(5%) (b) Develop a minimal spanning tree of the graph.

9. (10%) The binary search tree in Figure 2 was created by starting with a null tree and entering data from the keyboard. In what sequence were the data entered? If there is more than one possible sequence, identify the alternatives.

10. (10%) The shell sort algorithm is an improved version of the straight insertion sort. In the shell sort, a list of N elements is divided into K segments, where K is known as the increment. For example, in Figure 3, K is 3. The first, fourth, seventh, and tenth elements make up segment 1. For each pass, the data in each segment are sorted in Insertion Sort. Thus, after insertion sort, there are three different ordered lists. After each pass through the data, the increment is divided by two (K/2) until, in the final pass, it is 1. Please prove (explain) the time complexity of Shell sort is close to O(N log N).

(a) Please write down Michaelis-Menten equation. (6%)

(b) Please explain the physical meaning of for an enzyme. (6%)

(c) Please estimate for the enzyme by Lineweaver-Burk plot. (6%)

(d) Please explain how to determine the type of inhibition and KI for the two inhibitors.(6%)

2. If we consider a 850 MHz NMR spectrometer, the resonance of 1H nuclear is 850MHz. calculate the energy that is required to make the transition from the lower energy state to the higher state. Meanwhile, please explain how to calculate the population ratio of molecules in the higher and lower states? (8%)

3. Please explain the mechanism to form a hydrogen bond and compare it with covalent bond. Explain why hydrogen bond is so important in maintaining a protein structure.(8%)

4. Electrons have been explained to have different distributions outside of nuclei. Please explain what s orbital and p orbital are? Meanwhile, what is sp3hybridization? Give an example. (10%)

5. Lightning and thunder are natural phenomena. Please briefly explain the underlying mechanism of lightning. (10%)

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