添加 1 个边和数字的新图

new graph with adding 1 edges and number

在为 ACM-Contest 做准备 class 时,我们的老师给了我们一页已解决问题的打印页。在一页上写着,2 以下事实是正确的,但她不会说,why or what:

"with adding new 1 edge to a Directed Graph, how many of these may be true about number of strongly connected component of this graph?

+) at most 1 unit is increased.

++) at most 1 unit is decreased.

+++) maybe not changed.

++++) maybe decreased by more than 2 units.

任何人都可以与我们的团队一起清楚地扩展它吗?

(+) 为假(根据 "increase at most" 的宽泛解释,即暗示没有减少)并且 (++) 为假且 (++++) 为真,因为如果我们将路径的一端到另一端的反馈弧相加,使其成为一个循环,然后我们从 n 个强组件变为 1。(+++) 显然是正确的。

Before (4 strong components):
* --> * --> * --> *

After version A (1 strong component):
___________________
|                 |
v                 |
* --> * --> * --> *

After version B (4 strong components):
___________________
|                 |
|                 v
* --> * --> * --> *