June 2018 Update

Task/Catalan-numbers/360-Assembly/catalan-numbers.360

@@ -1,4 +1,4 @@
-CATALAN  CSECT
+CATALAN  CSECT        08/09/2015
          USING  CATALAN,R15
          LA     R7,1               c=1
          LA     R6,1               i=1

Task/Catalan-numbers/BBC-BASIC/catalan-numbers.bbc

@@ -1,8 +1,7 @@
-      FOR i% = 1 TO 15
-        PRINT FNcatalan(i%)
-      NEXT
-      END
-
-      DEF FNcatalan(n%)
-      IF n% = 0 THEN = 1
-      = 2 * (2 * n% - 1) * FNcatalan(n% - 1) / (n% + 1)
+      10 FOR i% = 1 TO 15
+      20   PRINT FNcatalan(i%)
+      30 NEXT
+      40 END
+      50 DEF FNcatalan(n%)
+      60   IF n% = 0 THEN = 1
+      70   = 2 * (2 * n% - 1) * FNcatalan(n% - 1) / (n% + 1)

Task/Catalan-numbers/Julia/catalan-numbers.julia

@@ -1 +1,4 @@
-Catalan(n::Integer) = div(binomial(2n, n), n+1)
+catalannum(n::Integer) = binomial(2n, n) ÷ (n + 1)
+
+@show catalannum.(1:15)
+@show catalannum(big(100))

Task/Catalan-numbers/Logo/catalan-numbers.logo

@@ -0,0 +1,11 @@
+to factorial :n
+  output ifelse [less? :n 1] 1 [product :n factorial difference :n 1]
+end
+to choose :n :r
+  output quotient factorial :n product factorial :r factorial difference :n :r
+end
+to catalan :n
+  output product (quotient sum :n 1) choose product 2 :n :n
+end
+
+repeat 15 [print catalan repcount]

Task/Catalan-numbers/MATLAB/catalan-numbers-1.m

@@ -1,4 +1,4 @@
-function n = catalanNumbers(n)
+function n = catalanNumber(n)
     for i = (1:length(n))
         n(i) = (1/(n(i)+1))*nchoosek(2*n(i),n(i));
     end

Task/Catalan-numbers/MATLAB/catalan-numbers-2.m

@@ -1,3 +1,3 @@
 function n = catalanNumbers(n)
-    n = arrayfun(@(n)prod(n+1:2*n)/prod(1:n+1), n);
+    n = [1 cumprod((2:4:4*n-6) ./ (2:n))];
 end

Task/Catalan-numbers/MATLAB/catalan-numbers-3.m

@@ -1,10 +1,10 @@
->> catalanNumbers(14)
+>> catalanNumber(14)
 
 ans =
 
      2674440
 
->> catalanNumbers((0:17))'
+>> catalanNumbers(18)'
 
 ans =
 

Task/Catalan-numbers/Modula-2/catalan-numbers.mod2

@@ -0,0 +1,65 @@
+MODULE CatalanNumbers;
+FROM FormatString IMPORT FormatString;
+FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
+
+PROCEDURE binomial(m,n : LONGCARD) : LONGCARD;
+VAR r,d : LONGCARD;
+BEGIN
+    r := 1;
+    d := m - n;
+    IF d>n THEN
+        n := d;
+        d := m - n;
+    END;
+    WHILE m>n DO
+        r := r * m;
+        DEC(m);
+        WHILE (d>1) AND NOT (r MOD d # 0) DO
+            r := r DIV d;
+            DEC(d)
+        END
+    END;
+    RETURN r
+END binomial;
+
+PROCEDURE catalan1(n : LONGCARD) : LONGCARD;
+BEGIN
+    RETURN binomial(2*n,n) DIV (1+n)
+END catalan1;
+
+PROCEDURE catalan2(n : LONGCARD) : LONGCARD;
+VAR i,sum : LONGCARD;
+BEGIN
+    IF n>1 THEN
+        sum := 0;
+        FOR i:=0 TO n-1 DO
+            sum := sum + catalan2(i) * catalan2(n - 1 - i)
+        END;
+        RETURN sum
+    ELSE
+        RETURN 1
+    END
+END catalan2;
+
+PROCEDURE catalan3(n : LONGCARD) : LONGCARD;
+BEGIN
+    IF n#0 THEN
+        RETURN 2  *(2 * n - 1) * catalan3(n - 1) DIV (1 + n)
+    ELSE
+        RETURN 1
+    END
+END catalan3;
+
+VAR
+    blah : LONGCARD = 123;
+    buf : ARRAY[0..63] OF CHAR;
+    i : LONGCARD;
+BEGIN
+    FormatString("\tdirect\tsumming\tfrac\n", buf);
+    WriteString(buf);
+    FOR i:=0 TO 15 DO
+        FormatString("%u\t%u\t%u\t%u\n", buf, i, catalan1(i), catalan2(i), catalan3(i));
+        WriteString(buf)
+    END;
+    ReadChar
+END CatalanNumbers.

