## catalan numbers

in lua

### Source Code

``````-- Catalan Number series implementation
-- See: http://en.wikipedia.org/wiki/Catalan_number

-- Utility functions

-- Returns the factorial of a given number
local function fact(n)
return n == 0 and 1 or n*fact(n-1)
end

-- Memoizes a function
local function memoize(f)
local _cache = {}
return function (v)
local _result = _cache[v]
if not _result then _cache[v] = f(v) end
return _cache[v]
end
end

-- Calculates the n-th Catalan number using a direct formula
local function catalan_direct(n)
return fact(2*n)/(fact(n+1)*fact(n))
end

-- Calculates the n-th Catalan number using a memoized formula
local function catalan_recursive(n)
if n == 0 then return 1 end
return catalan_recursive(n-1)*(2*(2*n-1)/(n+1))
end

-- Calculates the n-th Catalan number using a memoized memoized function
local catalan_recursive_memoized = memoize(catalan_recursive)

return {
direct = catalan_direct,
recursive = catalan_recursive,
memoized = catalan_recursive_memoized
}``````
``````-- Tests for catalan.lua
local catalan = require 'catalan'

local total, pass = 0, 0

local function dec(str, len)
return #str < len
and str .. (('.'):rep(len-#str))
or str:sub(1,len)
end

local function run(message, f)
total = total + 1
local ok, err = pcall(f)
if ok then pass = pass + 1 end
local status = ok and 'PASSED' or 'FAILED'
print(('%02d. %68s: %s'):format(total, dec(message,68), status))
end

run('10 first Catalan Numbers using direct formula', function()
assert(catalan.direct(0)  == 1)
assert(catalan.direct(1)  == 1)
assert(catalan.direct(2)  == 2)
assert(catalan.direct(3)  == 5)
assert(catalan.direct(4)  == 14)
assert(catalan.direct(5)  == 42)
assert(catalan.direct(6)  == 132)
assert(catalan.direct(7)  == 429)
assert(catalan.direct(8)  == 1430)
assert(catalan.direct(9)  == 4862)
assert(catalan.direct(10) == 16796)
end)

run('10 first Catalan Numbers using recursive formula', function()
assert(catalan.recursive(0)  == 1)
assert(catalan.recursive(1)  == 1)
assert(catalan.recursive(2)  == 2)
assert(catalan.recursive(3)  == 5)
assert(catalan.recursive(4)  == 14)
assert(catalan.recursive(5)  == 42)
assert(catalan.recursive(6)  == 132)
assert(catalan.recursive(7)  == 429)
assert(catalan.recursive(8)  == 1430)
assert(catalan.recursive(9)  == 4862)
assert(catalan.recursive(10) == 16796)
end)

run('10 first Catalan Numbers using recursive formula', function()
assert(catalan.memoized(0)  == 1)
assert(catalan.memoized(1)  == 1)
assert(catalan.memoized(2)  == 2)
assert(catalan.memoized(3)  == 5)
assert(catalan.memoized(4)  == 14)
assert(catalan.memoized(5)  == 42)
assert(catalan.memoized(6)  == 132)
assert(catalan.memoized(7)  == 429)
assert(catalan.memoized(8)  == 1430)
assert(catalan.memoized(9)  == 4862)
assert(catalan.memoized(10) == 16796)
end)

print(('-'):rep(80))
print(('Total : %02d: Pass: %02d - Failed : %02d - Success: %.2f %%')
:format(total, pass, total-pass, (pass*100/total)))
``````