Fiber Communications
题目描述
Farmer John wants to connect his N (1 <= N <= 1,000) barns (numbered 1..N) with a new fiber-optic network. However, the barns are located in a circle around the edge of a large pond, so he can only connect pairs of adjacent barns. The circular configuration means that barn N is adjacent to barn 1.
FJ doesn't need to connect all the barns, though, since only certain pairs of cows wish to communicate with each other. He wants to construct as few
connections as possible while still enabling all of these pairs to communicate through the network. Given the list of barns that wish to communicate with each other, determine the minimum number of lines that must be laid. To communicate from barn 1 to barn 3, lines must be laid from barn 1 to barn 2 and also from barn 2 to barn 3(or just from barn 3 to 1,if n=3).
FJ doesn't need to connect all the barns, though, since only certain pairs of cows wish to communicate with each other. He wants to construct as few
connections as possible while still enabling all of these pairs to communicate through the network. Given the list of barns that wish to communicate with each other, determine the minimum number of lines that must be laid. To communicate from barn 1 to barn 3, lines must be laid from barn 1 to barn 2 and also from barn 2 to barn 3(or just from barn 3 to 1,if n=3).
输入格式
* Line 1: Two integers, N and P (the number of communication pairs, 1 <= P <= 10,000)
* Lines 2..P+1: two integers describing a pair of barns between which communication is desired. No pair is duplicated in the list.
* Lines 2..P+1: two integers describing a pair of barns between which communication is desired. No pair is duplicated in the list.
输出格式
One line with a single integer which is the minimum number of direct connections FJ needs to make.
样例 1
输入
5 2 1 3 4 5
输出
3
题目来源：USACO 2002 February；FPS 共享题包，题包内第 1 题。保留原作者与原赛事署名。