1. Similarly minimum distance required maximum / minimum of the maximum distance by the min / max spanning a fixed condition, another condition found in the tree.
Example: trucking.
Seeking a path between two points, so as to minimize the maximum right side. First determine the maximum the maximum spanning tree, and then select the smallest edge weight from side between two points, the use of lca.
例题：Star Way to Heaven
The maximum number of paths to find the minimum distance stars. This is on top with different points using a minimum spanning tree, minimum spanning tree to find all the stars and the border with prim algorithm, the maximum value is the answer right side of the boundary between the two largest.
But our concern is why the minimum spanning tree acceptable. Because these two questions face much the same problem though, but this question is harder, it needed a new map (Figure ah would have been no
We want to go from the left to the right, then they would pass through some of the edges that connect between the stars, then we can consider, if the answer to make better, it must be through the right side under the same conditions (ie, distance) more large side. And we may have to pass through a lot of edges,
Meaning of the title tells us to take the minimum Collage of these rights, so that Italy is transformed into a right side to find the smallest maximum path, that is, the minimum spanning tree, is not it amazing! (I asked the force brother, Duanyue, zkq a long time before, and thank them)
2. Minimum bottleneck tree. That is where the largest side of the minimum spanning tree minimum weight, provable.
By contradiction, first assume that the minimum spanning tree is T1, to the maximum edge E1, an additional smaller maximum side spanning tree T2, the maximum side of E2.
If E2 <E1, T2 all the edge weight value is less than E1, E1 connecting the two connected components A, B at T1, A must be connected in T2, the two edges of connected components B (or the whole tree is not Unicom), these edges are less than E1, replacing them with E1, T1 is the total weight value is smaller, the minimum spanning tree T1 is contradictory.
Therefore, the maximum right side of the minimum spanning tree value is the minimum of all maximum weight spanning tree edge.
Evidence from "qq_21704477" of the original article.
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