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# Internet Connection | ||
|
||
March madness has started and everything is going perfectly as planned! Well, minus | ||
some issues with the coding questions... Because you're such an amazing | ||
organizer and the lovely people at ACM offer so much support, the event is far | ||
more popular than anyone could have imagined. | ||
|
||
It's nearly time to host the Hackathon, and you're beginning to realize that | ||
it's almost impossible to pack everyone into the Computer Science building for | ||
this event. The concern now becomes, where can we put students on campus so | ||
that they still have access to a strong Internet connection throughout the | ||
Hackathon? | ||
|
||
Thankfully, you managed to get a list of all the locations of available routers | ||
on campus, as well as how far they can reach. The list of all routers may look | ||
something like the following: | ||
|
||
``` | ||
Router located at x=4, y=7 with reach=3ft | ||
Router located at x=6, y=4 with reach=4ft | ||
Router located at x=10, y=10 with reach=3ft | ||
``` | ||
|
||
Imagining the campus as a grid on a Cartesian (2D) plane, we can picture where | ||
the routers are. Unfortunately for us, the school cheaped out when buying | ||
routers, so they opted for a large quantity of routers with bad service, but | ||
long range. | ||
|
||
A single router is not enough for a student to maintain a stable connection. To | ||
combat this while remaining cost-effective, the school has implemented a system | ||
where two routers can help boost each other's signals and offer a student a | ||
stable connection! | ||
|
||
If a student is within range of two different routers at once, their connection | ||
will be more than enough to sustain any activities they may try. Our goal is to | ||
ensure that every student has a stable connection for this Hackathon, so we | ||
will only look for areas that are in the range of 2 different routers to try | ||
and place them there. | ||
|
||
## Part 1 | ||
|
||
Given the long list of routers, **how many pairs of routers offer an area of | ||
any size where a student can maintain a stable connection?** | ||
|
||
## Part 2 | ||
|
||
To avoid scattering students all over campus in search of a good Internet | ||
connection, we have to optimize our space. We have all the spaces where | ||
students have a good Internet connection now, and we just need to figure out | ||
where the students should go. **What is the largest area of overlap that any | ||
pair of routers creates?** | ||
# Internet Connection | ||
|
||
March madness has started and everything is going perfectly as planned! Well, minus | ||
some issues with the coding questions... Because you're such an amazing | ||
organizer and the lovely people at ACM offer so much support, the event is far | ||
more popular than anyone could have imagined. | ||
|
||
It's nearly time to host the Hackathon, and you're beginning to realize that | ||
it's almost impossible to pack everyone into the Computer Science building for | ||
this event. The concern now becomes, where can we put students on campus so | ||
that they still have access to a strong Internet connection throughout the | ||
Hackathon? | ||
|
||
Thankfully, you managed to get a list of all the locations of available routers | ||
on campus, as well as how far they can reach. The list of all routers may look | ||
something like the following: | ||
|
||
``` | ||
Router located at x=4, y=7 with reach=3ft | ||
Router located at x=6, y=4 with reach=4ft | ||
Router located at x=10, y=10 with reach=3ft | ||
``` | ||
|
||
Imagining the campus as a grid on a Cartesian (2D) plane, we can picture where | ||
the routers are. Unfortunately for us, the school cheaped out when buying | ||
routers, so they opted for a large quantity of routers with bad service, but | ||
long range. | ||
|
||
A single router is not enough for a student to maintain a stable connection. To | ||
combat this while remaining cost-effective, the school has implemented a system | ||
where two routers can help boost each other's signals and offer a student a | ||
stable connection! | ||
|
||
If a student is within range of two different routers at once, their connection | ||
will be more than enough to sustain any activities they may try. Our goal is to | ||
ensure that every student has a stable connection for this Hackathon, so we | ||
will only look for areas that are in the range of 2 different routers to try | ||
and place them there. | ||
|
||
## Part 1 | ||
|
||
Given the long list of routers, **how many pairs of routers offer an area of | ||
any size where a student can maintain a stable connection?** | ||
|
||
## Part 2 | ||
|
||
To avoid scattering students all over campus in search of a good Internet | ||
connection, we have to optimize our space. We have all the spaces where | ||
students have a good Internet connection now, and we just need to figure out | ||
where the students should go. **What is the largest area of overlap that any | ||
pair of routers creates?** |