A caterpillar tree is a tree in which every node is on a central stalk or only one
graph edge away from the stalk. The figure below illustrates to the left a caterpillar tree
with 14 nodes (the stalk marked in blue), and on the right a non-caterpillar tree with 9 nodes.
Given the description of a tree, determine the least number of nodes that must be removed for
the tree to become a caterpillar tree. The tree will be described as a string of 0's and 1's.
Starting from some node in the tree, a '1' in the string traverses the tree to a previously
unvisited node, while a '0' backtracks to the previous node. The trees in the figure above
would be described as "11101011111010010001000100" and "1111100100110000", respectively,
if the traversals starts at node 1 and the nodes are visited in the numbered orders.
Create a class CaterpillarTree containing the method fewestRemovals which takes a String
tree containing the description of the tree (concatenate the elements to get the full description),
and returns an int containing the fewest number of nodes that must be removed for the tree
to become a caterpillar tree.