Day 14: use direct binary split instead of 2^n calculation

Day14.scala

@@ -43,23 +43,17 @@ def part1 =
 // part 2
 
 object Cycling:
-  private val memo = mutable.Map.empty[(Board, Int), Board]
-  private def getPower(b: Board, p: Int): Board = // b.cycle 2^p times
-    memo.getOrElseUpdate(
-      (b, p), {
-        if p == 0 then b.cycle
-        else getPower(getPower(b, p - 1), p - 1)
-      }
-    )
+  private val memo = mutable.Map.empty[(Board, Long), Board]
 
   def apply(b: Board, times: Long): Board =
-    @scala.annotation.tailrec
-    def loop(b: Board, i: Int): Board =
-      val pow = 1L << i
-      if pow > times then b
-      else if (pow & times) > 0 then loop(getPower(b, i), i + 1)
-      else loop(b, i + 1)
-    loop(b, 0)
+    if times == 0 then b
+    else
+      memo.getOrElseUpdate(
+        (b, times), {
+          val twice = apply(apply(b, times / 2), times / 2)
+          if times % 2 == 0 then twice else twice.cycle
+        }
+      )
 
 def part2 =
   println(Cycling(board, 1_000_000_000).load)