Definition of a tree (Taken from Wikipedia) A tree is an undirected graph \(G\) that satisfies any of the following equivalent conditions: \(G\) is connected and acyclic (contains no cycles). \(G\) is acyclic, and a simple cycle is formed if any edge is added to \(G\). \(G\) is connected, but would become disconnected if any single edge is removed from \(G\). \(G\) is connected and the 3-vertex complete graph \(K_3\) is not a minor of \(G\).

This is a commentary on the solution from Benjamin Qi. from permutation to tree generation Before we go into the solution of this problem it is good to be able to understand how to create a tree using a permutation. First how does a permutation \(a\) translate into a tree? Think of \(a[i]\) as the time in which node \(i\) is inserted to the tree. We’ll use the following \(a=42315\) for illustration.