单选题：To solve a problem with input size $$N$$ by divide and conquer,

To solve a problem with input size $$N$$ by divide and conquer, algorithm A divides the problem into 7 subproblems with size $$N/2$$ and the time recurrences is

$$T(N) = 7T(N/2)+\Theta(N^2)$$.

Now we attempt to design another algorithm B dividing the problem into $$a$$ subproblems with size $$N/4$$ and the time recurrences is

$$T(N) = aT(N/4)+\Theta(N^2)$$.

In order to beat algorithm A, what is the largest integer value of $$a$$ for which algorithm B would be asymptotically faster than algorithm A? @[D](3)

A. 14
B. 21
C. 28
D. 49



A.14
B.21
C.28
D.49


答案：D