Part I: Evaluation Function Now that you have the basic tree class working - and it is printing correctly - you can work on the Evaluation Function. This function is recursive by nature. This is very similar, in fact, to the code you just wrote for the Print Function. Things are a tad different. Unlike the Print Function, which utilized Preorder Depth-First recursion, the evaluate function must use Postorder Depth-First recursion. This is due to the fact that we need the result from the left and right recursive calls before we can perform a calculation.

Part II: Testing Once you have written the Evaluate Function, it needs to be tested with some valid data. Please make sure to use a valid tree... or your program will most likely crash (given a null child).

Not so necessary (add ons)

A novice SystemVerilog programmer has written the following decimal counter module which should zero the decimal_count on reset and then, when enabled, increment modulo 10 the decimal_count on every positive clock edge, module count_decimal_wrong. (c)

Which of the two previous problems might be solved more efficiently with a greedy algorithm? Indicate the problem and describe the greedy algorithm. Then give a clear and rigorous proof, with a drawing if it helps clarity, that your greedy algorithm always reaches the optimal solution. Derive the big-Theta time complexity. [6 marks] 8 CST0.2019.1.9 8 Algorithms (a) Consider a Binary Search Tree. Imagine inserting the keys 0, 1, 2, . . . , n (in that order) into the data structure, assumed initially empty. A simple raytraced image can be seen in Figure 1 and the basic algorithm in Figure 123. Ray tracing's big disadvantage is that it is slow. It takes minutes, or hours, to render a reasonably detailed scene.

Exact weights for salience factors are not required. Owners love the new hybrid cars. They all say that they have much better fuel economy than conventional vehicles. And it seems that the performance of hybrid cars matches all expectations. [14 marks] 11 CST.2004.13.12 12 Complexity Theory (a) Define a one-way function. [4 marks] (b) Explain why the existence of one-way functions would imply that P6=NP. [7 marks] (c) Recall that Reach is the problem of deciding, given a graph G a source vertex s and a target vertex t, whether G contains a path from s to t; and Sat is the problem of deciding whether a given Boolean formula is satisfiable. For each of the following statements, state whether it is true or false and justify your answer. (i) If Reach is NP-complete then P=NP. [3 marks] Supply two modified versions of the program that alter the swap function definition and, if necessary, its calls, to avoid this assert failure. One version should be in C, and the other should use C++ language features. [4 marks] (c) Describe the address-space layout (highlighting four areas of memory) of limited succession of regular numbers is determined by a couple (l, x), where l N is the quantity of components, and x : [1, l] N is a capability that characterizes those components. The case 11l = 0 characterizes the invalid succession. a) In Verilog, what is the contrast between nonstop task and non-impeding task? // taken array of 1000 elements to get some significant time as small array sorting will get executed within small time interval Describe in detail both Prim's and Kruskal's algorithms for finding a minimum cost spanning tree of an undirected graph with edges labelled with positive costs, an explain why they are correct.