14. (10 points) Consider the recurrence T(n) = T(3n/4)+T(n/4)+n and its recurrence tree.

a. What is the minimum distance between a leaf node and the root?

b. What is the maximum distance between a leaf node and the root?

c. How many subproblems are at level k? The root is at level 0.

d. What do the nodes at level k sum to? Assume level k is above any of the leaves.

e. What does the recurrence evaluate to?

14. (10 points) Consider the recurrence T(n)=T(*)+) +n and its recurrence tree. a. (1 point) What is the minimum distance between a leaf node and the root? A. login B. logg C. 10/3 b. (1 point) What is the maximum distance between a lcaf node and the root? A. login B. log, C. loga/3 D. n c (2 points) Ilow many subproblems are at level k? The root is at level 0. D. B. 24 C 24 D. 34 d. (2 points) What do nodes at level k sum to? Assume level k is above any of the leaves. An B. 2n c. )'n D. 2n e. (1 points) What does the recurrence evaluate to? A. T(n) = e(n) B. T(n) = (n log na) C. T(n) = (n) D. T() = (nlog n)