Data commit

Task/Catalan-numbers/D/catalan-numbers.d

@@ -0,0 +1,20 @@
+import std.stdio, std.algorithm, std.bigint, std.functional, std.range;
+
+auto product(R)(R r) { return reduce!q{a * b}(1.BigInt, r); }
+
+const cats1 = sequence!((a, n) => iota(n+2, 2*n+1).product / iota(1, n+1).product)(1);
+
+BigInt cats2a(in uint n) {
+    alias mcats2a = memoize!cats2a;
+    if (n == 0) return 1.BigInt;
+    return n.iota.map!(i => mcats2a(i) * mcats2a(n - 1 - i)).sum;
+}
+
+const cats2 = sequence!((a, n) => n.cats2a);
+
+const cats3 = recurrence!q{ (4*n - 2) * a[n - 1] / (n + 1) }(1.BigInt);
+
+void main() {
+    foreach (cats; TypeTuple!(cats1, cats2, cats3))
+        cats.take(15).writeln;
+}