1. ## Travelling salesman

Hi everybody,

I have this matrix.

- X Y Z Q
X 0 5 3 2
Y 5 0 4 1
Z 3 4 0 6
Q 2 1 6 0

X,Y,Z,Q are citys, numbers are miles. example: X-Y: 5 mile

My code must generate 3 random route (ex: XQZY, XYZQ, QZYX) and find min route.

X-Q-Z-Y =2+6+4=12mile
Y-Q-Z-X =1+6+3=10mile
Q-Z-Y-X =6+4+5=15mile

Min route is Y-Q-Z-X =10mile

Can you help me?

2. My code must generate 3 random route (ex: XQZY, XYZQ, QZYX) and find min route.
(a) What is a "random route"? (NB: mathematical descriptions are not appropriately explained by example. What are the conditions you can/want to/have to work with? Do you work with all 2^n sub-tour elimination conditions in a polyhedral description? Or is the combinatorial description all you want to use?)
(b) How do you want to generate a (random) construct defined as in (a)? Trying all (n-1)!/2 permutations? Solving a LP? Using a genetic algorithm? Using the approach you choose, how will your solutions distributed among all possible routes? Is it really random?

3. I can generate 3 random route but i don't know how can i calculate routes. How can i take the miles from matrix? which codes? I don't have any information.

My skill is beginner.

4. How would you, as a person, solve the task? Write down the matrix on a piece of paper, generate a random route, and then figure out how you would use the matrix before you try to figure out how to get the computer to use the matrix.

```int table[4][4] = {