# Travelling Salesman: Big O Complexity when starting city is fixed

We are studying the Travelling Salesman problem in my high school class, and I am wondering what the Big O complexity of the TSP is when you MUST start and end at the same city. For example, given 4 cities labelled A,B,C,D and you MUST start and end at A, what is the big O notation for this? Is ((n-1)!)/2 for both symmetrical and asymmetric cases?

Thanks

• It doesn't really make a difference as the solution is a cycle through the cities. You can start anywhere on the cycle. – Pontus Jul 13 '19 at 9:45

Held–Karp solves TSP in time $$O(n^22^n)$$, which is much faster than $$\Theta(n!)$$.