O - Highways
Time Limit:1000MS Memory Limit:10000KB 64bit IO Format:%I64d & %I64u
Submit
Status
Description
The island nation of Flatopia is perfectly flat. Unfortunately, Flatopia has a very poor system of public highways. The Flatopian government is aware of this problem and has already constructed a number of highways connecting some of the most important towns. However, there are still some towns that you can't reach via a highway. It is necessary to build more highways so that it will be possible to drive between any pair of towns without leaving the highway system.
Flatopian towns are numbered from 1 to N and town i has a position given by the Cartesian coordinates (xi, yi). Each highway connects exaclty two towns. All highways (both the original ones and the ones that are to be built) follow straight lines, and thus their length is equal to Cartesian distance between towns. All highways can be used in both directions. Highways can freely cross each other, but a driver can only switch between highways at a town that is located at the end of both highways.
The Flatopian government wants to minimize the cost of building new highways. However, they want to guarantee that every town is highway-reachable from every other town. Since Flatopia is so flat, the cost of a highway is always proportional to its length. Thus, the least expensive highway system will be the one that minimizes the total highways length.
Output
Write to the output a single line for each new highway that should be built in order to connect all towns with minimal possible total length of new highways. Each highway should be presented by printing town numbers that this highway connects, separated by a space.
If no new highways need to be built (all towns are already connected), then the output file should be created but it should be empty.
F
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
const int MAXN=850;
double xx[MAXN];
double yy[MAXN];
int rcd[MAXN];
int fa[MAXN];
struct load
{
int u,v;double w;
}aa[MAXN*MAXN/2];
int en,ens;
int cmp(load a,load b){return a.w<b.w;}
double dist(int a,int b)
{
return sqrt((xx[a]-xx[b])*(xx[a]-xx[b])+(yy[a]-yy[b])*(yy[a]-yy[b]));
}
int _find(int x)
{
if(x!=fa[x])
fa[x]=_find(fa[x]);
return fa[x];
}
void kual(int n,int m)
{
ens=0;
int i,cnt=0,last,a,b;
for(i=1;i<=n;i++)fa[i]=i;
sort(aa,aa+m,cmp);
for(i=0;i<m;i++)
{
int x=_find(aa[i].u);
int y=_find(aa[i].v);
if(x!=y)
{
fa[x]=y;
if(aa[i].w)printf("%d %d\n",aa[i].u,aa[i].v);
cnt++;
}
if(cnt==n-1)break;
}
}
int main()
{
int n,i,j,last;
while(~scanf("%d",&n))
{
if(n==1){scanf("%d",&n);for(i=1;i<=n;i++)scanf("%d",&j);continue;}
en=0;
for(i=1;i<=n;i++)
scanf("%lf%lf",&xx[i],&yy[i]);
for(i=1;i<n;i++)
for(j=i+1;j<=n;j++)
{
aa[en].u=i;aa[en].v=j;
aa[en++].w=dist(i,j);
}
scanf("%d",&last);
for(i=0;i<last;i++)
{
scanf("%d%d",&aa[en].u,&aa[en].v);
aa[en++].w=0;
}
kual(n,en);
}
return 0;
}
