Stacks and Queues

Stack Push/Pop

Push values onto a stack and pop them back in last-in, first-out order.

Algorithm

Basic Implementation

basic.py 
stack = []
for value in [10, 20, 30]:
    stack.append(value)
popped = []
while stack:
    popped.append(stack.pop())
print(" -> ".join(str(x) for x in popped))

The same three values from the trace are shown as stack states. The top cell is the next value a pop removes.

Step 1 - Start empty

There is no top value yet.

Empty stack before any push.top of stack(empty)

Step 2 - Push 10, then 20, then 30

Each push places the new value above the previous top.

After push 10, push 20, push 30: 30 is on top.top -> bottom302010

Step 3 - Pop removes 30 first

The top cell leaves first, so the remaining stack starts with 20.

After one pop: popped is 30; 20 is now on top.top -> bottompopped203010

Complexity

  • Time: O(1) per push/pop
  • Space: O(n)

Implementation notes

  • Python uses a plain list as the stack, with the right end as the top. stack.append(value) mutates that list in place to push, and stack.pop() removes and returns the most recently pushed value.
  • popped.append(stack.pop()) transfers the returned int reference into a separate output list while shrinking the stack. Both end operations are O(1) amortized for Python lists.
  • The persistent containers are just stack and popped; normal Python reference management owns their lifetime once no references remain. The trace shows [10, 20, 30] popping as 30, then 20, then 10.
top The top is the most recently pushed value.
LIFO A stack removes values in last-in, first-out order.