June 2018 Update

Task/Paraffins/Scala/paraffins.scala

@@ -0,0 +1,34 @@
+object Paraffins extends App {
+  val (nMax, nBranches) = (250, 4)
+  val rooted, unrooted = Array.tabulate(nMax + 1)(i => if (i < 2) BigInt(1) else BigInt(0))
+  val (unrooted, c) = (rooted.clone(), new Array[BigInt](nBranches))
+
+  for (n <- 1 to nMax) {
+    def tree(br: Int, n: Int, l: Int, inSum: Int, cnt: BigInt): Unit = {
+      var sum = inSum
+      for (b <- br + 1 to nBranches) {
+        sum += n
+        if (sum > nMax || (l * 2 >= sum && b >= nBranches)) return
+
+        if (b == br + 1) c(br) = rooted(n) * cnt
+        else {
+          c(br) = c(br) * (rooted(n) + BigInt(b - br - 1))
+          c(br) = c(br) / BigInt(b - br)
+        }
+        if (l * 2 < sum) unrooted(sum) = unrooted(sum) + c(br)
+        if (b < nBranches) rooted(sum) = rooted(sum) + c(br)
+
+        for (m <- n - 1 to 1 by -1) tree(b, m, l, sum, c(br))
+      }
+    }
+
+    def bicenter(s: Int): Unit = if ((s & 1) == 0) {
+      val halves = rooted(s / 2)
+      unrooted(s) = unrooted(s) + ((halves + BigInt(1)) * halves >> 1)
+    }
+
+    tree(0, n, n, 1, BigInt(1))
+    bicenter(n)
+    println(f"$n%3d:  ${unrooted(n)}%s")
+  }
+}