Data commit

Task/Catalan-numbers/Crystal/catalan-numbers.crystal

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+require "big"
+require "benchmark"
+
+def factorial(n : BigInt) : BigInt
+  (1..n).product(1.to_big_i)
+end
+
+def factorial(n : Int32 | Int64)
+  factorial n.to_big_i
+end
+
+# direct
+
+def catalan_direct(n)
+  factorial(2*n) / (factorial(n + 1) * factorial(n))
+end
+
+# recursive
+
+def catalan_rec1(n)
+  return 1 if n == 0
+  (0...n).reduce(0) do |sum, i|
+    sum + catalan_rec1(i) * catalan_rec1(n - 1 - i)
+  end
+end
+
+def catalan_rec2(n)
+  return 1 if n == 0
+  2*(2*n - 1) * catalan_rec2(n - 1) / (n + 1)
+end
+
+# performance and results
+
+Benchmark.bm do |b|
+  b.report("catalan_direct") { 16.times { |n| catalan_direct(n) } }
+  b.report("catalan_rec1") { 16.times { |n| catalan_rec1(n) } }
+  b.report("catalan_rec2") { 16.times { |n| catalan_rec2(n) } }
+end
+
+puts "\n       direct     rec1     rec2"
+16.times { |n| puts "%2d :%9d%9d%9d" % [n, catalan_direct(n), catalan_rec1(n), catalan_rec2(n)] }