Valid Parenthesis | Leet Code | CFAM |
Here is the solution for leetcode problem 20 Valid Parenthesis.
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The given Python code is a concise and efficient implementation of a function that checks the validity of a string containing only three types of brackets: '(', ')', '[', ']', '{', and '}'. The algorithm employs a stack data structure, a fundamental concept in computer science, to ensure that the brackets are properly nested. In this detailed explanation, we will explore the code's structure, purpose, and the underlying principles that make it effective.
Purpose and Context:
The primary purpose of the code is to determine whether a given string has balanced brackets. A string is considered valid if every opening bracket has a corresponding closing bracket and they are properly nested. For example, '()' is a valid string, while '(]' is not. The algorithm uses a stack to keep track of opening brackets and ensures that closing brackets match the most recent opening bracket encountered.
Understanding the Code:
Initialization:
In the initialization section, a list named opening is created to store the opening symbols of the three types of brackets. This list is essential for quickly identifying whether a character in the string is an opening bracket. Another list, stk, is initialized as an empty list. This list will act as a stack, a data structure that follows the Last In, First Out (LIFO) principle.
Iterating Through the String:
The code uses a for loop to iterate through each character (bracket) in the input string s. This iterative approach allows the algorithm to process each character individually and make decisions based on its type.
Checking Opening Brackets:
If the current character is found in the opening list, it means it is an opening bracket. In this case, the opening bracket is pushed onto the stack (stk). The stack will keep track of all opening brackets encountered in the string.
Checking Closing Brackets:
If the current character is not an opening bracket, it is assumed to be a closing bracket. The code then checks whether the stack is non-empty and whether the corresponding opening bracket at the top of the stack matches the current closing bracket. If there is a match, the opening bracket is popped from the stack. If there is no match, the function immediately returns False, indicating that the string is not valid.
Final Check and Return
After iterating through all characters in the string, the function checks whether the stack is empty. If it is, all opening brackets have been successfully matched with their corresponding closing brackets, and the string is considered valid. If the stack is not empty, there are unmatched brackets, and the function returns False.
Stack Implementation:
The stack is a crucial component of this algorithm. A stack is a data structure that follows the Last In, First Out (LIFO) principle, meaning that the last element added is the first one to be removed. In this case, the stack is used to keep track of opening brackets encountered in the string. When a closing bracket is encountered, the algorithm checks the stack to ensure that there is a matching opening bracket at the top of the stack.
The use of a stack is particularly appropriate for this problem because it allows for efficient tracking of opening brackets' positions. The algorithm can easily determine the most recent opening bracket encountered, which is crucial for validating the correctness of the bracket pairs.
Time Complexity:
The time complexity of the algorithm is O(n), where n is the length of the input string. This linear time complexity is achieved because each character in the string is processed once, and the operations within the loop take constant time. The algorithm's efficiency is notable, especially for large strings.
Space Complexity:
The space complexity is also O(n), where n is the length of the input string. In the worst-case scenario, the stack could contain all opening brackets from the string. The space complexity is directly proportional to the length of the input string.
Benefits of Using a Stack:
The decision to use a stack in this algorithm is based on the nature of the problem. Stacks are well-suited for managing nested structures, and the bracket validation problem inherently involves the concept of proper nesting. The stack allows the algorithm to keep track of the most recent opening bracket encountered and efficiently check for matching closing brackets.
Conclusion:
In conclusion, the provided Python code efficiently solves the problem of validating strings with brackets using a stack data structure. The algorithm's design, implementation, and use of fundamental programming concepts contribute to its effectiveness.
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