CodeForces - 1108F MST Unification

最新推荐文章于 2020-10-30 17:40:48 发布

a-free-man

最新推荐文章于 2020-10-30 17:40:48 发布

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分类专栏： # MST # Codeforces

本文链接：https://blog.youkuaiyun.com/Wen_Yongqi/article/details/86768534

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博客介绍了如何在不改变最小生成树(MST)成本的情况下，通过增加边的权重使得MST唯一。文章提供了一个使用Kruskal算法的解决方案，对于边权相等的情况，优先选择未连接节点最多的边，冲突边则加1，复杂度为O(m log m)。同时提到Prim算法也可用于解决此问题。

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http://codeforces.com/contest/1108/problem/F

You are given an undirected weighted connected graph with nn vertices and mm edges without loops and multiple edges.

The ii -th edge is ei=(ui,vi,wi)ei=(ui,vi,wi) ; the distance between vertices uiui and vivi along the edge eiei is wiwi (1≤wi1≤wi ). The graph is connected, i. e. for any pair of vertices, there is at least one path between them consisting only of edges of the given graph.

A minimum spanning tree (MST) in case of positive weights is a subset of the edges of a connected weighted undirected graph that connects all the vertices together and has minimum total cost among all such subsets (total cost is the sum of costs of chosen edges).

You can modify the given graph. The only operation you can perform is the following: increase the weight of some edge by 11 . You can increase the weight of each edge multiple (possib