It is often more convenient to represent an ordered tree as a rooted binary tree, so that each node can be stored in the same amount of memory. The conversion is performed by the following steps:
This is illustrated by the following:
In most cases, the height of the tree (the number of edges in the longest root-to-leaf path) increases after the conversion. This is undesirable because the complexity of many algorithms on trees depends on its height.0 0 / | \ / 1 2 3 ===> 1 / \ \ 4 5 2 / \ 4 3 \ 5
You are asked to write a program that computes the height of the tree before and after the conversion.
The input is given by a number of lines giving the directions taken in a depth-first traversal of the trees. There is one line for each tree. For example, the tree above would give dudduduudu, meaning 0 down to 1, 1 up to 0, 0 down to 2, etc. The input is terminated by a line whose first character is #. You may assume that each tree has at least 2 and no more than 10000 nodes.
For each tree, print the heights of the tree before and after the conversion specified above. Use the format:
where t is the case number (starting from 1), h1 is the height of the tree before the conversion, and h2 is the height of the tree after the conversion.Tree t: h1 => h2
dudduduudu ddddduuuuu dddduduuuu dddduuduuu #
Tree 1: 2 => 4 Tree 2: 5 => 5 Tree 3: 4 => 5 Tree 4: 4 => 4