poj2553 强连通缩点
The Bottom of a Graph
| Time Limit: 3000MS | Memory Limit: 65536K | |
| Total Submissions: 10114 | Accepted: 4184 |
Description
We will use the following (standard) definitions from graph theory. Let V be a nonempty and finite set, its elements being called vertices (or nodes). Let E be a subset of the Cartesian product V×V, its elements being called edges. Then G=(V,E) is called a directed graph.
Let n be a positive integer, and let p=(e1,...,en) be a sequence of length n of edges ei∈E such that ei=(vi,vi+1) for a sequence of vertices (v1,...,vn+1). Then p is called a path from vertex v1 to vertex vn+1 in Gand we say that vn+1 is reachable from v1, writing (v1→vn+1).
Here are some new definitions. A node v in a graph G=(V,E) is called a sink, if for every node w in G that is reachable from v, v is also reachable from w. The bottom of a graph is the subset of all nodes that are sinks, i.e., bottom(G)={v∈V|∀w∈V:(v→w)⇒(w→v)}. You have to calculate the bottom of certain graphs.
Let n be a positive integer, and let p=(e1,...,en) be a sequence of length n of edges ei∈E such that ei=(vi,vi+1) for a sequence of vertices (v1,...,vn+1). Then p is called a path from vertex v1 to vertex vn+1 in Gand we say that vn+1 is reachable from v1, writing (v1→vn+1).
Here are some new definitions. A node v in a graph G=(V,E) is called a sink, if for every node w in G that is reachable from v, v is also reachable from w. The bottom of a graph is the subset of all nodes that are sinks, i.e., bottom(G)={v∈V|∀w∈V:(v→w)⇒(w→v)}. You have to calculate the bottom of certain graphs.
Input
The input contains several test cases, each of which corresponds to a directed graph G. Each test case starts with an integer number v, denoting the number of vertices of G=(V,E), where the vertices will be identified by the integer numbers in the set V={1,...,v}. You may assume that 1<=v<=5000. That is followed by a non-negative integer e and, thereafter, e pairs of vertex identifiers v1,w1,...,ve,we with the meaning that (vi,wi)∈E. There are no edges other than specified by these pairs. The last test case is followed by a zero.
Output
For each test case output the bottom of the specified graph on a single line. To this end, print the numbers of all nodes that are sinks in sorted order separated by a single space character. If the bottom is empty, print an empty line.
Sample Input
3 3 1 3 2 3 3 1 2 1 1 2 0
Sample Output
1 3 2
题意:
n个点，m条边，并且是单向边。求有多少个顶点，满足它能到的点也能够到达它。
思路:
对于强连通中的点，肯定能够互相到达，所以可以强连通缩点，此时只要找到出度为0的点，其连通分量连所有的点就是答案。因为
如果该点的出度不为0，那么肯定有新的该点能够到达的点，由于已经缩点了，不可能出现有强连通的情况，所以出度不为0的点不满足要求。
/* * Author: sweat123 * Created Time: 2016/6/25 14:32:24 * File Name: main.cpp */ #include<set> #include<map> #include<queue> #include<stack> #include<cmath> #include<string> #include<vector> #include<cstdio> #include<time.h> #include<cstring> #include<iostream> #include<algorithm> #define INF 1<<30 #define MOD 1000000007 #define ll long long #define lson l,m,rt<<1 #define rson m+1,r,rt<<1|1 #define pi acos(-1.0) using namespace std; const int MAXN = 5010; struct node{ int from; int to; int next; }edge[MAXN*10]; int pre[MAXN],vis[MAXN],dfn[MAXN],low[MAXN],n,m,ind; int f[MAXN],siz[MAXN],num,dep,out[MAXN],in[MAXN]; stack<int>s; vector<int>p[MAXN]; void add(int x,int y){ edge[ind].from = x; edge[ind].to = y; edge[ind].next = pre[x]; pre[x] = ind ++; } void dfs(int rt){ dfn[rt] = low[rt] = ++dep; vis[rt] = 1; s.push(rt); for(int i = pre[rt]; i != -1; i = edge[i].next){ int t = edge[i].to; if(!dfn[t]){ dfs(t); low[rt] = min(low[rt],low[t]); } else if(vis[t]){ low[rt] = min(low[rt],dfn[t]); } } if(low[rt] == dfn[rt]){ ++num; while(!s.empty()){ int tp = s.top(); s.pop(); vis[tp] = 0; f[tp] = num; siz[num] ++; p[num].push_back(tp); if(tp == rt)break; } } } void setcc(){ num = 0; dep = 0; memset(in,0,sizeof(in)); memset(out,0,sizeof(out)); memset(dfn,0,sizeof(dfn)); memset(low,0,sizeof(low)); for(int i = 1; i <= n; i++){ if(!dfn[i]){ dfs(i); } } memset(pre,-1,sizeof(pre)); int ret = ind; for(int i = 0; i < ret; i++){ int x = f[edge[i].from]; int y = f[edge[i].to]; if(x == y)continue; add(x,y); out[x] ++; in[y] ++; } vector<int>ans; for(int i = 1; i <= num; i++){ if(!out[i]){ for(int j = 0; j < p[i].size(); j++){ ans.push_back(p[i][j]); } } } sort(ans.begin(),ans.end()); for(int i = 0; i < ans.size(); i++){ if(i == 0)printf("%d",ans[i]); else printf(" %d",ans[i]); } printf("\n"); } int main(){ while(~scanf("%d",&n)){ if(n == 0)break; scanf("%d",&m); if(n == 1){ printf("1\n"); continue; } ind = 0; for(int i = 1; i <= n; i++){ p[i].clear(); } memset(pre,-1,sizeof(pre)); while(!s.empty())s.pop(); memset(f,-1,sizeof(f)); memset(siz,0,sizeof(siz)); for(int i = 1; i <= m; i++){ int x,y; scanf("%d%d",&x,&y); add(x,y); } setcc(); } return 0; }
The Bottom of a Graph
| Time Limit: 3000MS | Memory Limit: 65536K | |
| Total Submissions: 10114 | Accepted: 4184 |
Description
We will use the following (standard) definitions from graph theory. Let V be a nonempty and finite set, its elements being called vertices (or nodes). Let E be a subset of the Cartesian product V×V, its elements being called edges. Then G=(V,E) is called a directed graph.
Let n be a positive integer, and let p=(e1,...,en) be a sequence of length n of edges ei∈E such that ei=(vi,vi+1) for a sequence of vertices (v1,...,vn+1). Then p is called a path from vertex v1 to vertex vn+1 in Gand we say that vn+1 is reachable from v1, writing (v1→vn+1).
Here are some new definitions. A node v in a graph G=(V,E) is called a sink, if for every node w in G that is reachable from v, v is also reachable from w. The bottom of a graph is the subset of all nodes that are sinks, i.e., bottom(G)={v∈V|∀w∈V:(v→w)⇒(w→v)}. You have to calculate the bottom of certain graphs.
Let n be a positive integer, and let p=(e1,...,en) be a sequence of length n of edges ei∈E such that ei=(vi,vi+1) for a sequence of vertices (v1,...,vn+1). Then p is called a path from vertex v1 to vertex vn+1 in Gand we say that vn+1 is reachable from v1, writing (v1→vn+1).
Here are some new definitions. A node v in a graph G=(V,E) is called a sink, if for every node w in G that is reachable from v, v is also reachable from w. The bottom of a graph is the subset of all nodes that are sinks, i.e., bottom(G)={v∈V|∀w∈V:(v→w)⇒(w→v)}. You have to calculate the bottom of certain graphs.
Input
The input contains several test cases, each of which corresponds to a directed graph G. Each test case starts with an integer number v, denoting the number of vertices of G=(V,E), where the vertices will be identified by the integer numbers in the set V={1,...,v}. You may assume that 1<=v<=5000. That is followed by a non-negative integer e and, thereafter, e pairs of vertex identifiers v1,w1,...,ve,we with the meaning that (vi,wi)∈E. There are no edges other than specified by these pairs. The last test case is followed by a zero.
Output
For each test case output the bottom of the specified graph on a single line. To this end, print the numbers of all nodes that are sinks in sorted order separated by a single space character. If the bottom is empty, print an empty line.
Sample Input
3 3 1 3 2 3 3 1 2 1 1 2 0
Sample Output
1 3 2
