Opening and Closing Gates Validation| Algorithm to find whether people are safe or not

Opening and Closing Gates Validation| Algorithm to find whether people are safe or not

In a water reservation system, gates are used to control the flow of water, and ensuring that the gates are properly opened and closed is crucial for the safety of the city. If there are any opening gates that don’t have corresponding closing gates, the water will leak out, posing a danger to the residents.In this problem, we are tasked with ensuring that for every opening gate, there is a matching closing gate in the correct order, similar to the balanced parentheses problem. If the system’s gates are correctly paired, we return the number of valid gate pairs. If there is an imbalance in the gates, we return -1 to indicate a failure.

Problem Overview

Given a sequence of opening ( and closing ) gates, we need to:
  1. Verify that each opening gate has a corresponding closing gate.
  2. Ensure that the closing gates do not appear without a preceding opening gate.
  3. Count the number of valid opening-closing pairs if the gates are balanced, or return -1 if the gates are imbalanced.

Approach to Solve the Problem

This problem is similar to the “balanced parentheses” problem. We can use a stack to track the opening gates. For each closing gate, we check if there is a corresponding opening gate to match it. If at the end of the traversal, all gates are matched, we count the valid pairs; otherwise, we return -1.

Algorithm Steps

  1. Initialize a stack: The stack will store the indices of opening gates.
  2. Traverse the string: For each character in the string:
    • If it’s an opening gate (, push it onto the stack.
    • If it’s a closing gate ), check if the stack is empty. If the stack is not empty, pop the stack (matching the opening gate with the closing gate).
    • If the stack is empty when a closing gate appears, return -1, indicating an imbalance.
  3. Count valid pairs: For each valid pair (an opening and a closing gate), increment the count.
  4. Final check: If there are no unclosed opening gates left in the stack, return the count. Otherwise, return -1.

Python Code Implementation

python
def validate_gates(gates): stack = [] valid_pairs = 0# Traverse the gates sequence for gate in gates: if gate == '(': stack.append(gate) # Push opening gate onto stack elif gate == ')': if stack: # Check if there's a matching opening gate stack.pop() # Pop the opening gate and count the pair valid_pairs += 1 else: return -1 # Return -1 if no matching opening gate# If stack is empty, all gates are balanced return valid_pairs if not stack else -1# Example usage gates = "()()" print(validate_gates(gates)) # Outputs: 2

Explanation of the Code

  1. Input: The input gates is a string representing the sequence of gates (i.e., '(' for opening gates and ')' for closing gates).
  2. Stack: We use a stack to store opening gates and ensure that each closing gate corresponds to an opening gate.
  3. Traversal: As we traverse the string:
    • For each '(', we push it onto the stack.
    • For each ')', we check if there is a matching '(' in the stack. If so, we pop the stack and increment the valid_pairs counter.
    • If we encounter a ')' with no matching '(', the gates are imbalanced, and we return -1.
  4. Final Check: If the stack is empty at the end, all gates are balanced, and we return the number of valid pairs. If the stack is not empty, there are unclosed gates, and we return -1.

Time Complexity

The time complexity of the solution is O(n)O(n), where nn is the length of the input string. Each gate is processed once, and each operation (push or pop) on the stack takes constant time.

Example Walkthrough

Example 1:

Input: gates = "()()"
  1. Traverse the string:
    • First '(': Push to the stack.
    • First ')': Pop from the stack, valid pair found, increment count.
    • Second '(': Push to the stack.
    • Second ')': Pop from the stack, valid pair found, increment count.
  2. Final count: 2 valid pairs.
Output: 2

Example 2:

Input: gates = "(()"
  1. Traverse the string:
    • First '(': Push to the stack.
    • Second '(': Push to the stack.
    • First ')': Pop from the stack, valid pair found, increment count.
  2. The stack is not empty, indicating an imbalance.
Output: -1

Conclusion

This solution efficiently validates the water reservation system’s gate design by checking for balanced opening and closing gates. The stack-based approach ensures that we can handle large input sizes within linear time complexity. If the gates are properly balanced, the algorithm counts the valid pairs, otherwise, it returns -1 to indicate an imbalance.SEO Keywords: Opening and closing gates validation, balanced parentheses, stack-based algorithm, water reservation system safety, string manipulation.Click here to know more our program!Opening and Closing Gates Validation