Final answer:
An array-based implementation of a stack uses an array to store elements, with a 'top' index indicating the last item's position. Pushing adds an item at the incremented 'top' index, while popping removes the item at the current 'top'. Handling stack overflow and underflow is critical for avoiding errors.
Step-by-step explanation:
Array-Based Implementation of a Stack
The array-based implementation of a stack employs an array structure to simulate a stack's Last-In-First-Out (LIFO) behavior. An array with a fixed size is defined to hold the stack's elements. A stack typically has two fundamental operations - push (to add an item to the top of the stack) and pop (to remove the top item from the stack).
To implement a stack using an array, we maintain a pointer or an index, commonly called top, that represents the position at which the next element will be inserted or the last element resides. Initially, this top is set to -1, indicating that the stack is empty. When a new element is pushed onto the stack, the top is increased by one, and the element is placed at that index in the array. When an element is popped from the stack, the element at the current top index is returned and the top is decremented by one.
Crucially, stack overflow can occur if one tries to push an element when the array is already full. Conversely, stack underflow is a condition where one attempts to pop an element from an empty stack. These situations need to be handled within any stack implementation to prevent runtime errors.