#!/usr/bin/python
# Copyright Joel Friedman 2018.  For use in UBC's Math 441 course.
#

from gurobipy import *

######################################################## 
# Set up the variables and constraints
######################################################## 

n = 5     # number of cities

jfTSP = Model('Baby_TSP')

x = jfTSP.addVars(n,n, vtype=GRB.BINARY, name='ArcsTaken')
u = jfTSP.addVars(n, lb = 0, ub = n-1, vtype=GRB.INTEGER, name='order')

jfTSP.addConstrs( ( x[i,i] == 0   for i in range(n) ), name='ZeroDiag' )
jfTSP.addConstrs( ( x.sum(i,'*') == 1  for i in range(n) ), name='LeaveCities')
jfTSP.addConstrs( ( x.sum('*',i) == 1  for i in range(1,n) ), name='EnterCities')

jfTSP.addConstrs( ( u[i] - u[j] + n * x[i,j] <= n-1   
  for i in range(1,n)  for j in range(n) ),  name='orderRespected')

jfTSP.setObjective( x[0,1] , GRB.MAXIMIZE )
jfTSP.optimize()
jfTSP.printAttr("X")