…rtant requirement. We must be able to make range searches, e.g. homes with prices from $80 to $162. In case of a BST, it’s easy to get all the nodes in a range just by doing an inorder traversal of the tree and keeping a counter. For a hashtable it is somewhat expensive which makes it reasonable to stick with BSTs in this case.
Theorem. A finite undirected connected graph is an Euler graph if and only if exactly two vertices are of odd degree or all vertices are of even degree. In the latter case, every Euler path of the graph is a circuit, and in the former case, none is. 
…self. There should always be two parts to a recursive function: the recursive case and the base case. The recursive case is when the function calls itself. The base case is when the function stops calling itself. This prevents infinite loops.