t a) Find an optimal parenthesization of a matrix-chain product whose sequence of dimensions is < 15, 30, 9, 36, 15, 150, 18 > b) Determine an LCS of < A, B, B, A, B, A, B, A> and < B, A, B, A, A, B, A, A, B > c) Given the following recursive functions: 4Q(n, k-1, k-1) n = 1 02A(n) = = 02A(n-1)+4Q(n, k-1, k-1) n>1 Q(n, x-1, 0) +Q(n,x1,y1) n = 1, x>0, y > 0 Q(n, x-1, 0) n=1,x>0, y = 0 02A(n-1) Q(n, x, y) = +Q(n, x-1, 0) +Q(n,x1,y1) n> 1, x> 0, y > 0 02A(n - 1) +Q(n, x-1,0) n> 1, x > 0, y = 0 02A(n - 1) n> 1, x = 0, y = 0, Find a mathematical formula to compute it or use the dynamic programming method to write a pseudocode algorithm to avoid the multiple recalculations.