Question 1 a) b) Find an optimal parenthesization of a matrix-chain product whose sequence of dimensions is Determine an LCS of and Given the following recursive functions: c) [ 4Q(n, k-1, k-1) Q(n,x , 0) Qn, x 1, 0) 02A (n)-102A(n-l) + 4Q(n , k-1,k-I) n>1 +0,x 1,y-I) n-,x > 0, y>0 n= 1,x>0,y=0 02A(n 1) Q(n, x, y) =1 +Q(n,x-1.0) +Qm,x 1,y-1) n> 1,x>0, y>0 02A(n 1) +Q(n,x-1,0) n > 1,x > 0, y = 0 O2A(n 1) Find a mathematical formula to compute it or use the dynamic programming method to write a pseudocode algorithm to avoid the multiple recalculations