## ยง Remembering Eulerian and Hamiltonian cycles

I used to keep forgetting the difference. Here's how I remember it now.
We know that an *euler tour* always exists for a tree. Indeed, it's
a handy data structure
that can be used to convet LCA (lowest common ancestor) into RMQ(range minimum query).
So, the "Euler tour" must exist for a tree. See that when we perform a tour
on the tree, we *definitely* walk a vertex twice (once when entering, once when
exiting). It seems like we walk the (undirected) edges twice as well.
However, if we consider the edges as *directed edges*, then we're only walking
the edges once.
- So an euler tour must correspond to a tour where we walk over each edgeexactly once.
- A hamiltonian tour must (by complementarity) correspond to a tour where weover each vertex exactly once.