Stacks and Queues

Queue from Two Stacks

Implement queue behavior with an input stack and an output stack.

Algorithm

The replay uses the same three values in every language, so this Lua DSA implementation can be compared directly with the rest of the DSA track.

input stack Enqueue pushes new values onto the input stack.
output stack When the output stack is empty, transferring all input values reverses them into dequeue order.

Visual walkthrough

The two-stack queue keeps cheap enqueues in the input stack, then reverses that stack only when dequeue needs the output stack.

Step 1 - Enqueue pushes onto the input stack

After enqueueing 10, 20, 30, the newest input value is on top of the input stack.

After enqueues: input top is 30; output is empty.input stack top -> bottomoutput stack top -> bottomremoved30(empty)(empty)2010

Step 2 - Transfer reverses into output order

Moving every input value to the output stack turns 10 into the next pop.

After transfer: output top is 10, so dequeue returns the oldest value.input stackoutput stack top -> bottomremoved(empty)10(empty)2030

Step 3 - Dequeue pops from output

The output stack pops 10 first while 20 becomes the next front.

After one dequeue: removed is 10; output top is now 20.input stackoutput stack top -> bottomremoved(empty)201030

Basic Implementation

basic.lua 
local function render(values)
    local parts = {}
    for i, value in ipairs(values) do parts[i] = tostring(value) end
    return table.concat(parts, " -> ")
end

local in_stack = {}
local out_stack = {}
for _, value in ipairs({10, 20, 30}) do table.insert(in_stack, value) end
while #in_stack > 0 do table.insert(out_stack, table.remove(in_stack)) end
local removed = {}
while #out_stack > 0 do table.insert(removed, table.remove(out_stack)) end
print(render(removed))

Complexity

  • Time: O(1) amortized per operation
  • Space: O(n)

Implementation notes

  • local in_stack = {} and local out_stack = {} start as two empty Lua tables, matching the trace state [] and [].
  • Enqueue iterates ipairs({10, 20, 30}) and uses table.insert(in_stack, value), so the input stack becomes [10, 20, 30].
  • In this source, the stack top is the end of the table.
  • The transfer loop runs while #in_stack > 0 and moves values with table.insert(out_stack, table.remove(in_stack)).
  • Bare table.remove(in_stack) pops the last value, so the transfer reverses the order into out_stack = [30, 20, 10] and leaves in_stack = [].
  • Dequeue then pops from the output stack with table.insert(removed, table.remove(out_stack)).
  • Popping the end of [30, 20, 10] returns 10 first, then 20, then 30.
  • The trace ends with removed = [10, 20, 30] and out_stack = [].
  • render(removed) uses ipairs and table.concat(parts, " -> "), so print(render(removed)) outputs 10 -> 20 -> 30.