S - it is a line
Create a matrix
F[i][j] is a decision with i on j a symbol
If S[i] it is a closing bracket, F[i][j] =1 + F[i+1][j]
If S[i] a closing bracket that is two cases:
1) We add a closing bracket - 1 + min(F[i+1][k] + F[k+1][j]), where i<k<=j
2) Is in line closing - min(F[i+1][k-1], F[k+1][j]), where S[k] = S[i] and i<k<=j

Interesting... But what you output? Please explain to me

> 1) We add a closing bracket - 1 + min(F[i+1][k] + F[k+1][j]), where i<k<=j

if we want to add a bracket we can add it in (i+1)position.
and dont necessary too check all the kind.

sorry for my poor english.
GOOD LUCK!!!