Balanced Brackets: Understanding and Implementing the Concept
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Chapter 1: Introduction to Balanced Brackets
In programming, a bracket is defined as one of the following characters: (, ), {, }, [, or ]. A pair of brackets is deemed matched when an opening bracket (such as (, [, or {) appears before its corresponding closing bracket (like ), ], or }). The three categories of matched brackets include: [], {}, and ().
An essential aspect of brackets is that a matching pair is not considered balanced if the brackets contained within are not paired correctly. For instance, the sequence {[(])} fails to be balanced, as the contents between the outer brackets { and } do not match: the square brackets contain an unpaired opening bracket, (, and the parentheses enclose an unpaired closing square bracket, ].
A sequence of brackets is regarded as balanced if it fulfills these criteria:
- There are no unmatched brackets.
- The subset of brackets contained within a matched pair also forms a matched set.
Given strings of brackets, the goal is to assess whether each sequence is balanced. If a string is balanced, the output should be "YES"; otherwise, it should be "NO".
Hints:
- No additional hints.
Example:
- The string {[()]} satisfies both conditions for being balanced.
- The string {[(])} is unbalanced due to the mismatched brackets within the outer pair: [(]).
- The string {{[[(())]]}} is balanced as it meets both criteria.
Chapter 1.1: The Stack Data Structure
To evaluate whether a string of brackets is balanced, we can utilize a stack data structure. When encountering a left bracket, we push it onto the stack. For a right bracket, we attempt to match it with the top element of the stack. If they correspond, we pop the stack. Ultimately, if the stack is empty after processing the entire string, the brackets are balanced.
Subsection 1.1.1: Visualizing the Stack Process
Section 1.2: Implementation Details
To implement this logic in code:
- If the input consists solely of a single bracket, it cannot be balanced.
- Use a for loop to iterate through the input string. When encountering a right bracket, check if its matching left counterpart is at the top of the stack. If it matches, pop the item; if not, return "NO".
- For a left bracket, simply push it onto the stack.
- Finally, check if the stack is empty. If it is, return "YES"; otherwise, return "NO".
To optimize performance and prevent time limit exceedance, we can terminate the loop if the stack size exceeds half of the input string's length.
Chapter 2: Conclusion
In summary, understanding the principles of balanced brackets and employing a stack-based approach can significantly enhance your programming skills.