solution to tautogram graph problem
A Totogram is a puzzle played on a board that has a graph structure, with edges connecting some pairs of vertices. The edges of the graph form a rooted tree with a particular structure: the root has exactly three children, every other non-leaf node has exactly two children, and the leaves are all at the same depth k in the tree. This graph has the property that every vertex has exactly 1 or 3 neighbors. A sample board with k = 3 is shown in Figure 1. (Note that a Totogram is almost a balanced binary tree, except that the root has three subtrees instead of two.) To play the Totogram, the player arranges a set of N tiles numbered from 1 to N, where N is the number of vertices in the graph (which, in turn, is a function of k), on the vertices of the board. Their score is equal to the maximum absolute value of the difference between any pair of adjacent vertices, and the goal is to find an arrangement that makes the score as low as possible.
Commandline: python totogram.py k