges in Python.
 - Day 16: 36:10
 - Day 17: 180:00
 - Day 18: 24:04
-- Day 19: days, super fun, but hard for me
+- Day 19: days (super fun, but hard for me)
 - Day 20:
 - Day 21: 28:40 (16th - brute force but still not so bad)
 - Day 22: 185:00 (should not have been so slow but was fun)
 - Day 23: days
 - Day 24: days
-- Day 25: 
+- Day 25: 29:20 (slow)
 
 ## AoC 2019
 
@@ -137,7 +137,8 @@ Solutions and utility script for Advent of Code challenges in Python.
 - Day 19: 40:00   (Way too slow! Oversight error. Come on.)
 - Day 20: days    (Not actually that hard but I struggled for no reason.) 
 - Day 21: days    (But it was super fun!)
-- Day 22:
+- Day 22: days    (Needed some help...)
+- Day 23:
 
 ## AoC 2020