September 2017 Update

Task/Paraffins/Zkl/paraffins.zkl

@@ -0,0 +1,35 @@
+var BN=Import("zklBigNum");
+
+const nMax=100, nBranches=4;
+
+var rooted  =(nMax+1).pump(List.createLong(nMax+1).write,BN.fp(0)),
+    unrooted=(nMax+1).pump(List.createLong(nMax+1).write,BN.fp(0));
+rooted[0]=BN(1); rooted[1]=BN(1); unrooted[0]=BN(1); unrooted[1]=BN(1);
+
+fcn tree(br,n,l,inSum,cnt){
+   var c=(nBranches).pump(List().write,0);  // happens only once
+
+   sum := inSum;
+   foreach b in ([br + 1 .. nBranches]){
+      sum += n;
+      if (sum > nMax or (l * 2 >= sum and b >= nBranches)) return();
+      if (b == br + 1) c[br] = rooted[n] * cnt; // -->BigInt
+      else{
+	 c[br].mul(rooted[n] + b - br - 1);
+	 c[br].div(b - br);
+      }
+      if (l * 2 < sum) unrooted[sum].add(c[br]);
+      if (b < nBranches) rooted[sum].add(c[br]);
+      foreach m in ([n-1 .. 1,-1]) { tree(b, m, l, sum, c[br]); }
+   }
+}
+
+fcn bicenter(s){
+   if (s.isEven) unrooted[s].add(rooted[s / 2] * (rooted[s / 2] + 1) / 2);
+}
+
+foreach n in ([1 .. nMax]){
+   tree(0, n, n, 1, BN(1));
+   bicenter(n);
+   println(n, ": ", unrooted[n]);
+}