Give asymptotic upper and lower bounds for t(n) in each of the following recurrences. assume
that t(n) is constant for n ≤ 3. make your bounds as tight as possible, and justify your answers.
(a) t(n) = 2t(n/3) + n lg n
(b) t(n) = 3t(n/5) + lg2 n
(c) t(n) = t(n/2) + 2n
(d) t(n) = t(n) + θ(lg lg n)
(e) t(n) = 10t(n/3) + 17n1.2
(f) t(n) = 7t(n/2) + n
(g) t(n) = t(n/2 + √n) + √

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Write a program that inserts the digits of an integer into an array in originalorderfollowed by reverse order. first, promptthe user to enter a positive integer(> 0). determine the number of digits of the integer. create a dynamically allocated integer arrayof a size twice the number of digits.now insert the digits in original order which will occupy half of the array. then, insert the digits in reverse order.finally, output thedigits in thearray.use at least two functions to organize your program.