1236题意:一个有向图,1,求至少从几个点出发可以遍历该图,2:,求至少添加多少边,使强连通。而,HDU的只有后面一问。
解;先缩点,第一问只需找所有入度为0的点即可。,第2问,max(入度为0的点,出度为0点)。也写了2个小时。。虽然1A,但是因为细节卡了,不应该。
代码详细说:
#include<iostream> //0ms 1A poj1236
#include<vector>
#include<cstdio>
#include<cstring>
#include<stack>
using namespace std;
int n;
vector<vector<int> >edges(101);
int visited[101];
int low[101];
int dfn[101];
int ind[101];int outd[101]; //统计出入度
int Strongly_connected_branch[101]; //并为一个强连通,标记为1.2.3...
int num;int times;
stack<int>s;
bool instack[101];
void tarjan(int u) //dfs
{
low[u]=dfn[u]=times++;
instack[u]=1;
s.push(u);
int len=edges[u].size();
for(int i=0;i<len;i++)
{
int v=edges[u][i];
if(visited[v]==0) //小心细节!
{
visited[v]=1;
tarjan(v);
if(low[u]>low[v])low[u]=low[v];
}
else if(instack[v]&&low[u]>dfn[v]) //有向图,要问是否在栈中,后向边,V为U某个祖先
{
low[u]=dfn[v];
}
}
if(dfn[u]==low[u]) //在一个SCC
{
num++;int temp;
do
{
temp=s.top();
instack[temp]=0;
s.pop();
Strongly_connected_branch[temp]=num;
} while(temp!=u);
}
}
void readin() //读入数据
{
scanf("%d",&n);
int to;
for(int i=1;i<=n;i++)
{
scanf("%d",&to);
while(to!=0)
{
edges[i].push_back(to);
scanf("%d",&to);
}
}
}
int ind0,outd0;
void initialize() //初始化
{
ind0=outd0=num=times=0;
}
void solve()
{
for(int i=1;i<=n;i++) //原图未必连通
if(visited[i]==0)
{
visited[i]=1;
tarjan(i);
}
for(int i=1;i<=n;i++) //自己思得:枚举所有边,在不同scc中的,这样统计其出入度,缩点只是把所有SCC分开
{ //这样统计,出入度为0的肯定没问题,但是是收缩后的图(原图中有几条边SCC间连任连几条)的出入度,
int len=edges[i].size();
for(int j=0;j<len;j++)
{
int v=edges[i][j];
if(Strongly_connected_branch[v]!=Strongly_connected_branch[i])
{
outd[Strongly_connected_branch[i]]++;
ind[Strongly_connected_branch[v]]++;
}
}
}
for(int i=1;i<=num;i++)
{
//cout<<"out:"<<outd[i]<<"in:"<<ind[i]<<endl;
if(outd[i]==0)outd0++;
if(ind[i]==0)ind0++;
}
}
int main()
{
readin();
initialize();
solve();
int max0=outd0;
if(num==1){printf("1\n0\n");return 0 ;} //如果原来就强连通,特判
if(ind0>max0)max0=ind0;
printf("%d\n%d\n",ind0,max0);
return 0;
}
#include<iostream> //hdu 260ms
#include<vector>
#include<cstdio>
#include<cstring>
#include<stack>
using namespace std;
int n;int m;
vector<vector<int> >edges(20001);
int visited[20001];
int low[20001];
int dfn[20001];
int ind[20001];int outd[20001]; //统计出入度
int Strongly_connected_branch[20001]; //并为一个强连通,标记为1.2.3...
int num;int times;
stack<int>s;
bool instack[20001];
void tarjan(int u)
{
low[u]=dfn[u]=times++;
instack[u]=1;
s.push(u);
int len=edges[u].size();
for(int i=0;i<len;i++)
{
int v=edges[u][i];
if(visited[v]==0)
{
visited[v]=1;
tarjan(v);
if(low[u]>low[v])low[u]=low[v];
}
else if(instack[v]&&low[u]>dfn[v]) //有向图,要问是否在栈中,后向边,V为U某个祖先
{
low[u]=dfn[v];
}
}
if(dfn[u]==low[u]) //在一个SCC
{
num++;int temp;
do
{
temp=s.top();
instack[temp]=0;
s.pop();
Strongly_connected_branch[temp]=num;
} while(temp!=u);
}
}
void readin()
{
scanf("%d%d",&n,&m);
int from,to;
for(int i=1;i<=m;i++)
{
scanf("%d%d",&from,&to);
edges[from].push_back(to);
}
}
int ind0,outd0;
void initialize() //多组数据,必需初始化
{
ind0=outd0=num=times=0;
for(int i=0;i<=n;i++)
{
instack[i]=low[i]=dfn[i]=visited[i]=ind[i]=outd[i]=0;
edges[i].clear();
Strongly_connected_branch[i]=-1;
}
}
void solve()
{
for(int i=1;i<=n;i++)
if(visited[i]==0)
{
visited[i]=1;
tarjan(i);
}
for(int i=1;i<=n;i++) //自己思得:枚举所有边,在不同scc中的,这样统计其出入度,缩点只是把所有SCC分开
{ //这样统计,出入度为0的肯定没问题,但是是收缩后的图(原图中有几条边SCC间连任连几条)的出入度,
int len=edges[i].size();
for(int j=0;j<len;j++)
{
int v=edges[i][j];
if(Strongly_connected_branch[v]!=Strongly_connected_branch[i])
{
outd[Strongly_connected_branch[i]]++;
ind[Strongly_connected_branch[v]]++;
}
}
}
for(int i=1;i<=num;i++)
{
if(outd[i]==0)outd0++;
if(ind[i]==0)ind0++;
}
}
int main()
{
int tcase;
scanf("%d",&tcase);
while(tcase--)
{
initialize();
readin();
solve();
int max0=outd0;
if(num==1){printf("0\n");continue;}
if(ind0>max0)max0=ind0;
printf("%d\n",max0);
}
return 0;
}