Uva673 Balanced brackets

But what does A and B in that problem have to do with this? Can't quite understand

We need to check if the parentheses in a string match. That is, for every open parenthesis, it must have a corresponding close parenthesis to match it. If any unmatched parentheses occur, then the string is not balanced.
To solve this problem, we can use the stack data structure. Iterate over each character in the string, pushing it onto the stack if it is an open parenthesis(e.g., "("," {", "[")) or popping an open parenthesis from the top of the stack if it is a close parenthesis(e.g.,") ", "} ", "] ") to check if they match. If it does not match, then the string is not balanced. If the stack is not empty after the string is traversed, then the string is not balanced.
Therefore, we can use stacks to check whether the parentheses match, which is why this problem has to do with stacks and balancing parentheses.