answer a) and b)

equation for a) should be t(n)=4t(n/3)+n

Problem 1: For each integer n > 1 we define a tree Tos recursively, as follows. Ti and Tz consist of only a single node. For n > 3. T. is obtained from three copies of Tin/3), one copy of Tm/21, and three additional nodes, by connecting them as follows: T/31 Tina Tw/3) Tinal Notations a) and represent the floor and ceiling functions, the first one rounds a real number i to the largest integer a 3r and the second one rounds or to the smallest integer b. Let t(n) be the number of nodes in T. (a) Give a recurrence equation for t(n) and justify it. (b) Draw Tio. (You can use a drawing software or draw it by hand, and include a pdf file in the latex source.) (c) Give the asymptotic formula for t(n), by using Master Theorem to solve the recurrence from part (a). Justify your solution