Question

Suppose an initially empty stack \(S\) has performed a total of 25 push operations, 12 top operations, and 10 pop operations, 3 of which generated a StackEmpty exception that was caught and ignored. What is the current size of \(S ?\)

Short answer

The current size of the stack is 18.

Step-by-step solution

Understanding the Operations

The stack initially starts empty. A push operation adds an element to the stack, a pop operation removes the top element, and a top operation does not change the stack size but allows inspection of the top element. There were 3 pop operations that generated a StackEmpty exception, which means the stack was empty during those attempts.

Count the Net Push Operations

There were a total of 25 push operations. Since each push adds an element to the stack, the current count of elements added to the stack would be 25.

Count the Successful Pop Operations

There were 10 pop operations, but 3 of them failed due to an empty stack, leaving 7 successful pop operations. Since each successful pop removes one element from the stack, subtract 7 from the count of elements added.

Calculate the Final Size of the Stack

Subtracting the number of successful pop operations (7) from the total number of push operations (25), we get: \(25 - 7 = 18\). Therefore, the stack currently contains 18 elements.

Key concepts

push operation

The push operation is fundamental in the stack data structure. When you 'push' an element, it adds that element to the top of the stack. This operation increases the stack's size by one. For example, if you push 25 elements onto an initially empty stack, the stack now contains 25 elements. There’s no limitation other than the stack’s maximum size, which may be set by the surrounding environment or program.

pop operation

A pop operation is used to remove the element at the top of the stack. This decreases the stack’s size by one. However, if you try to pop an element from an empty stack, a StackEmpty exception is raised. For instance, in the given problem, out of 10 pop attempts, 3 encountered this exception, leaving only 7 successful pops. These 7 successful pops are what actually change the stack's size.

StackEmpty exception

A StackEmpty exception occurs when a pop operation is attempted on an empty stack. This is crucial to understand because it prevents illegal operations and ensures the program handles empty stack scenarios gracefully. In our example, there were 3 such exceptions out of 10 pop operations, indicating that 3 attempts were made to pop elements from an already empty stack. These exceptions were caught and ignored, meaning the stack size remained unchanged during these operations.

stack size calculation

To calculate the current size of the stack, you need to account for each push and successful pop operation. Start with the total number of push operations, then subtract the number of successful pop operations. As explained, if you start with 25 pushes and successfully pop 7 times, the stack size would be calculated as follows: \[\text{Current Size} = \text{Pushes} - \text{Successful Pops} = 25 - 7 = 18\]

stack data structure

A stack is a linear data structure that follows a Last In, First Out (LIFO) principle. This means the last element added (pushed) to the stack will be the first one removed (popped). The stack supports mainly three operations:

• Push: Add an element to the top.
• Pop: Remove the top element.
• Top/Peek: Inspect the top element without removing it.

Stacks are widely used in various applications, including function calls in programming languages, expression evaluation, and syntax parsing.