7. Consider the usual algorithm for determining whether a sequence of parentheses is balanced. The maximum number of parentheses that appear on the stack AT ANY ONE TIME when the algorithm analyzes: (()(())(()))?a) 1b) 2c) 3d) 4 or more
Question
- Consider the usual algorithm for determining whether a sequence of parentheses is balanced. The maximum number of parentheses that appear on the stack AT ANY ONE TIME when the algorithm analyzes: (()(())(()))?a) 1b) 2c) 3d) 4 or more
Solution
The algorithm for determining whether a sequence of parentheses is balanced works by pushing each opening parenthesis onto a stack and popping them off the stack when a closing parenthesis is encountered. The maximum number of parentheses that appear on the stack at any one time is the maximum depth of nested parentheses in the sequence.
Let's analyze the sequence: (()(())(()))
- Push first '(': Stack is '('
- Push second '(': Stack is '(('
- Pop on encountering ')': Stack is '('
- Push '(': Stack is '(('
- Pop on encountering ')': Stack is '('
- Pop on encountering ')': Stack is empty
- Push '(': Stack is '('
- Push second '(': Stack is '(('
- Pop on encountering ')': Stack is '('
- Pop on encountering ')': Stack is empty
The maximum number of parentheses on the stack at any one time during this sequence is 2. So, the answer is (b) 2.
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