DP recurrence:
C(0) = 1
C(n) = sum_{j=0}^{n-1} C(j) * C(n-1-j)
let catalan n =
let dp = Array.make (n + 1) 0 in
dp.(0) <- 1;
for i = 1 to n do
for j = 0 to i - 1 do
dp.(i) <- dp.(i) + dp.(j) * dp.(i - 1 - j)
done
done;
dp.(n)
C(5) = 42 — also the count of distinct binary trees with 5 internal
nodes, balanced paren strings of length 10, monotonic lattice paths,
etc.
106 baseline programs total.
giles
d4eb57fa07