Rewrite the factorial Prolog program fact (0, 1). fact (N, R) :- N> 0, N1 is N-1, fact (N1, R1), R is N. R1. to make it tail recursive (see Exercise 4.17). Draw search trees of subgoals and explain Prolog's responses based on the trees for the following goals (see Figure 4.1): (a) god (15, 10, x). (b) append(X, Y, [1, 2]). = Rewrite the Prolog clauses for Euclid's algorithm (gcd) in Figure 4.1 to use the cut instead of the test not(V 0). How much does this improve the efficiency of the program? Redraw the search tree of Exercise 4.21(a) to show how the cut prunes the tree.