I'm a person using english as the second language and reading CLRS book at a slow pace due to my poor english. I have a problem with understanding the meaning of the word 'alternative'. In page 303 on CLRS, says:
we should convince ourselves that exhaustively checking all possible parenthesizations does not yield an efficient algorithm.Denote the number of alternative parenthesizations of a sequence of n matrices by P(n). Since we can split a sequence of n matrices between the kth and (k+1)st matrices for any k = 1,2,...,n-1 and then parenthesize the two resulting subsequences independently, we obtain the recurrence ...(omitted)
What is the word 'alternative parenthesizations'? is this word equivalent to the 'all possible parenthesizations' in the above block quote? searching dictionary for the word 'alternative' is not helpful to me. Thank you in advance.