For a given string, find the longest palindrome that is a sub-string of the original string (ignoring whitespace)

sub_palindrome.lua

#!/usr/bin/env luajit

local string = string
local socket = require 'socket'

--- Returns the character at index i (just some syntactic sugar for str:gsub(i,i))
-- @usage ('foobar'):c(3) == 'o' -- True
-- @string i Index of character within string
-- @returns Character at index i within string
function string:c(i)
  return self:sub(i,i)
end

--- Extend string type (test if string is palindrome)
function string:is_palindrome()
  return string.reverse(self) == self
end

--- Expands a string to build the largest possible palindrome with its middle 
-- character(s) at index i
-- @number i Index within string to start outward palindrome-test expansion from
-- @returns Longest palindrome expandable from position i within the string
function string:expand_palindrome(i)
  assert(i>0 and i<self:len(), 'Argument out of bounds')

  local a = i-1
  local z = i+1
  local n = #self

  -- Handle even length possibilities
  if self:c(a) ~= self:c(z) then
    if self:c(a) == self:c(i) then
      a = a-1
    elseif self:c(i) == self:c(z) then
      z = z+1
    else
      return self:c(i) -- Short circuit
    end
  end

  -- Expand outward from middle of string
  while a > 0 and z < n do
    if self:c(a) ~= self:c(z) then break end

    a = a-1
    z = z+1
  end

  return self:sub(a+1,z-1)
end

--- Finds the longest palindrome that is a substring of the given string 
-- (ignoring anything that is not a letter)
-- @string self Given string to search
-- @treturn string The longest palindrome within the string
function string:longest_sub_palindrome()
  local str = self:gsub('[^%a]', ''):lower()
  local ptr = 1
  local max = #str
  local longest = ''

  -- Quick check if string is a palindrome, itself
  if str:is_palindrome() then
    return str
  end

  -- Search for sub-palindromes by expanding left and right from a given character
  while ptr < max do
    local pal = str:expand_palindrome(ptr)

    if pal:len() > longest:len() then
      longest = pal
    end

    -- Stop searching if there arent enough chars left to make a longer palindrome than the current longest
    if longest:len() / 2 > max - ptr then
      break
    end
    
    ptr = ptr + 1
  end

  return longest
end

local tests = {
  "Here's a test that should return 'racecar' if everything goes right.",
  "Have you ever heard the saying, 'A man, a plan, a canal: Panama,' while driving a too-hot-to-hoot racecar?",
  "Degas, are we not drawn onward, we freer few, drawn onward to new eras aged?",
  "abcdefgh ijklmnopqrs tuv w x y z",
  "No 'x' in 'Nixon.'"
}

for _,str in ipairs(tests) do
  local tstart  = socket.gettime()
  local longest = str:longest_sub_palindrome()
  local tend    = socket.gettime()
  local time    = ('%.3f ms'):format((tend-tstart)*1000)

  print(time .. ' - ' .. longest)
end

--[[ Example output:
0.260 ms - racecar
0.284 ms - amanaplanacanalpanama
0.019 ms - degasarewenotdrawnonwardwefreerfewdrawnonwardtonewerasaged
0.010 ms - a
0.006 ms - noxinnixon
]]