题目链接:
http://poj.org/problem?id=2553
The Bottom of a Graph
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. 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). 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 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 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 Source |
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题目意思:
给一幅有向图,求这样的节点i的集合,使得如果i到其他任意节点j可达的话,j也有路劲可达i。
解题思路:
tarjan+缩点+统计出度为0的强连通分量,并输出其中的节点。
代码:
//#include<CSpreadSheet.h> #include<iostream> #include<cmath> #include<cstdio> #include<sstream> #include<cstdlib> #include<string> #include<string.h> #include<cstring> #include<algorithm> #include<vector> #include<map> #include<set> #include<stack> #include<list> #include<queue> #include<ctime> #include<bitset> #include<cmath> #define eps 1e-6 #define INF 0x3f3f3f3f #define PI acos(-1.0) #define ll __int64 #define LL long long #define lson l,m,(rt<<1) #define rson m+1,r,(rt<<1)|1 #define M 1000000007 //#pragma comment(linker, "/STACK:1024000000,1024000000") using namespace std; #define Maxn 5500 int low[Maxn],dfn[Maxn],sta[Maxn],n,m; int dep,bc,sc,in[Maxn]; bool iss[Maxn]; vector<vector<int> >myv; int de[Maxn]; void tarjan(int cur) { int ne; low[cur]=dfn[cur]=++dep; sta[++sc]=cur; iss[cur]=true; for(int i=0;i<myv[cur].size();i++) { ne=myv[cur][i]; if(!dfn[ne]) { tarjan(ne); low[cur]=min(low[cur],low[ne]); } else if(iss[ne]&&dfn[ne]<low[cur]) low[cur]=dfn[ne]; } if(low[cur]==dfn[cur]) { bc++; do { ne=sta[sc--]; in[ne]=bc; iss[ne]=false; }while(ne!=cur); } } void solve() { sc=bc=dep=0; memset(iss,false,sizeof(iss)); memset(dfn,0,sizeof(dfn)); for(int i=1;i<=n;i++) if(!dfn[i]) tarjan(i); } int main() { //freopen("in.txt","r",stdin); //freopen("out.txt","w",stdout); while(scanf("%d",&n)&&n) { scanf("%d",&m); myv.clear(); myv.resize(n+1); for(int i=1;i<=m;i++) { int a,b; scanf("%d%d",&a,&b); myv[a].push_back(b); } solve(); memset(de,0,sizeof(de)); for(int i=1;i<=n;i++) { for(int j=0;j<myv[i].size();j++) { int ne=myv[i][j]; if(in[i]!=in[ne]) de[in[i]]++; } } bool fi=true; for(int i=1;i<=n;i++) { if(!de[in[i]]) { if(!fi) putchar(' '); else fi=false; printf("%d",i); } } printf("\n"); } return 0; }