- List of all possible hamilton circuits,
- Calculate the weight of each circuit found in Step 1
- Pick the circuit that has the
**smallest**weight.

Here is the list of (5-1)! = 24 circuits.

Note that the circuit listed on the right is the circuit on the left, traced in the opposite direction. This was why we said above we can cut

A-B-C-D-E-A<=> 500 + 305 + 320 + 302 + 205 = 1632 <=>A-E-D-C-B-A

A-B-C-E-D-A<=> 500 + 305 + 165 + 302 + 185 = 1457 <=>A-D-E-C-B-A

A-B-D-C-E-A<=> 500 + 360 + 320 + 165 + 205 = 1550 <=>A-E-C-D-B-A

A-B-D-E-C-A<=> 500 + 360 + 302 + 165 + 200 = 1527 <=>A-C-E-D-B-A

A-B-E-C-D-A<=> 500 + 340 + 165 + 320 + 185 = 1510 <=>A-D-C-E-B-A

A-B-E-D-C-A<=> 500 + 340 + 302 + 320 + 200 = 1622 <=>A-C-D-E-B-A

A-C-B-D-E-A<=> 200 + 305 + 360 + 302 + 205 = 1372 <=>A-E-D-B-C-A

A-C-B-E-D-A<=> 200 + 305 + 340 + 302 + 185 = 1332 <=>A-D-E-B-C-A

A-C-D-B-E-A<=> 200 + 320 + 360 + 340 + 205 = 1425 <=>A-E-B-D-C-A

A-C-E-B-D-A<=> 200 + 165 + 340 + 360 + 185 = 1250 <=>A-D-B-E-C-A

A-D-B-C-E-A<=> 185 + 360 + 305 + 165 + 205 = 1220 <=>A-E-C-B-D-A

A-D-C-B-E-A<=> 185 + 320 + 305 + 340 + 205 = 1355 <=>A-E-B-C-D-A

The Optimal Solution is shown below.

### Pros

- Easy to understand

- Can give an
**optimal**(best) Solution

- Easy to understand
### Cons

- Not a practical algorithm in many cases

- It is
**inefficient algorithm**. That is the number of steps needed to carry it out grows disproportionally with the size of the problem.

- Not a practical algorithm in many cases