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POWhy is this OCaml code so slow?
 

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  1. POWhy is this OCaml code so slow?
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    <p>I am a OCaml newbie. I wrote a simple program in OCaml to generate the fair and square numbers ( a number that is a palindrome and the square of another palindrome, more details here: <a href="https://code.google.com/codejam/contest/2270488/dashboard#s=p2" rel="nofollow">https://code.google.com/codejam/contest/2270488/dashboard#s=p2</a> ) as follows:</p> <p>Update 1: Optimized algorithm (takes around 20 secs on my laptop):</p> <pre><code>open Printf;; let rec _is_palindrome s i j = i &gt;= j || (s.[i] = s.[j] &amp;&amp; _is_palindrome s (i + 1) (j - 1)) ;; let is_palindrome s = let sl = String.length s in sl &gt; 0 &amp;&amp; (_is_palindrome s 0 (sl - 1)) ;; let rec del_zeros s = let sl = String.length s in if (sl &lt; 1) then s else (if s.[0] = '0' then del_zeros (String.sub s 1 (sl - 1)) else s ) ;; let c2i c = Char.code c - Char.code '0' ;; let i2c i = Char.chr (i + Char.code '0') ;; (* only for finding fair and square numbers *) let square s = let slen = String.length s in if slen &lt; 1 then "" else let reslen = 2 * slen in let t = ref 0 in t := 0; (* fast check *) (let i = reslen/2 in for j = (slen - 1) downto 0 do if (i - 1 - j) &gt;= 0 &amp;&amp; (i - 1 - j) &lt; slen then t := !t + (c2i s.[j]) * (c2i s.[i - 1 - j]); done; if !t &gt; 9 then (* jump out *) raise (Invalid_argument "carry"); ); (let res = String.make reslen '0' in (* do the square cal now *) for i = (reslen - 1) downto 1 do t := 0; for j = (slen - 1) downto 0 do if (i - 1 - j) &gt;= 0 &amp;&amp; (i - 1 - j) &lt; slen then t := !t + (c2i s.[j]) * (c2i s.[i - 1 - j]); done; if !t &gt; 9 then (* jump out *) raise (Invalid_argument "carry"); res.[i] &lt;- i2c !t; done; del_zeros res ); ;; let rec check_fs fsns p = try let sq = square p in if (is_palindrome sq) then sq :: fsns else fsns with Invalid_argument "carry" -&gt; fsns ;; (* build the fair and square number list *) (* dfs *) let rec create_fair_square_nums fsns p sum max_num_digs = let l = String.length p in if l &gt; max_num_digs || sum &gt; 9 then fsns else let fsns = create_fair_square_nums fsns ("0" ^ p ^ "0") sum max_num_digs in let fsns = create_fair_square_nums fsns ("1" ^ p ^ "1") (sum + 1) max_num_digs in let fsns = create_fair_square_nums fsns ("2" ^ p ^ "2") (sum + 4) max_num_digs in let fsns = create_fair_square_nums fsns ("3" ^ p ^ "3") (sum + 9) max_num_digs in let fsns = check_fs fsns p in fsns ;; let rec print_fsns fsns = List.iter (fun s -&gt; printf "%s " s) fsns; printf "\n" ;; let num_str_cmp s1 s2 = let len1 = String.length s1 in let len2 = String.length s2 in match (len1 - len2) with | 0 -&gt; String.compare s1 s2 | cmp -&gt; cmp ;; (* works *) let max_dig = 51;; let fsns = let fsns = create_fair_square_nums [] "" 0 max_dig in let fsns = create_fair_square_nums fsns "0" 0 max_dig in let fsns = create_fair_square_nums fsns "1" 1 max_dig in let fsns = create_fair_square_nums fsns "2" 4 max_dig in create_fair_square_nums fsns "3" 9 max_dig ;; let fsns = List.sort num_str_cmp fsns;; print_fsns fsns;; </code></pre> <p>My original code (naive solution, too slow):</p> <pre><code>open Printf;; let rec _is_palindrome s i j = if i &lt; j then if s.[i] = s.