Solution Review: Reverse Parentheses

Solution

• We don’t need to flip the balanced parentheses, so we remove them first. If all the balanced parentheses are removed, we’ll be left with the parentheses of the form )))((((.

• Let’s name the total number of open parenthesis as OpenCount and the total number of closed parenthesis as CloseCount.

• When OpenCount is even, then CloseCount is also even. Their half-element reversal will make the expression balanced.

• When OpenCount is odd and CloseCount iis also odd, we have to perform OpenCount/2 and CloseCount/2 reversals. We’ll be left with )(, which needs 2 more reversals. The formula is derived from this:

  • $Total$

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