Problem solving with programming: Maximum nesting depth of a paranthesis expression



Problem solving with programming: Maximum nesting depth of a paranthesis expression

Given a parenthesis expression, We have to find the maximum nesting depth.

For example: the expression ()((()))(()) has a maximum nesting depth of 3.
The expression ((()())) has a maximum nesting depth of 3.
Let us output -1 for an unbalanced expressions such as (())) or ()(

This is a simple problem that can be asked in different forms. One such example can be
Given a sequence of jobs executed by a machine. What is the maximum number of parallel jobs executed at any point of time. 
One more variation of this problem can be
Given a maximum capacity of a computer center, and a sequence of people arrived, how many people have to wait for their turn.

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