[j] then _is_palindrome s (i + 1) (j - 1) else false else true ;; let is_palindrome s = if (String.length s &lt; 1) then false else _is_palindrome s 0 ((String.length s) - 1) ;; let rec del_zeros s = let sl = String.length s in if (sl &lt; 1) then s else (if s.[0] = '0' then del_zeros (String.sub s 1 (sl - 1)) else s ) ;; let c2i c = Char.code c - Char.code '0' ;; let i2c i = Char.chr (i + Char.code '0') ;; (* only positive number *) let square s = (* including the carry dig *) let slen = String.length s in let res = ( if slen &gt; 0 then let reslen = 2 * slen in let res = String.make reslen '0' in let t = ref 0 in for i = (reslen - 1) downto 1 do t := c2i (res.[i]); for j = (slen - 1) downto 0 do if (i - 1 - j) &gt;= 0 &amp;&amp; (i - 1 - j) &lt; slen then (t := !t + (c2i s.[j]) * (c2i s.[i - 1 - j]); (* printf "%d, %d: %d\n" j (i - 1 - j) !t; *) ) done; (* printf "%d: %d\n" i !t; *) if !t &gt; 9 then (res.[i - 1] &lt;- Char.chr (Char.code res.[i - 1] + (!t / 10)); t := !t mod 10 ); res.[i] &lt;- i2c !t; done; res; else "" ) in (* printf "square %s -&gt; %s\n" s res; *) del_zeros res ;; let extend_palindrome new_ps n = ("0" ^ n ^ "0") :: ("1" ^ n ^ "1") :: ("2" ^ n ^ "2") :: ("3" ^ n ^ "3") :: new_ps ;; let rec extend_palindromes new_ps ps = match ps with | [] -&gt; new_ps | h :: t -&gt; let new_ps = extend_palindrome new_ps h in extend_palindromes new_ps t ;; let rec check_fs fsns ps = match ps with | [] -&gt; fsns | h :: t -&gt; let sq = square h in if (is_palindrome sq) then check_fs (sq :: fsns) t else check_fs fsns t ;; (* build the fair and square number list *) let rec create_fair_square_nums fsns ps max_num_digs = match ps with | h :: t -&gt; if String.length h &gt; max_num_digs then fsns else let ps = extend_palindromes [] ps in let fsns = check_fs fsns ps in create_fair_square_nums fsns ps max_num_digs | [] -&gt; raise (Invalid_argument "fsn should not be []") ;; let rec print_fsns fsns = List.iter (fun s -&gt; printf "%s " s) fsns; printf "\n" ;; let num_str_cmp s1 s2 = let len1 = String.length s1 in let len2 = String.length s2 in match (len1 - len2) with | 0 -&gt; String.compare s1 s2 | cmp -&gt; cmp ;; (* works *) let max_dig = 50;; let fsns = let fsns0 = create_fair_square_nums [] [""] max_dig in let fsns1 = create_fair_square_nums [] ["0"; "1"; "2"; "3"] max_dig in (* print_fsns fsns0; print_fsns fsns1; *) ["0"; "1"; "4"; "9"] @ fsns0 @ fsns1 ;; (* print_fsns fsns;; *) let fsns = List.sort num_str_cmp fsns;; print_fsns fsns;; </code></pre> <p>This code generates the fair and square numbers which is within 10^100.</p> <p>This code should have some (or many) problems regarding the performance. It run for more than 30 mins before I killed it. When max_dig = 14 it finishes quickly (&lt; 1min).</p> <p>Any suggestion on improving this code or criticism to it are both welcome.</p>
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      1. POWhy is this OCaml code so slow?
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    1. COThis isn't an OCaml question. Your algorithm is just too slow for the large2 input. I suggest you read the [contest analysis](http://code.google.com/codejam/contest/2270488/dashboard#s=a&a=2) from Google.
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      1. POWhy is this OCaml code so slow?
      1. UScygin
    2. COThanks @cygin . Yes, the algorithm has problem. The optimized one works great (< 20 secs) now.
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