2. Still Hungry! (12 points). Suppose we still have an infinitely large pizza, and we still wish to determine what is the maximum number of pizza pieces that we can produce, but this time our cuts are shaped like Vs. The figure below illustrates the most pieces we can make, for n = 1 and n = 2 V-shaped cuts. Note that it's important to remember that the size of the pizza is so large that you can consider the cuts to be infinitely long, and the points of the Vs can be placed anywhere that maximizes the number of regions. 2,7 Let Z(n) denote the number of slices, given n V-shaped cuts in the pie. From the illustration above, we see that Z(1) = 2, and Z (2) = 7, and we can also infer from the description that Z(0) = 1. (a) [2 marks] What is the value of Z (3)? (b) [5 marks) Write an expression for 7(n) in terms of function S) from the previous problem. This will require lots of sketching! It may help to realize that a drawn Vis just half of a drawn X. Z(n) = (c) (5 marks] What is Z(n) as a function of n? Your solution should not be a recurrence, contain a summation, or use asymptotic notation. 2. Still Hungry! (12 points). Suppose we still have an infinitely large pizza, and we still wish to determine what is the maximum number of pizza pieces that we can produce, but this time our cuts are shaped like Vs. The figure below illustrates the most pieces we can make, for n = 1 and n = 2 V-shaped cuts. Note that it's important to remember that the size of the pizza is so large that you can consider the cuts to be infinitely long, and the points of the Vs can be placed anywhere that maximizes the number of regions. 2,7 Let Z(n) denote the number of slices, given n V-shaped cuts in the pie. From the illustration above, we see that Z(1) = 2, and Z (2) = 7, and we can also infer from the description that Z(0) = 1. (a) [2 marks] What is the value of Z (3)? (b) [5 marks) Write an expression for 7(n) in terms of function S) from the previous problem. This will require lots of sketching! It may help to realize that a drawn Vis just half of a drawn X. Z(n) = (c) (5 marks] What is Z(n) as a function of n? Your solution should not be a recurrence, contain a summation, or use asymptotic notation