Question: (20 points) Consider the recurrence relation T(0)T(1) -2 and for n 2 1, T(n) - 5%:ii T(i)T(i-1). Consider the problem of computing T(n) from n.

(20 points) Consider the recurrence relation T(0)T(1) -2 and for n

(20 points) Consider the recurrence relation T(0)T(1) -2 and for n 2 1, T(n) - 5%:ii T(i)T(i-1). Consider the problem of computing T(n) from n. (a) Show that if you implement this recursion directly, the algorithm would use exponential time in n. (b) Explain how, by not recomputing the same T(i) value twice, one can obtain an algorithm for this prob- lem that uses only O(n2) time. (c) Give an algorithm for this problem that only use O(n) time

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