Ural 1416 Confidential
This post is written in Chinese. Please consider using Google Translate
第一问是求最小生成树,第二问是求次小生成树。如果次小生成树不存在(本身就是一棵树),则输出-1。
/*
* Problem: Ural1416 Confidential
* Author: Guo Jiabao
* Time: 2009.4.14 9:34
* State: Solved
* Memo: 次小生成树 Prim
*/
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
const int MAXN=501,MAXM=MAXN*MAXN*4,INF=0x7FFFFFFF;
using namespace std;
struct edge
{
edge *next,*op;
int t,c;
bool mst;
}ES[MAXM],*V[MAXN],*MST[MAXN],*CLS[MAXN];
int N,M,EC=-1,MinST,Ans,NMST;
int DM[MAXN],F[MAXN];
inline void addedge(edge **V,int a,int b,int c)
{
ES[++EC].next=V[a];
V[a]=ES+EC; V[a]->t=b; V[a]->c=c;
ES[++EC].next=V[b];
V[b]=ES+EC; V[b]->t=a; V[b]->c=c;
V[a]->op=V[b]; V[b]->op=V[a];
V[a]->mst=V[b]->mst=false;
}
void init()
{
int i,a,b,c;
freopen("conf.in","r",stdin);
freopen("conf.out","w",stdout);
scanf("%d%d",&N,&M);
for (i=1;i<=M;i++)
{
scanf("%d%d%d",&a,&b,&c);
addedge(V,a,b,c);
}
Ans=INF;
}
void prim()
{
int i,j,Mini;
for (i=1;i<=N;i++)
DM[i]=INF;
for (i=1;i;)
{
DM[i]=-INF;
for (edge *e=V[i];e;e=e->next)
{
if (e->c < DM[j=e->t])
{
DM[j]=e->c;
CLS[j]=e->op;
}
}
Mini=INF;i=0;
for (j=1;j<=N;j++)
if (DM[j]!=-INF && DM[j]<Mini)
{
Mini=DM[j];
i=j;
}
}
for (i=2;i<=N;i++)
{
MinST+=CLS[i]->c;
CLS[i]->mst=CLS[i]->op->mst=true;
addedge(MST,CLS[i]->t,CLS[i]->op->t,CLS[i]->c);
}
}
void dfs(int i)
{
for (edge *e=MST[i];e;e=e->next)
{
int j=e->t;
if (F[j]==-INF)
{
F[j]=F[i];
if (e->c > F[j])
F[j]=e->c;
dfs(j);
}
}
}
void smst()
{
int i,j;
for (i=1;i<=N;i++)
{
for (j=1;j<=N;j++)
F[j]=-INF;
F[i]++;
dfs(i);
for (edge *e=V[i];e;e=e->next)
{
if (!e->mst)
{
NMST=MinST + e->c -F[e->t];
if (NMST < Ans)
Ans=NMST;
}
}
}
}
int main()
{
init();
prim();
smst();
if (Ans==INF)
Ans=-1;
printf("Cost: %dnCost: %dn",MinST,Ans);
return 0;
}