Two Queues Make A Stack

November 5, 2013

In the previous exercise we implemented queues. Today’s exercise will use those queues to solve exercise 10.1-7 from CLRS:

Show how to implement a stack using two queues. Analyze the running time of the stack operations.

You may assume that the queue operations enqueue, dequeue, and isEmpty are provided. You should provide the stack operations push, pop and isEmpty.

Your task is to implement stacks using two queues, as directed above. When you are finished, you are welcome to read a suggested solution, or to post your own solution or discuss the exercise in the comments below.


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8 Responses to “Two Queues Make A Stack”

  1. Jussi Piitulainen said

    This uses the queues from that previous exercise. In both implementations, the stack is represented as just one queue. The auxiliary queue is made when needed.

    (define (make-stack) (make-queue))

    (define (push1 s x) (enqueue s x))

    (define (top1 s)
      (do ((q s (tail q)))
          ((empty? (tail q)) (head q))))

    (define (pop1 s)
      (do ((p (make-queue) (enqueue p (head q)))
           (q s (tail q)))
          ((empty? (tail q)) p)))

    (define (push2 s x)
      (do ((p (enqueue (make-queue) x)
              (enqueue p (head q)))
           (q s (tail q)))
          ((empty? q) p)))

    (define (top2 s) (head s))

    (define (pop2 s) (tail s))

    This test procedure takes the implemented operations as arguments.

    (define (test make push top pop) ;expect (o x o x)
      (list (top (push (make) 'o))
            (top (push (push (make) 'o) 'x))
            (top (pop (push (push (make) 'o) 'x)))
            (if (empty? (pop (push (make) 'o))) 'x 'o)))

    Best wishes.

  2. Robert Fisher said

    A C++ version using the standard library queues.

    #include <iostream>
    #include <queue>
    template<typename T>
    struct stack {
        std::queue<T> q1;
        std::queue<T> q2;
        void push(T t)
        T pop()
            T t;
            while (!q1.empty()) {
                t = q1.front();
                if (!q1.empty()) q2.push(t);
            while (!q2.empty()) {
                T x = q2.front();
            return t;
        bool empty()
            return q1.empty();
    int main()
        stack<int> s;
        std::cout << s.pop() << std::endl;
        std::cout << s.pop() << std::endl;
        std::cout << s.pop() << std::endl;
        std::cout << s.pop() << std::endl;
        std::cout << s.pop() << std::endl;
        std::cout << s.pop() << std::endl;
  3. Solution in SML, using the queues posted in the previous exercise.

    signature STACK = sig
        type 'a stack
        exception EmptyS
        val empty: 'a stack
        val push: 'a stack -> 'a -> 'a stack
        val pop: 'a stack -> 'a * 'a stack
    functor QStack(Q: QUEUE) :> STACK = struct
        type 'a stack = 'a Q.queue * 'a Q.queue
        exception EmptyS
        val empty = (Q.empty, Q.empty)
        fun push (xs, ys) x = (Q.enqueue xs x, ys)
        fun isEmpty (xs, ys) = Q.isEmpty xs andalso Q.isEmpty ys
        fun popAndSwap (xs, ys) =
                val (x, xs') = Q.dequeue xs
                if Q.isEmpty xs'
                then (x, (ys, xs'))
                else popAndSwap (xs', Q.enqueue ys x)
        fun pop (s as (xs, ys)) =
            if isEmpty s then raise EmptyS else popAndSwap s

    Best wishes to you and your family.

  4. bob said

    (define (gcd m n)
    (cond ((< m n) (gcd m (- n m)))
    ((< n m) (gcd (- m n) n))
    (else m)))

  5. bob said

    (define (gcd m n)
    (cond ((< m n) (gcd m (- n m)))
    ((< n m) (gcd (- m n) n))
    (else m)))

  6. Lal said

    Let the two given queues be named as queue1 and queue2. The algorithm to implement a stack by using two queues works as :

    Push : Enqueue elements to queue1.
    Pop : Dequeue all the elements except the last one from queue1 into queue2.
    Return the last element of queue1.
    Interchange the names of queue1 and queue2.

    For example and code

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