Day 19

19.py

@@ -0,0 +1,84 @@
+#!/usr/bin/python3
+
+"""Solution for day 19 of Advent of Code 2016.
+
+There are two different solutions presented here. The "manually" methods simulate the present-thieving step by step
+to get the results. I used these to figure out the patterns to both part 1 and part 2 and thus write simple, super
+quick formulae to get the answer.
+
+For part 1, the results look something like this:
+
+  Number of Elves |  Winning Elf
+  1               |  0
+  2               |  0
+  3               |  2
+  4               |  0
+  5               |  2
+  6               |  4
+  7               |  6
+  8               |  0
+
+So if the number of elves is a power of two, then the first elf wins. Otherwise, the winning elf is the one with a
+number double the difference between the last power of two and the number of elves.
+
+For part 2, the results are more complicated (as you'd expect!):
+
+  Number of Elves |  Winning Elf
+  1               |  0
+  2               |  0
+  3               |  2
+  4               |  0
+  5               |  1
+  6               |  2
+  7               |  4
+  8               |  6
+  9               |  8
+  10              |  0
+  11              |  1
+  12              |  2
+  13              |  3
+  ...             |  ...
+  18              |  8
+  19              |  10
+  20              |  12
+  ...             |  ...
+  28              |  0
+
+The points where elf 0 wins (and the sequence resets) now follow the pattern 3^n+1 (instead of 2^n from part 1).
+Between those points, the winning elf increases by 1 for the first 3^n elves, then by 2 thereafter.
+"""
+
+import math
+
+seed = 3004953
+
+print('Part one: %s' % (1 + 2 * int(seed - 2 ** math.floor(math.log(seed, 2)))))
+
+lp = 3 ** int(math.floor(0.0001 + math.log(seed - 1, 3)))  # Add a small amount to avoid floating point errors
+print('Part two: %s' % ((seed - lp) * (1 + max(0, (seed - 2 * lp) / (lp + 1)))))
+
+
+def run_part1_manually(n):
+    elves = {}
+    for i in range(n):
+        elves[i] = i + 1 if i < n - 1 else 0
+    current = 0
+    while len(elves) > 1:
+        neighbour = elves[current]
+        elves[current] = elves[neighbour]
+        del elves[neighbour]
+        current = elves[current]
+    return elves.keys()[0]
+
+
+def run_part2_manually(n):
+    elves = range(n)
+    current = 0
+    while len(elves) > 1:
+        target = (current + int(math.floor(len(elves) / 2))) % len(elves)
+        del elves[target]
+        if target > current:
+            current = (current + 1) % len(elves)
+        else:
+            current %= len(elves)
+    return elves[0]