Stacks and Queues

Queue from Two Stacks

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

Algorithm

Basic Implementation

basic.cs 
using System;
using System.Collections.Generic;
using System.Linq;

class Program {
    static string Render(List<int> values) => string.Join(" -> ", values);
    static void Main() {
        var inStack = new Stack<int>();
        var outStack = new Stack<int>();
        foreach (var value in new[] {10, 20, 30}) inStack.Push(value);
        while (inStack.Count > 0) outStack.Push(inStack.Pop());
        var removed = new List<int>();
        while (outStack.Count > 0) removed.Add(outStack.Pop());
        Console.WriteLine(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

  • Stack<int> is the BCL LIFO container; both stacks use managed backing storage that grows as needed and is reclaimed by GC. Pop() would throw on an empty stack, so each transfer/removal loop is guarded by Count > 0.
  • Moving every item from inStack to outStack reverses order once, making the batched transfer explicit before values are collected into a List<int> only for deterministic rendering.
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.