Fast implementation of queues in Lua?

Question

I am making a game using Lua and I need to use Breadth-first search to implement a fast path-finding algorithm which finds the shortest path between the enemy AI and the player.

I will have up to 3 enemies using this algorithm at once and map is a 2-dimensional tile-based maze. I have already implemented collision detection so now all that is left to do is get a way for the enemies to find the shortest path to the player in a way that can be done quickly and and preferably about 80-90 times per second per enemy.

When I previously implemented breadth-first search, I used a queue in C++. From what I have read about Lua, stack implementations using tables are very efficient since the elements don't need to be shifted after push() (AKA table.insert) and pop() (table.remove) operations. However, I have theorized that queues with large sizes can be very inefficient in Lua, because if you want to insert/remove something from index 1 of a table, all other elements in the table must be shifted either upward or downward in the table.

Thus, I would like to ask some simple questions for those experienced in Lua. What is the simplest and/or fastest implementation of a queue in this language? Is it even possible to have a fast queue in Lua or is it just generally accepted that Lua will always be forced to "shift" all elements for a queue operation such as pop() or append()?

EDIT: I understand that the underlying implementation of "shifting elements" in Lua tables is written in C and is therefore quite optimized. I just would like to know if I have any better options for queues before I begin to write a simple table implementation.

Answer 1

A fast implementation of queue(actually double queue) in Lua is done by the book Programming in Lua:

List = {}
function List.new ()
  return {first = 0, last = -1}
end

It can insert or remove an element at both ends in constant time, the key is to store both first and last.

function List.pushleft (list, value)
  local first = list.first - 1
  list.first = first
  list[first] = value
end

function List.pushright (list, value)
  local last = list.last + 1
  list.last = last
  list[last] = value
end

function List.popleft (list)
  local first = list.first
  if first > list.last then error("list is empty") end
  local value = list[first]
  list[first] = nil        -- to allow garbage collection
  list.first = first + 1
  return value
end

function List.popright (list)
  local last = list.last
  if list.first > last then error("list is empty") end
  local value = list[last]
  list[last] = nil         -- to allow garbage collection
  list.last = last - 1
  return value
end