Solving the Square Bracket Problem on SPOJ: A Comprehensive Guide

The problem presented on SPOJ involves determining the balance of square brackets in a given string. Understanding and implementing an efficient solution that meets the problem's requirements is crucial for competitive programmers. This article provides a detailed explanation of the approach, code implementation, and complexity analysis.

Problem Breakdown

The problem statement typically involves a string that consists exclusively of square brackets, both opening [ and closing ]. The objective is to determine if the given string of brackets is balanced. A string of square brackets is considered balanced if every opening bracket is correctly matched with a closing bracket in the correct order.

Approach

To solve this problem, a stack data structure can be effectively utilized. The idea is to simulate a stack using a Python list, where each opening bracket is pushed onto the stack, and each closing bracket is popped from the stack. This process ensures that the brackets are nested correctly, and the stack remains empty when the string is processed completely.

Step-by-Step Solution

Initialize a Stack: Use a list to simulate the stack. Iterate Through Each Character: For each character in the string: Push the opening bracket [ onto the stack. Pop the top of the stack when a closing bracket ] is encountered, provided the stack is not empty. If the stack is empty when a closing bracket is found, return that the sequence is unbalanced. Final Check: After processing all characters, if the stack is empty, the brackets are balanced. Otherwise, they are unbalanced.

Python Code Example

def is_balanced_sequence(sequence):
    stack  []
    for char in sequence:
        if char  '[':
            (char)
        elif char  ']':
            if stack:
                stack.pop()
            else:
                return False
    return len(stack)  0

Additionally, the input is read as follows:

import sys
n  int(input())
for _ in range(n):
    sequence  input().strip()
    print(is_balanced_sequence(sequence))

Explanation of the Code

Function: The function is_balanced_sequence(sequence) takes a string of square brackets as input and returns True if the sequence is balanced, or False otherwise. Stack Operations: (char) adds an opening bracket to the stack. stack.pop() removes the last added opening bracket when a closing bracket is encountered. Final Check: If the stack is empty after processing the entire string, it returns True, indicating a balanced sequence. Otherwise, it returns False, signifying an unbalanced sequence.

Complexity Analysis

Time Complexity: The time complexity of the solution is O(n), where n is the length of the string. Each character is processed exactly once. Space Complexity: The space complexity is O(n) in the worst case, which occurs when all characters are opening brackets, and the stack must store all of them.

This method efficiently checks the balance of square brackets and should perform well within the constraints typically set by competitive programming platforms like SPOJ.