Input: weighted complete graph

Enter the vertices separated by single comma: A,B,C,D,E
A | B | C | D | E
A-> 0,1,1,1,1 # enter the cost matrix as an adjacency matrix, separated by single comma 
B-> 1,0,1,1,1
C-> 1,1,0,1,1
D-> 1,1,1,0,1
E-> 1,1,1,1,0

Output: Hamiltonian cycle, with step-by-step swaps

Tour: ['A', 'B', 'C', 'D', 'E'], total distance: 5

Procedure:

1. Construct Minimum Spanning Tree with Prim's algorithm.
2. Preorder traversal, and set the score to the weight sum.
3. Heuristic: find the largest edge first, then other edges.
   1. Choose another edge.
   2. Cross: (a, b) with (c, d) --> (a,c)
   3. If total weight of new tour is smaller, update tour and start from 3 again.