need help with part 3 and part 4 of question 3

3. Random Trees The nx.random_tree (n) command can be used to generate a random tree on the n vertices represented in python by range( n ) (in order). Such a tree can be converted into a sequence of n2 numbers, its Prfer code by the python function pruefer_code , defined as follows: Conversely, the following function tree_pruefer constructs a tree from a Prfer code. ]: def tree_pruefer(code): \# initialize graph and defects n= len(code) +2 tree = nx.empty_graph(n) degrees =[1 for x in tree] for y in code: degrees[y]+= 1 \# add edges for y in code: 9]:T2= tree_pruefer (code ) 1. Construct random trees on n=10,11,12 nodes (one each is enough). For each such tree, draw it, compute its Prfer code and then convert the code back into a tree. Do you get your old tree back? 1. Construct random trees on n=10,11,12 nodes (one each is enough). For each such tree, draw it, compute its Prfer code and then convert the code back into a tree. Do you get your old tree back? In [173]: \( \begin{array}{ll}T=\mathrm{nx} \cdot \text { random_tree }(11) \\ \mathrm{nx} \cdot \mathrm{draw}(\mathrm{T}, * * \text { opts) }\end{array} \) 7 \[ \begin{array}{l} {[177]: \begin{array}{l} \text { code }=\text { pruefer_code }(T) \\ \text { code } \end{array}} \\ \mathrm{t}[177]:[8,0,8,6,2,10,10,10,10] \end{array} \] Yes, the original tree and the tree constructed from the Prfer code are the same, as can be seen by comparing the draw outputs. 2. For a few randomly chosen Prfer codes, construct the corresponding tree, draw it if you want, and convert it back into a Prfer code. Do you get your old code back? code2 In [183]:code2=pruefercode(T5)code2 Out [183]:[3,0,0] In [184]:n=7code=np,randomrandint(n,size=n2)code In [186]:code2= pruefer_code (T7) code2 out [186]:[0,6,5,5,0] The output will show the original Prufer code, the reconstructed Prufer code and a boolean indicating if the two codes match. If the code and the reconstructed code match, then we have gotten the same tree back 3. Which labelled tree on n nodes {0,1,,n1} corresponds to the Prfer code [0,1,2,,n3] ? ... your comments here... 4. Which labelled tree on n nodes {0,1,,n1} corresponds to a Prfer code which has n2 identical entries