POJ 2553 The Bottom of a Graph 强连通分量+缩点 tarjan or kosaraju

题目的意思是求有向图中满足“自己可达的顶点都能到达自己”的顶点个数

显然，在一个强连通分量中，每个点都符合要求，但是 如果强连通分量中有某个点跟外面的某个点相连了，这个强连通分量就不符合要求了，很显然，外面的点是无法回到这个点上的，如果能回到这个点，就是强连通分量中的一员了，这是矛盾的。

那么结论就是，缩点后，求出度为0的强连通分量中的顶点。

tarjan写的

#include <iostream>
#include <map>
#include <cstdio>
#include <stack>
#include <cstring>
#include <algorithm>
#define MAXN 5005
#define MAXM 50005
#define INF 1000000000
using namespace std;
int n, m;
int scc;//强连通分量
int index;//每个节点的dfs访问次序编号
int dfn[MAXN];//标记结点i的dfs访问次序
int low[MAXN];//记录节点u或u的子树中的所有节点的最小标号
int fa[MAXN];//属于哪个分支
bool instack[MAXN];//是否在栈中
int in[MAXN], head[MAXN], e;
int out[MAXN];//出度
stack <int>s;
struct Edge
{
    int v, next;
}edge[MAXM];
void insert(int x, int y)
{
    edge[e].v = y;
    edge[e].next = head[x];
    head[x] = e++;
}
void tarjan(int u)
{
    dfn[u] = low[u] = ++index;
    s.push(u);
    instack[u] = true;
    for (int j = head[u]; j != -1; j = edge[j].next)
    {
        int v = edge[j].v;
        if(dfn[v] == 0)//未曾访问过
        {
            tarjan(v);
            low[u] = min(low[u], low[v]);
        }
        else if(instack[v])
            low[u] = min(low[u], dfn[v]);
    }
    if(dfn[u] == low[u])
    {
        scc++;
        while(1)
        {
            int tmp = s.top();
            s.pop();
            instack[tmp] = 0;
            fa[tmp] = scc;
            if(tmp == u) break;
        }
    }
}
void init()
{
    scc = index = 0;
    memset(dfn, 0, sizeof(dfn));
    memset(instack, 0, sizeof(instack));
    e = 0;
    memset(head, -1, sizeof(head));
    memset(in, 0, sizeof(in));
    memset(out, 0, sizeof(out));

}
void solve()
{
    for (int i = 1;i <= n; i++)
    {
        if (!dfn[i])
            tarjan(i);
    }
    for (int i = 1;i <= n; i++)
    {
        for(int j = head[i]; j != -1; j = edge[j].next)
        {
            int u = fa[i];
            int v = fa[edge[j].v];
            if(u != v)
            {
                out[u]++;
                in[v]++;
            }
        }
    }
    for(int i = 1; i <= n; i++)
    if(out[fa[i]] == 0) printf("%d ", i);
    printf("\n");
}

int main()
{
    int x, y;
    while(scanf("%d", &n) != EOF && n)
    {
        init();
        scanf("%d", &m);
        while(m--)
        {
            scanf("%d%d", &x, &y);
            insert(x, y);
        }
        solve();
    }
    return 0;
}

 

用Kosaraju写的

 

/*
ID: sdj22251
PROG: subset
LANG: C++
*/
#include <iostream>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <cstring>
#include <cmath>
#include <ctime>
#define LOCA
#define MAXN 5005
#define INF 100000000
#define eps 1e-7
using namespace std;
struct Edge
{
    int v, next;
}edge[10 * MAXN], revedge[10 * MAXN];
int head[MAXN], revhead[MAXN], e, visited[MAXN];
int order[MAXN], cnt, id[MAXN], used[MAXN];
int uu[5 * MAXN], vv[5 * MAXN], out[MAXN], pos;
int n, m;
void init()
{
    e = 0;
    memset(head, -1, sizeof(head));
    memset(revhead, -1, sizeof(revhead));
    memset(out, 0 , sizeof(out));
    memset(used, 0, sizeof(used));
}
void insert(const int &x, const int &y)
{
    edge[e].v = y;
    edge[e].next = head[x];
    head[x] = e;
    revedge[e].v = x;
    revedge[e].next = revhead[y];
    revhead[y] = e;
    e++;
}
void readdata()
{
    for(int i = 0; i < m; i++)
    {
        scanf("%d%d", &uu[i], &vv[i]);
        insert(uu[i], vv[i]);
    }
}
void dfs(int u)
{
    visited[u] = 1;
    for(int i = head[u]; i != -1; i = edge[i].next)
    {
        int v = edge[i].v;
        if(!visited[v])
            dfs(v);
    }
    order[cnt++] = u;
}
void dfs_rev(int u)
{
    visited[u] = 1;
    id[u] = cnt;
    for(int i = revhead[u]; i != -1; i = revedge[i].next)
    {
        int v = revedge[i].v;
        if(!visited[v])
            dfs_rev(v);
    }
}
void Kosaraju()
{
    init();
    readdata();
    memset(visited, 0, sizeof(visited));
    cnt = 0;
    for(int i = 1; i <= n; i++)
    {
        if(!visited[i])
            dfs(i);
    }
    memset(visited, 0, sizeof(visited));
    cnt = 0;
    for(int i = n - 1; i >= 0; i--)
    {
        if(!visited[order[i]])
        {
            cnt++;
            dfs_rev(order[i]);
        }
    }
    for(int i = 0; i < m; i++)
    {
        int u = id[uu[i]];
        int v = id[vv[i]];
        if(u != v) out[u]++;
    }
    for(int i = 1; i <= cnt; i++)
    {
        if(out[i] == 0)
        {
            used[i] = 1;
        }
    }
}
int main()
{
    while(scanf("%d", &n) != EOF && n)
    {
        scanf("%d", &m);
        Kosaraju();
        int ans[MAXN];
        int ct = 0;
        for(int i = 1; i <= n; i++)
        {
            int t = id[i];
            if(used[t] == 1)
                ans[ct++] = i;
        }
        if(ct == 0) printf("\n");
        else
        {
            for(int i = 0; i < ct - 1; i++)
            printf("%d ", ans[i]);
            printf("%d\n", ans[ct - 1]);
        }
    }
    return 0;
}