如何使用优先级队列实现堆栈？

Question

A priority queue is used to implement a stack that stores characters.

Push(C) is used to implement Insert(Q,C,K) where K is the appropriate key chosen by the implementation.

Pop is implemented as Delete_Min(Q) ,for a sequence of operations in what order must the keys be chosen , strictly decreasing or strictly increasing ?

Answer 1

Let me begin by saying that priority queue and stack are two completely different data structures with different uses and applications. One can not always be used to implement the other.

Yes, there are instances where a data structure can be defined in terms of another: for example you can create a stack or queue using a linked list (quite trivially actually), however implementing a stack using a priority queue will not always work. Why?

Because a stack is first in last out. The last thing you push on a stack WILL be the first thing to pop out. A stack's sole job is to keep the order of pushed items intact and pop in the reverse order.

A priority queue however, will always give you the minimum (or maximum based on implementation) with a pop. A priority queue will have to -by definition- restructure itself to always maintain the "heap property". This means the original order in which you pushed will not necessarily be preserved.

Now, your question should be phrased as "In what situation will a priority queue and a stack behave the same way?"

You mentioned your priority queue pop() will delete the minimum value from your queue which indicates you have a min-heap at hand. In this scenario the only case where a series of pops from priority queue will resemble those that of a stack, would be when the items were all pushed in non-increasing order. It does not have to be strictly decreasing. (think about pushing all of the same values).