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Roads and Libraries
Roads and Libraries
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To enhance your community’s infrastructure, consider the "Roads and Libraries" initiative. This program focuses on improving road networks and expanding library resources, ensuring better connectivity and access to knowledge. Explore our promotional items, which include detailed project plans and funding options, to support these essential upgrades. Investing in roads and libraries not only improves daily commutes but also fosters educational growth and community development. Get involved today!
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Hey there! I think investing in both roads and libraries is crucial for any community. Roads keep us connected and moving forward, while libraries are like treasure troves of knowledge and inspiration. By improving both, we're enhancing our quality of life and opportunities for everyone.
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Idea: we can get a library to two cities either by 1.) using 1 library + 1 road or 2.) 2 libraries. We can get a library to a three citites with 1.) 1 library + 2 roads or 2.) three libraries. In this sense, a road is effectively the same as a library, so we want to choose whichever is cheapest. Inductively, from the last observation, if the cost of a library is less than a road, we should just build all libraries.
Alternatively, we want to maximally build roads to connect the towns, as we can minimise the number of libraries. By forming a minimum spanning tree (with a DSU), we can work out 1.) the number of disjoint sets (and hence the number of libraries) and 2.) the number of roads.
In all honesty, I copied the DSU code from GeeksForGeeks and modified it slightly such that I know when I've bothered to make a new connection, or if the connection is redundant.