How do i detect a cycle in a undirected graph and drop the edge with the maximum weight in that cycle?

Question

I know DFS or union-find can be used to detect a cycle. But is there a quick way to find the edge with the maximum weight in that cycle?

Answer 1

No, DFS and sequential search is the optimal solution. Just find the cycle and go through its edges to find the maximum weight edge. The complexity doesn't really matter here - you had to find the cycle anyway and the complexity of finding the maximum edge is the same.

Answer 2

没有一个好的方法只能执行一次，但是如果要迭代直到图形非循环，则将留下最小的生成树，该树可以在线性运算时间内进行计算。