You are required to implement correctly and efficiently linear time transformations between three different representations for a multi-way tree:
R1: parent representation: for each key you are given the parent key, in a vector. R2: multi-way tree representation: for each node you have the key and a vector of children nodes
R3: binary tree representation: for each node, you have the key, and two pointers: one to the first child node, and one to the brother on the right (i.e. the next brother node)
Also, you are required to write a pretty print procedure on R3, which performs a preorder traversal on the binary representation and outputs the tree in a friendly manner (see the image on the next page for an example).
Therefore, you are given as input a multi-way tree in the parent representation (R1). You are required to implement T1, which transforms the tree to a multi-way representation (R2), then T2, which transforms from the multi-way representation to the binary representation (R3). Then, on the binary representation, you are asked to write a pretty print procedure (using a pre-order traversal).
You should be able to design the necessary data structures by yourselves. You may use intermediate structures (i.e. additional memory).
Evaluation
You should run your algorithms on a sample input tree (you may use the one in the example provided on the next page). Output (in a readable manner) the tree in each of the three representations (for R1 simply print the parent vector; for R3 it is enough to call the pretty print procedure).
Explain what data structures you employed for the R2 and R3 representations.
You should assess the efficiency of your methods: i.e. do your transformations run in O(n)? Also, explain the necessity for any additional memory employed by your algorithms.
