local function min(a, b, c)
  local min_val = a

  if b < min_val then min_val = b end
  if c < min_val then min_val = c end

  return min_val

end

----------------------------------
--- Levenshtein distance function.
-- @tparam string s1
-- @tparam string s2
-- @treturn number the levenshtein distance
-- @within Metrics
return function(s1, s2)
  if s1 == s2 then return 0 end
  if s1:len() == 0 then return s2:len() end
  if s2:len() == 0 then return s1:len() end
  if s1:len() < s2:len() then s1, s2 = s2, s1 end

  local t = {}
  for i=1, #s1+1 do
    t[i] = {i-1}
  end

  for i=1, #s2+1 do
    t[1][i] = i-1
  end

  local cost
  for i=2, #s1+1 do

    for j=2, #s2+1 do
      cost = (s1:sub(i-1,i-1) == s2:sub(j-1,j-1) and 0) or 1
      t[i][j] = min(
      t[i-1][j] + 1,
      t[i][j-1] + 1,
      t[i-1][j-1] + cost)
    end

  end

  return t[#s1+1][#s2+1]

end