Problem 2: For each integer n 1 we define a tree T, recursively, as follows. Ti consists of only a single node. For n 2 2, Tn is obtained from four copies of Tin/2] and three additional nodes, by connecting them as follows: n/2 n/2 n/2 Let s(n) be the number of nodes in T (a) Give a recurrence equation for s(n) and justify it. (b) Determine the exact values of s(n) for n-1,2,3, 4,5,6,7,8,9. (Use the table formatting, as show at the end of the homework.) (c) Draw Ts. (You can use a drawing software or draw it by hand, and include a pdf file in the latex source.) (d) Give the asymptotic formula for s(n), by solving the recurrence from part (a). Justify your solution. Problem 2: For each integer n 1 we define a tree T, recursively, as follows. Ti consists of only a single node. For n 2 2, Tn is obtained from four copies of Tin/2] and three additional nodes, by connecting them as follows: n/2 n/2 n/2 Let s(n) be the number of nodes in T (a) Give a recurrence equation for s(n) and justify it. (b) Determine the exact values of s(n) for n-1,2,3, 4,5,6,7,8,9. (Use the table formatting, as show at the end of the homework.) (c) Draw Ts. (You can use a drawing software or draw it by hand, and include a pdf file in the latex source.) (d) Give the asymptotic formula for s(n), by solving the recurrence from part (a). Justify your solution