Held-Karp
=========

Implementation of [Held-Karp](https://en.wikipedia.org/wiki/Held-Karp_algorithm),
an algorithm that solves the Traveling Salesman Problem using dynamic
programming with memoization.

Held-Karp solves the problem by calculating lowest cost on subsets of the
larger problem, and re-uses the intermediate results. Its runtime is
O(n^2 * 2^n), and it requires O(2^n * n) space.


Usage
-----

The implementation comes with a distance matrix generator taking an input size:

   $ python held-karp.py 5
     0 49 34 96 74
    49  0 10 94 43
    34 10  0 21  6
    96 94 21  0 70
    74 43  6 70  0
   
   (215, [0, 3, 2, 4, 1])

It is also possible to supply a distance matrix in a CSV format:

   $ python held-karp.py ex.csv
     0  2  9 10
     1  0  6  4
    15  7  0  8
     6  3 12  0
   
   (21, [0, 2, 3, 1])