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Given a string str, the task is to find the bracket numbers, i.e., for each bracket in str, return i if the bracket is the ith opening or closing bracket to appear in the string.

Question

Given a string str, the task is to find the bracket numbers, i.e., for each bracket in str, return i if the bracket is the ith opening or closing bracket to appear in the string.

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Solution

Here is a Python solution for the problem:

def find_bracket_numbers(s):
    # Initialize the open_bracket list and counter
    open_bracket = []
    counter = 1
    # Initialize the result list with the same length as the input string
    result = [0]*len(s)
    
    # Iterate over the string
    for i in range(len(s)):
        # If the character is an opening bracket
        if s[i] == '(':
            # Append the counter to the open_bracket list
            open_bracket.append(counter)
            # Set the corresponding element in the result list to the counter
            result[i] = counter
            # Increment the counter
            counter += 1
        # If the character is a closing bracket
        elif s[i] == ')':
            # Set the corresponding element in the result list to the last element in the open_bracket list
            result[i] = open_bracket[-1]
            # Remove the last element from the open_bracket list
            open_bracket.pop()
    
    # Return the result list
    return result

This function works by maintaining a list of the numbers of the opening brackets that have not yet been closed. When it encounters an opening bracket, it increments the counter and adds the new number to the list and the result. When it encounters a closing bracket, it adds the number of the most recent unclosed opening bracket to the result and removes that number from the list.

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