From 31f44a275f52068d8f38d80971e5cd0113afd969 Mon Sep 17 00:00:00 2001
From: Simmo Saan <simmo.saan@gmail.com>
Date: Thu, 21 Dec 2023 19:57:43 +0200
Subject: [PATCH] Add broken diamond counting solution to 2023 day 21 part 2

---
 .../eu/sim642/adventofcode2023/Day21.scala    | 120 +++++++++++++++++-
 .../sim642/adventofcode2023/Day21Test.scala   |   8 +-
 2 files changed, 120 insertions(+), 8 deletions(-)

diff --git a/src/main/scala/eu/sim642/adventofcode2023/Day21.scala b/src/main/scala/eu/sim642/adventofcode2023/Day21.scala
index 6b886029..3334fc6d 100644
--- a/src/main/scala/eu/sim642/adventofcode2023/Day21.scala
+++ b/src/main/scala/eu/sim642/adventofcode2023/Day21.scala
@@ -68,19 +68,125 @@ object Day21 {
       //println((q, r))
 
       val x1 = 0
-      val y1 = NaivePart2Solution.countReachableExactlyInfinite(grid, r)
+      val y0 = NaivePart2Solution.countReachableExactlyInfinite(grid, r)
       val x2 = 1
-      val y2 = NaivePart2Solution.countReachableExactlyInfinite(grid, r + 131)
+      val y1 = NaivePart2Solution.countReachableExactlyInfinite(grid, r + 131)
       val x3 = 2
-      val y3 = NaivePart2Solution.countReachableExactlyInfinite(grid, r + 2 * 131)
+      val y2 = NaivePart2Solution.countReachableExactlyInfinite(grid, r + 2 * 131)
+
+      //def f(x: Long): Long = {
+      //  y0 * (x - x2) * (x - x3) / (x1 - x2) / (x1 - x3) +
+      //    y1 * (x - x1) * (x - x3) / (x2 - x1) / (x2 - x3) +
+      //    y2 * (x - x1) * (x - x2) / (x3 - x1) / (x3 - x2)
+      //}
 
       def f(x: Long): Long = {
-        y1 * (x - x2) * (x - x3) / (x1 - x2) / (x1 - x3) +
-          y2 * (x - x1) * (x - x3) / (x2 - x1) / (x2 - x3) +
-          y3 * (x - x1) * (x - x2) / (x3 - x1) / (x3 - x2)
+        y0 * (x - 1) * (x - 2) / 2 - y1 * x * (x - 2) + y2 * x * (x - 1) / 2
+      }
+      /*
+
+      /\
+      \/
+
+
+       */
+
+      println(y0)
+      println(y1)
+      println(y2)
+
+      // y0 0 (1) [1, 0, 0] = innerEven
+      // y1 1 (9) [1, 4, 4] = innerEven + 4 * outer + 4 * innerOdd
+      // y2 2 (25) [9, 12, 4] = innerEven + 4 * outer + 4 * innerOdd + 8 * outer + 8 * innerEven
+
+      // y4 3 (49) [9, 24, 16] = innerEven + 4 * outer + 4 * innerOdd + 8 * outer + 8 * innerEven + 12 * outer + 12 * innerOdd
+
+
+      /*
+      f(0) = 1A
+       AA
+      AAAA
+      AAAA
+       AA
+
+      f(1) = 1A + 4B + 2X + 2Y
+             BB
+            BBBB
+            BBBB
+          XY BB YX
+         XXYY  YYXX
+         YYXX  XXYY
+       BB YX AA XY BB
+      BBBB  AAAA  BBBB
+      BBBB  AAAA  BBBB
+       BB YX AA XY BB
+         YYXX  XXYY
+         XXYY  YYXX
+          XY BB YX
+            BBBB
+            BBBB
+             BB
+
+    f(2) = 9A + 4B + 6X + 6Y
+             AA
+            AAAA
+            AAAA
+          YX AA XY
+         YYXX  XXYY
+         XXYY  YYXX
+       AA XY BB YX AA
+      AAAA  BBBB  AAAA
+      AAAA  BBBB  AAAA
+    YX AA XY BB YX AA XY
+   YYXX  XXYY  YYXX  XXYY
+   XXYY  YYXX  XXYY  YYXX
+ AA XY BB YX AA XY BB YX AA
+AAAA  BBBB  AAAA  BBBB  AAAA
+AAAA  BBBB  AAAA  BBBB  AAAA
+ AA XY BB YX AA XY BB YX AA
+   XXYY  YYXX  XXYY  YYXX
+   YYXX  XXYY  YYXX  XXYY
+    YX AA XY BB YX AA XY
+      AAAA  BBBB  AAAA
+      AAAA  BBBB  AAAA
+       AA XY BB YX AA
+         XXYY  YYXX
+         YYXX  XXYY
+          YX AA XY
+            AAAA
+            AAAA
+             AA
+
+      f(3) = 9A + 16B +
+      */
+
+
+      def f2(n: Long): Long = {
+        val a = y0 // A
+        val xy = (y2 - y1 - 8 * a).toDouble / 4 // X + Y
+        val b = (y1 - y0 - 2 * xy) / 4 // B
+        //val xy = (-8 * y0 - y1 + y2) / 4
+        //val b = (6 * y0 + 3 * y1 - y2) / 8
+        println((a, b, xy))
+
+        val c = (2 * n + 1) * (2 * n + 1)
+        // n:  0, 1, 2,  3, ...
+        // ca: 1, 1, 9,  9, ...
+        // cb: 0, 4, 4, 16, ...
+        val ca = (2 * (n / 2) + 1) * (2 * (n / 2) + 1)
+        //val cb = inners - ca
+        val cb = (2 * ((n + 1) / 2)) * (2 * ((n + 1) / 2))
+        val cxy = (c - ca - cb) / 2
+        val r = ca * a + cb * b + cxy * xy
+        println((n, r))
+        println((ca, cb, cxy))
+        r.toLong
       }
 
-      f(q)
+      //assert(f2(0) == y0)
+      //assert(f2(1) == y1)
+      //assert(f2(2) == y2)
+      f2(q)
     }
   }
 
diff --git a/src/test/scala/eu/sim642/adventofcode2023/Day21Test.scala b/src/test/scala/eu/sim642/adventofcode2023/Day21Test.scala
index deb5f6eb..74295d2d 100644
--- a/src/test/scala/eu/sim642/adventofcode2023/Day21Test.scala
+++ b/src/test/scala/eu/sim642/adventofcode2023/Day21Test.scala
@@ -72,11 +72,17 @@ object Day21Test {
         //(512, 228690),
         //(1024, 912913),
 
-        (131, 15130),
+        //(131, 15130),
         //(2 * 131, 60085),
         //(3 * 131, 134866),
         //(4 * 131, 239473),
         //(5 * 131, 373906),
+
+        (65, 3778),
+        (65 + 1 * 131, 33695),
+        (65 + 2 * 131, 93438),
+        (65 + 3 * 131, 183007),
+        (65 + 4 * 131, 302402),
       )
 
       forAll(stepsExpectedReachable) { (steps, expectedReachable) =>