The Unique MST
http://poj.org/problem?id=1679
题解：次小生成树
C++版本一
Prim算法
/*
*@Author: STZG
*@Language: C++
*/
//#include
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#include
C++版本二
#include
#include
#include
#define ll long long
#define pb push_back
#define INF 0x3f3f3f3f
#define FI first
#define SE second
#define MP make_pair
#define PI pair
#define lson l,m,rt<<1,ls,rs
#define rson m+1,r,rt<<1|1,ls,rs
#define test printf("here!!!\n")
using namespace std;
const int mx=100+10;
int n,m;
int dis[mx];
int vis[mx];
int mp[mx][mx];
int sum;
int maxd[mx][mx];
int pre[mx];
int connect[mx][mx];
void prim()
{
sum=0;
memset(maxd,0,sizeof(maxd));
memset(connect,0,sizeof(connect));
for (int i=1;i<=n;++i)
{
dis[i]=mp[1][i];
pre[i]=1;
vis[i]=0;
}
dis[1]=0;
vis[1]=1;
int now=1;
for (int i=1;idis[j])
{
minn=dis[j];
now=j;
}
}
sum+=dis[now];
vis[now]=1;
connect[now][pre[now]]=connect[pre[now]][now]=1;
for (int j=1;j<=n;++j)
{
if (vis[j])
{
maxd[j][now]=maxd[now][j]=max(maxd[j][pre[now]],dis[now]);
}
else if (dis[j]>mp[now][j])
{
dis[j]=mp[now][j];
pre[j]=now;
}
}
}
}
int sprim()
{
int ans=INF;
for (int i=1;i<=n;++i)
{
for (int j=i+1;j<=n;++j)
{
if (!connect[i][j]&&mp[i][j]!=INF)
{
ans=min(ans,sum+mp[i][j]-maxd[i][j]);
}
}
}
return ans;
}
int main()
{
int x,y,w,t;
scanf("%d",&t);
while (t--)
{
memset(mp,INF,sizeof(mp));
scanf("%d%d",&n,&m);
for (int i=1;i<=m;++i)
{
scanf("%d%d%d",&x,&y,&w);
mp[x][y]=w;
mp[y][x]=w;
}
prim();
int res=sprim();
if (sum==res) printf("Not Unique!\n");
else printf("%d\n",sum);
}
}
C++版本三
Kruskal算法
#include
#include
#include
#define ll long long
#define pb push_back
#define INF 0x3f3f3f3f
#define FI first
#define SE second
#define MP make_pair
#define PI pair
#define lson l,m,rt<<1,ls,rs
#define rson m+1,r,rt<<1|1,ls,rs
#define test printf("here!!!\n")
using namespace std;
const int mx=1e4+10;
const int MX=5e3+10;
int n,m;
struct Node
{
int st;
int to;
ll w;
friend bool operator <(const Node &a,const Node &b)
{
return a.w>1]+1;
for (int i=1;i<=n;++i)
{
head[i]=0,dis[i]=0,vis[i]=0,pre[i]=i,sz[i]=1;
}
memset(ma,0,sizeof(ma));
memset(fa,0,sizeof(fa));
memset(use,0,sizeof(use));
dis[0]=-1;
}
int unfd(int x)
{
int r=x;
while (r!=pre[r]) r=pre[r];
int t;
while (x!=pre[x])
{
t=pre[x];
pre[x]=r;
x=t;
}
return r;
}
int unjoin(int x,int y)
{
int fx=unfd(x),fy=unfd(y);
if (fx!=fy)
{
if (sz[fx]dis[v])
{
int loog=lg[dis[u]-dis[v]];
maxn=max(ma[u][loog],maxn);
u=fa[u][loog];
}
if (u==v) return maxn;
for (int i=lg[dis[u]];i>=0;--i)
{
if (fa[u][i]!=fa[v][i])
{
maxn=max(max(ma[u][i],ma[v][i]),maxn);
u=fa[u][i];
v=fa[v][i];
}
}
return max(max(ma[u][0],ma[v][0]),maxn);
}
int main()
{
int t;
scanf("%d",&t);
while (t--)
{
scanf("%d%d",&n,&m);
int x,y;
ll z;
init();
for (int i=1;i<=m;++i)
{
scanf("%d%d%lld",&vec[i].st,&vec[i].to,&vec[i].w);
}
sort(vec+1,vec+m+1);
kruskal();
dfs(1,0);
ll ans=0x3f3f3f3f3f3f3f3f;
for (int i=1;i<=m;++i)
{
if (!use[i])
{
ans=min(ans,sum-LCA(vec[i].st,vec[i].to)+vec[i].w);
}
}
if (ans==sum) printf("Not Unique!\n");
else printf("%lld\n",sum);
}
} C++版本四
#include
#include
#include
#include
#include
#define INF 0x3f3f3f3f
using namespace std;
int n,m;
struct data
{
int u,v,w;
bool vis;
} p[20010];
vectorG[110];
int per[110],maxd[110][110];
bool cmp(data a,data b)
{
return a.w < b.w;
}
int Union_Find(int x)
{
return x == per[x] ? x: per[x] = Union_Find(per[x]);
}
void kruskal()
{
sort(p,p+m,cmp);
for(int i=0; i<=n; i++)//初始化
{
G[i].clear();
G[i].push_back(i);
per[i]=i;
}
int sum=0,k=0;//sum是最小生成树的值
for(int i=0; isum)
printf("%d\n",sum);
else
printf("Not Unique!\n");
}
int main()
{
int T;
scanf("%d\n",&T);
while(T--)
{
scanf("%d%d",&n,&m);
for(int i=0; i