From d720534eaf3e5eb860bf16e6e9f356dd3208051c Mon Sep 17 00:00:00 2001
From: Martin Potier <martin.potier@marvid.fr>
Date: Fri, 11 Dec 2020 09:30:17 +0200
Subject: [PATCH] Day 10 - part 2

yeaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaah
---
 day10/main.hs | 32 +++++++++++++++++++++-----------
 1 file changed, 21 insertions(+), 11 deletions(-)

diff --git a/day10/main.hs b/day10/main.hs
index cf2a7bd..c3e17d0 100755
--- a/day10/main.hs
+++ b/day10/main.hs
@@ -32,24 +32,34 @@ solvePart1 xs = finally
 
 --------------------------------------------------------------------------------
 -- 1 -> 1 possibility
--- 1 1 -> 2 poss
--- 1 1 1 -> 4 poss
--- 1 1 1 1 -> 6 poss
--- 1 1 1 1 1 -> 8 poss
+-- 1 1 -> 2 possibilities
+-- 1 1 1 -> 4 possibilities
+-- 1 1 1 1 -> 7 (!) possibilities
+-- 1 1 1 1 1 -> ? possibilities
 --
 --------------------------------------------------------------------------------
 cleanup :: [[Int]] -> [[Int]]
 cleanup = filter (\v -> (any (/= 3) v) && (length v > 1))
 
-est :: [[Int]] -> [Int]
-est = map combinations
+
+-- That is the actual problem right here:
+-- ··· -> 2^3 - 1 = 7
+-- ···· -> 2^4 - 1 - 2 = 13
+-- ····· -> 2^5 - 1 - 2 - 3 = 26
+combinations :: [Int] -> Int
+combinations v =
+    (2 ^ n)           -- All the ways to take any on/off combination in n
+  - (sum [1..(n-2)])  -- All the ways to take n+ consecutive in n (illegal),
+                      -- *except* for n=1 and n=2 which are legal
   where
-    combinations v = (2 ^ l) - (2 ^ (l `div` 3))
-      where
-        l = (length v) - 1
+    n = (length v) - 1
 
 estimatePermutations :: [Int] -> Int
-estimatePermutations = getProduct . foldMap Product . est . cleanup . group
+estimatePermutations = getProduct
+                     . foldMap Product
+                     . map combinations
+                     . cleanup
+                     . group
 
 distanceMap :: [Int] -> [Int]
 distanceMap xs = map (\(x,y) -> y - x) $ zip (0:sorted) (sorted ++ [(last sorted)+3])
@@ -77,6 +87,6 @@ main = do
   print $ distanceMap smallExample
   print $ solvePart2 smallExample
   print $ distanceMap biggerExample
-  print $ (est . cleanup . group) $ distanceMap biggerExample
+  print $ (map combinations . cleanup . group) $ distanceMap biggerExample
   print $ solvePart2 biggerExample
   print $ solvePart2 input