Merge pull request #4287 from drbaggy/master

Update README.md

3 files changed, 29 insertions, 3 deletions

diff --git a/challenge-117/james-smith/README.md b/challenge-117/james-smith/README.md
index aa4a62c493..e17e38bcbc 100644
--- a/challenge-117/james-smith/README.md
+++ b/challenge-117/james-smith/README.md
@@ -53,7 +53,12 @@ sub triangle {
 }
 ```
 
-### Now the counts... Schroder numbers
+Note we don't "collect" routes in a datastructure and then print them all at the end, but instead render directly from within the
+function. For `$N` larger than `10` the memory requirements for storing this information increases significantly, so this code is limited purely by disk rather than memory.
+
+### Now the counts... Schröder numbers
+
+*It's amazing what you find out about when you google the answers you get!*
 
 Due to the "memory" storage issues we can change the problem to one of counting rather than listing...
 The first approach is to just convert the `triangle` method above to count - we introduce a cache
@@ -72,8 +77,14 @@ sub schroder_cache_array {
 }
 ```
 
-But as we've said before recursion is a curse - so to remove the function
-overhead of recursion we can re-write this like this:
+But as we've said before recursion is a curse - but we notice that
+```
+  T0,m = 1                          
+  Tn,0 = Tn-1,0 + Tn-1,1
+  Tn,m = Tn-1,m + Tn-1,m+1 + Tn,m-1
+```
+We can use that to define each row of a triangle with `Sn` as the last
+value.
 
 ```perl
 sub schroder_non_recursive {
@@ -88,6 +99,13 @@ sub schroder_non_recursive {
 }
 ```
 
+We again use the row "flip" as we only need one row and the previous
+one to get values...
+
+Googling for `2, 6, 22, 90, 394` came up with https://en.wikipedia.org/wiki/Schröder_number, a page
+about Schröder numbers - which gives up the following faster (about twice as fast as above) solution -
+as Scrhoder numbers can be written as a recurrence relation:
+
 ```perl
 sub schroder_recurrence_rel {
   my( $size, @S ) = ( shift, 1, 2 );
diff --git a/challenge-117/james-smith/blog.txt b/challenge-117/james-smith/blog.txt
new file mode 100644
index 0000000000..8d12b20b58
--- /dev/null
+++ b/challenge-117/james-smith/blog.txt
@@ -0,0 +1 @@
+https://github.com/drbaggy/perlweeklychallenge-club/blob/master/challenge-117/james-smith/
diff --git a/challenge-117/james-smith/perl/ch-2.pl b/challenge-117/james-smith/perl/ch-2.pl
index 854c9244b2..248d8d2dfe 100644
--- a/challenge-117/james-smith/perl/ch-2.pl
+++ b/challenge-117/james-smith/perl/ch-2.pl
@@ -142,3 +142,10 @@ sub schroder_recurrence_rel {
   }
   return $S[ $size ];
 }
+
+##
+# 1, 2, 6, 22, 90, 394,
+# 1806, 8558, 41586, 206098, 1037718,
+# 5293446, 27297738, 142078746, 745387038, 3937603038,
+# 20927156706, 111818026018, 600318853926, 3236724317174, 17518619320890,
+# 95149655201962, 518431875418926, 2832923350929742, 15521467648875090