an algorithm for checking whether expression of '(' &')'only is ' well parenthesized'

Answer 1

This is a typical intro to CS assignment which has many solutions online... Most often solved via a "stack" implementation.

See source(s) below for reference to some solutions.

PS: Ivanhoe... Your solution will not work... What about "))((" ?
Your method only tests if equal number of left & right... Does not test for legal nesting!

Answer 2

create a counter, set it to 0 and loop through the string to be checked
every time ( occurs add 1 to the counter
every time ) occurs subtract 1 from the counter
at the end of the string check if the counter is 0
if not then the brackets dont match