It is necessary to monitor the dens

It is necessary to monitor the density of vehicles in all
streets as well as crossroads for smart traffic
management. From the estimated density of vehicles,
the Smart Traffic System can detect and even predict
potential traffic jams and modify traffic flows.
The traffic system of the city consists of two-way
streets. Each street connects two crossroads. As all
the streets in the city are equipped with sensors for traffic monitoring, the layout of traffic
system is optimized carefully. Thus, for each pair of crossroads, there is at most one street to
connect them. It means that the traffic system with all streets and crossroads can be considered
as a tree. To prepare for future city expansion, there can be a crossroad that connects to only a
single street. Future streets can be built from such crossroads.
Instead of using cameras (regular or infrared devices) that can be affected by light condition or
visual occlusion, all streets are equipped with sensors embedded on the ground. Sensors can
monitor the pressure and motion by vehicles on the surface to estimate the traffic flow.
Sensor stations are used to collect data from sensors in nearby regions and send to Smart
Traffic System. A sensor station can be deployed in the center of a crossroad or in the middle
of a street.
- If a sensor station is placed in a crossroad, it can collect data from sensors in that
crossroad, in all streets connecting with that crossroad and in the crossroads at the other
ends of these streets.
- If a sensor station is in the middle of a street, the sensor station can collect data from
sensors in that street, in the crossroads at the two ends of that street, and all streets
connecting with these two crossroads.
Please determine the minimum number of sensor stations to collect data from all sensors in the
traffic system of the city.