Finding the count of external Parenthesis

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I am trying to figure out the solution for finding the count of external parenthesis.
You will have more clarity on what i mean by external parenthesis in the below examples. Assume that the given expression will always be valid.

(a+b)                   //External parenthesis count =  1
(a+b)*(a-b)             //External parenthesis count =  0 
((a+b)*(a-b))           //External parenthesis count =  1
(((a+b)*(a-b)))         //External parenthesis count =  2
((a))                   //External parenthesis count =  2
(a + (b*c))             //External parenthesis count =  1
(a+b)+c                 //External parenthesis count =  0

I have tried this and somehow not able to get the right logic.
So i am reaching out for ideas. I am looking more from a logic perspective.

Posted 31-Jul-15 3:25am

Prasad A

Updated 31-Jul-15 23:54pm

Patrice T

v5

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Sergey Alexandrovich Kryukov 31-Jul-15 9:44am

Define "external" precisely. Are then the parenthesis which can be removed symmetrically, the way the expression will remain the same? Do you also have to check up the balance? Why counting them? Anyway, the problem looks relatively trivial. What have you tried so far?
—SA

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F-ES Sitecore · Answer 1 · 2015-07-31T03:50:00

SQL

(a+b)                   //External parenthesis count =  1
(a+b)*(a-b)             //External parenthesis count =  0 
((a+b)*(a-b))           //External parenthesis count =  1
(((a+b)*(a-b)))         //External parenthesis count =  2
((a))                   //External parenthesis count =  2
(a + (b*c))             //External parenthesis count =  1
(a+b)+c                 //External parenthesis count =  0

For each ( ) pair delete ones (including the parenthesis) that don't contain any parenthesis themselves, eg (a+b) doesn't but (a + (b*c)) does.

SQL

                   //External parenthesis count =  1
*             //External parenthesis count =  0 
(*)           //External parenthesis count =  1
((*))         //External parenthesis count =  2
()                   //External parenthesis count =  2
(a + )             //External parenthesis count =  1
+c                 //External parenthesis count =  0

Now just count the parenthesis pairs left. Note this doesn't work for (a+b) or ((a)) so you might need a special case for when parenthesis only exists at the beginning and end.

Matt T Heffron · Answer 2 · 2015-07-31T12:27:00

externalCount = 0
loop
  if first or last chars are not parens
    exit loop
  Remove the external pair of parentheses.
  If the result is not well-formed
    exit loop
  externalCount++
  repeat loop
end loop

To determine if it is well-formed:

counter = 0
scan across the expression:
  if '(' then counter++
  if ')' then counter--
well formed if at end of the scan the counter is 0 and never went negative.

Finding the count of external Parenthesis

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