Which Data Structure Can Help to Check That Expression Has Balanced Parentheses or Not?
When dealing with expressions that involve parentheses, it is often necessary to check whether the parentheses are balanced or not. A balanced expression means that every opening parenthesis has a corresponding closing parenthesis, and they are properly nested within each other.
In computer science and programming, there are several data structures that can be used to efficiently solve this problem. Let’s explore three commonly used data structures:
1. Stack
A stack is a linear data structure that follows the Last-In-First-Out (LIFO) principle. It can be visualized as a stack of plates where the last plate added is the first one to be removed.
To check whether an expression has balanced parentheses using a stack, we iterate through each character in the expression. If we encounter an opening parenthesis, we push it onto the stack.
If we encounter a closing parenthesis, we check if the stack is empty or if the top element of the stack is its corresponding opening parenthesis. If either of these conditions is not met, then the expression doesn’t have balanced parentheses.
This approach works because the last opening parenthesis encountered must have its corresponding closing parenthesis after it. The stack helps us keep track of unmatched parentheses.
2. Queue
A queue is another linear data structure that follows the First-In-First-Out (FIFO) principle. It can be visualized as a queue of people waiting in line, where the person who arrives first gets served first.
To check whether an expression has balanced parentheses using a queue, we iterate through each character in the expression just like with a stack. However, instead of pushing opening parentheses onto a stack, we enqueue them into a queue.
When encountering a closing parenthesis, we check if the front element of the queue is its corresponding opening parenthesis. If it is, we dequeue the opening parenthesis from the queue; otherwise, the expression is not balanced.
Using a queue for this problem may not be as efficient as using a stack, but it can still provide a solution. It ensures that each closing parenthesis matches the first unmatched opening parenthesis encountered.
3. Counters
An alternative approach to using data structures like stacks or queues is to use counters. We can maintain separate counters for opening and closing parentheses while iterating through the expression.
When encountering an opening parenthesis, we increment the opening counter. When encountering a closing parenthesis, we decrement the opening counter if it is greater than zero; otherwise, we increment the closing counter. If at any point during iteration, the closing counter becomes greater than the opening counter, then the expression doesn’t have balanced parentheses.
This approach eliminates the need for extra data structures like stacks or queues but may not be as intuitive as using them.
Conclusion
In summary, when dealing with expressions that involve parentheses, we can use various data structures to check whether they are balanced or not. The stack data structure provides an efficient solution by keeping track of unmatched parentheses using a Last-In-First-Out (LIFO) approach.
The queue data structure offers an alternative solution by following a First-In-First-Out (FIFO) approach. Additionally, simple counters can also be used to solve this problem without relying on any specific data structure.
No matter which approach you choose, understanding and implementing these techniques will help you efficiently determine whether an expression has balanced parentheses or not in your programming projects.