Task/Catalan-numbers/OCaml/catalan-numbers.ocaml

@@ -1,12 +1,54 @@
-let catalan : int ref = ref 0 in
-Printf.printf "%d ," 1 ;
-for i = 2 to 9  do
-let nm : int ref = ref 1 in
-let den : int ref = ref 1 in
-for k = 2 to i do
-nm := (!nm)*(i+k);
-den := (!den)*k;
-catalan := (!nm)/(!den) ;
-done;
-print_int (!catalan); print_string "," ;
-done;;
+let imp_catalan n =
+  let return = ref 1 in
+  for i = 1 to n do
+    return := !return * 2 * (2 * i - 1) / (i + 1)
+  done;
+  !return
+
+let rec catalan = function
+  | 0 -> 1
+  | n -> catalan (n - 1) * 2 * (2 * n - 1) / (n + 1)
+
+let memoize f =
+  let cache = Hashtbl.create 20 in
+  fun n ->
+    match Hashtbl.find_opt cache n with
+    | None ->
+      let x = f n in
+      Hashtbl.replace cache n x;
+      x
+    | Some x -> x
+
+let catalan_cache = Hashtbl.create 20
+
+let rec memo_catalan n =
+  if n = 0 then 1 else
+    match Hashtbl.find_opt catalan_cache n with
+    | None ->
+      let x = memo_catalan (n - 1) * 2 * (2 * n - 1) / (n + 1) in
+      Hashtbl.replace catalan_cache n x;
+      x
+    | Some x -> x
+
+let () =
+  if not !Sys.interactive then
+    let bench label f n times =
+      let start = Unix.gettimeofday () in
+      begin
+        for i = 1 to times do f n done;
+        let stop = Unix.gettimeofday () in
+        Printf.printf "%s (%d runs) : %.3f\n"
+          label times (stop -. start)
+      end in
+    let show f g h f' n =
+      for i = 0 to n do
+        Printf.printf "%2d %7d %7d %7d %7d\n"
+          i (f i) (g i) (h i) (f' i)
+      done
+    in
+    List.iter (fun (l, f) -> bench l f 15 10_000_000)
+      ["imperative", imp_catalan;
+       "recursive", catalan;
+       "hand-memoized", memo_catalan;
+       "memoized", (memoize catalan)];
+    show imp_catalan catalan memo_catalan (memoize catalan) 15

Task/Catalan-numbers/Oforth/catalan-numbers.oforth

@@ -1 +1,2 @@
-: catalan(n) n ifZero: [ 1 ] else: [ catalan(n 1-) 2 n * 1- * 2 * n 1+ / ] ;
+: catalan( n -- m )
+    n ifZero: [ 1 ] else: [ catalan( n 1- ) 2 n * 1- * 2 * n 1+ / ] ;

Task/Catalan-numbers/Perl-6/catalan-numbers-2.pl6

@@ -1 +1,5 @@
 constant Catalan = 1, |[\*] (2, 6 ... *) Z/ 2 .. *;
+
+
+# In both cases, the sixteen first values can be seen with:
+.say for Catalan[^16];

Task/Catalan-numbers/R/catalan-numbers.r

@@ -1,4 +1,4 @@
 catalan <- function(n) choose(2*n, n)/(n + 1)
-catalan(1:15)
-# [1]       1       2       5      14      42     132     429    1430    4862
-#[10]   16796   58786  208012  742900 2674440 9694845
+catalan(0:15)
+ [1]       1       1       2       5      14      42     132     429    1430
+[10]    4862   16796   58786  208012  742900 2674440 9694845

Task/Catalan-numbers/Scala/catalan-numbers.scala

@@ -3,7 +3,7 @@ object Catalan {
   def catalan(n: BigInt) = factorial(2 * n) / (factorial(n + 1) * factorial(n))
 
   def main(args: Array[String]) {
-    for (n <- 1 to 15) {
+    for (n <- 0 to 15) {
       println("catalan(" + n + ") = " + catalan(n))
     }
   }

Task/Catalan-numbers/Stata/catalan-numbers.stata

@@ -0,0 +1,5 @@
+clear
+set obs 15
+gen catalan=1 in 1
+replace catalan=catalan[_n-1]*2*(2*_n-3)/_n in 2/l
+list, noobs noh