Stacks and Queues

Queue from Two Stacks

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

Algorithm

Basic Implementation

basic.js 
function render(values) {
    return values.join(" -> ");
}
const inStack = [];
const outStack = [];
for (const value of [10, 20, 30]) {
    inStack.push(value);
}
while (inStack.length > 0) {
    outStack.push(inStack.pop());
}
const removed = [];
while (outStack.length > 0) {
    removed.push(outStack.pop());
}
console.log(render(removed));

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

Complexity

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

Implementation notes

  • JavaScript represents both stacks with mutable Array objects holding Number values. Enqueue appends to inStack with push, so the input stack becomes [10, 20, 30] without replacing the array.
  • Transfer uses inStack.pop() and outStack.push(...) until the input stack is empty. Each value moves once from input to output, giving the usual amortized queue cost even though this replay performs the transfer in one batch.
  • The transfer reverses stack order: the replay moves from inStack = [10, 20, 30], outStack = [] to inStack = [], outStack = [30, 20, 10]. Popping outStack then removes 10, 20, and 30 in FIFO order into removed = [10, 20, 30].
  • render(removed) uses values.join(" -> "), so console.log prints 10 -> 20 -> 30. Allocation is limited to the short input literal, inStack, outStack, removed, and the joined output string, all managed by the JavaScript runtime GC.
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.