# BusyRoute

In terms of algorithmic logic, this involves solving the Travelling Salesman Problem (TSP) for the first case, which is complete for the $\textsf{FP}^{\textsf{NP}}$ complexity class (read: very hard). We approach this problem with backtracking ($O(N!)$) for small ($N \leq 8$) problem instances, the Held-Karp dynamic programming algorithm ($O(N^2 2^N)$) for larger instances ($N \leq 15$), and the Nearest Neighbour and 2-Opt approximation heuristics for even larger instances, though it seems unlikely most users would actually be planning such large itineraries.