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 Swift 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.swift 
func render(_ values: [Int]) -> String {
    values.map(String.init).joined(separator: " -> ")
}

var inStack: [Int] = []
var outStack: [Int] = []
for value in [10, 20, 30] { inStack.append(value) }
while !inStack.isEmpty { outStack.append(inStack.removeLast()) }
var removed: [Int] = []
while !outStack.isEmpty { removed.append(outStack.removeLast()) }
print(render(removed))

Complexity

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

Implementation notes

  • var inStack: [Int] = [] and var outStack: [Int] = [] are mutable Swift arrays used as stack storage; the back of each array is the stack top.
  • Enqueue is the loop for value in [10, 20, 30] { inStack.append(value) }, which appends each Int to the input stack.
  • The transfer loop while !inStack.isEmpty guards removeLast(), so the source has no optional return or sentinel path while moving values into outStack.
  • outStack.append(inStack.removeLast()) reverses the input stack, changing [10, 20, 30] into output stack state [30, 20, 10].
  • var removed: [Int] = [] then collects dequeues with removed.append(outStack.removeLast()) while outStack is non-empty.
  • The trace records empty stacks, inStack = [10, 20, 30], transfer to inStack = [] and outStack = [30, 20, 10], then removed = [10, 20, 30] with outStack = [].
  • render(_:) maps each Int to String and joins with " -> ", so print(render(removed)) outputs 10 -> 20 -> 30.