1. A binary tree has ten nodes. The inorder and preorder traversals of the binary tree are shown as follows.
 Inorder: FKCGJBDEAI
 Preorder: GFCKDJBIEA
Draw the tree.

a. Determine the entropy of the data set. (4 points)

b. Determine the average entropy of the resulting subsets obtained by splitting on attribute A. (4 points)

c. How much information gain is obtained if attribute A is selected for the root node of the decision tree? (2 points) Note: Please use the values: log23 = 1.6 and log25 = 2.3. Hint: Entropy = is distribution for event i

3. To transmit text across a network, an English character is usually encoded in 8 bits in which bits 0~6 are the ASCII code and bit 7 is used for parity checking. Suppose a string of 5 characters, infni, is to be transmitted and odd-parity checking is adopted. Let the ASCII code of i be 1101001, the ASCII code of n be 1101110, and the ASCII code of f be 1100110. What is the sequence of 40 bits encoded for the 5-character string? Please show the sequence in hexadecimal (base 16) form.

4. Suppose we have an array A containing 9 integers: 240, 119, 682, 341, 225, 556, 122, 661, 245, i.e. A = [240, 119, 682, 341, 225, 556, 122, 661, 245] with the first index being 0. Please convert the array A into a maxheap and show the content of A after conversion. Note that the conversion should be done in-place.

4. Consider a weighted graph (the edges show the costs) as follows. Please use the Kruskal Algorithm to get the corresponding minimum (cost) spanning tree. Not only the result but also the whole procedure steps should be presented in your answer.

3. Consider the following processes. Please draw the schedules (Gantt Chart) and calculate the average waiting time for the Preemptive Shortest Job First, and Round Robin (time-quantum = 4 ms) scheduling policies, respectively.

2. Alice writes the following code and expects that the process prints “Hello Kitty” four times. However, the process prints “Hello Kitty” three times only! Please describe the reason why Alice’s code prints “Hello Kitty” three times instead of four.

1. Please explain the five states that a process may be in.

4. What will be shown on the screen after running the following program? (10%)

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