3. In last Time, we studied Euclid's algorithm for computing the greatest common divisor (ged) of two positive integers: the largest integer which divides them both. Here we wll look at an alternative algorithm based on divide-and-conquer (a) Explain why the following rule is true (2gcd(a/2, b/2) if a, b are both even gcd(a, b/2) f a is odd, b is even gcd(a/2, b)if a is even, b is odd gcd((a b)/2,b) if a, b are both odd gcd(a, b)- (b) Give an efficient divide-and-conquer algorithm for greatest common divisor, based on the above. (c) Express the running time of your algorithm for the case where a and b are both n-bit numbers. Recall that dividing by two results in the removal of one bit from a value. You will want to express this as T (2n)-... (d) Find a closed form for the recurrence relation you gave in the previous part. Note that this won't work for using the master theorem. 3. In last Time, we studied Euclid's algorithm for computing the greatest common divisor (ged) of two positive integers: the largest integer which divides them both. Here we wll look at an alternative algorithm based on divide-and-conquer (a) Explain why the following rule is true (2gcd(a/2, b/2) if a, b are both even gcd(a, b/2) f a is odd, b is even gcd(a/2, b)if a is even, b is odd gcd((a b)/2,b) if a, b are both odd gcd(a, b)- (b) Give an efficient divide-and-conquer algorithm for greatest common divisor, based on the above. (c) Express the running time of your algorithm for the case where a and b are both n-bit numbers. Recall that dividing by two results in the removal of one bit from a value. You will want to express this as T (2n)-... (d) Find a closed form for the recurrence relation you gave in the previous part. Note that this won't work for using the master theorem