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 Python 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.py 
in_stack = []
out_stack = []

def enqueue(value):
    in_stack.append(value)

def transfer():
    while in_stack:
        out_stack.append(in_stack.pop())

def dequeue():
    if not out_stack:
        transfer()
    return out_stack.pop()

for value in [10, 20, 30]:
    enqueue(value)
removed = [dequeue(), dequeue(), dequeue()]
print(" -> ".join(str(x) for x in removed))

Complexity

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

Implementation notes

  • Python uses two plain lists, in_stack and out_stack, as stacks. Enqueue is in_stack.append(value), and dequeue returns out_stack.pop() from the end; no deque is used in this lesson.
  • When out_stack is empty, transfer() mutates both lists in a while in_stack loop: in_stack.pop() removes the newest input value and out_stack.append(...) reverses the order for FIFO pops. Each value moves between stacks at most once before removal, giving the amortized behavior.
  • The stack lists and removed result list are the only persistent containers; normal Python GC owns them once no references remain. The trace shows [10, 20, 30] transfer to [30, 20, 10], then pop back out as [10, 20, 30].