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 Ruby 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.rb 
in_stack = []
out_stack = []
[10, 20, 30].each { |value| in_stack.push(value) }
out_stack.push(in_stack.pop) until in_stack.empty?
removed = []
removed << out_stack.pop until out_stack.empty?
puts removed.join(" -> ")

Complexity

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

Implementation notes

  • This checked Ruby source is straight-line code, not a queue class: in_stack and out_stack are both arrays used as stacks.
  • Enqueue uses in_stack.push(value) for 10, 20, and 30, leaving the input stack as [10, 20, 30].
  • Transfer uses out_stack.push(in_stack.pop) until in_stack.empty?; each pop removes and returns the last input value.
  • That transfer reverses the stack order, producing out_stack as [30, 20, 10] in the trace.
  • Dequeue order then comes from out_stack.pop, which removes 10, then 20, then 30.
  • Both transfer and removal loops are guarded with empty?, so this lesson does not rely on Ruby Array#pop returning nil from an empty array.
  • removed << out_stack.pop records the returned values as [10, 20, 30].
  • puts removed.join(" -> ") prints 10 -> 20 -> 30.