[USACO07DEC]Building Roads S

题目描述

Farmer John had just acquired several new farms! He wants to connect the farms with roads so that he can travel from any farm to any other farm via a sequence of roads; roads already connect some of the farms. Each of the N (1 ≤ N ≤ 1,000) farms (conveniently numbered 1..N) is represented by a position (Xi, Yi) on the plane (0 ≤ Xi ≤ 1,000,000; 0 ≤ Yi ≤ 1,000,000). Given the preexisting M roads (1 ≤ M ≤ 1,000) as pairs of connected farms, help Farmer John determine the smallest length of additional roads he must build to connect all his farms. 给定 $n$ 个点的坐标,第 $i$ 个点的坐标为 $(x_i,y_i)$,这 $n$ 个点编号为 $1$ 到 $n$。给定 $m$ 条边,第 $i$ 条边连接第 $u_i$ 个点和第 $v_i$ 个点。现在要求你添加一些边,并且能使得任意一点都可以连通其他所有点。求添加的边的总长度的最小值。

输入输出格式

输入格式


\* Line 1: Two space-separated integers: N and M \* Lines 2..N+1: Two space-separated integers: Xi and Yi \* Lines N+2..N+M+2: Two space-separated integers: i and j, indicating that there is already a road connecting the farm i and farm j. 第一行两个整数 $n,m$ 代表点数与边数。 接下来 $n$ 行每行两个整数 $x_i,y_i$ 代表第 $i$ 个点的坐标。 接下来 $m$ 行每行两个整数 $u_i,v_i$ 代表第 $i$ 条边连接第 $u_i$ 个点和第 $v_i$ 个点。

输出格式


\* Line 1: Smallest length of additional roads required to connect all farms, printed without rounding to two decimal places. Be sure to calculate distances as 64-bit floating point numbers. 一行一个实数代表添加的边的最小长度,要求保留两位小数,为了避免误差, 请用 $64$ 位实型变量进行计算。

输入输出样例

输入样例 #1

4 1
1 1
3 1
2 3
4 3
1 4

输出样例 #1

4.00

说明

### 数据规模与约定 对于 $100\%$ 的整数,$1 \le n,m \le 1000$,$1 \le x_i,y_i \le 10^6$,$1 \le u_i,v_i \le n$。 ### 说明 Translated by 一只书虫仔。