poj_1236_Network of Schools

最新推荐文章于 2024-02-06 19:17:23 发布

cxy7tv

最新推荐文章于 2024-02-06 19:17:23 发布

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CC 4.0 BY-SA版权

文章标签： poj SCC

本文链接：https://blog.youkuaiyun.com/cxy7tv/article/details/51147077

本文介绍了一种基于Tarjan算法实现的强连通分量检测方法，并通过具体的C++实现展示了如何找到图中的所有强连通分量及它们之间的连接特性。此外，还讨论了如何基于这些信息来确定图中的顶点是否有出入边。

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<pre name="code" class="cpp">#include<iostream>    
#include<cstdio>    
#include<sstream>        
#include<string>        
#include<vector>        
#include<list>        
#include<set>        
#include<map>        
#include<stack>        
#include<queue>        
#include<algorithm>        
#include<cmath>        
#pragma warning(disable:4996)        
using std::cin;  
using std::cout;  
using std::endl;  
using std::stringstream;  
using std::string;  
using std::vector;  
using std::list;  
using std::pair;  
using std::set;  
using std::multiset;  
using std::map;  
using std::multimap;  
using std::stack;  
using std::queue;  
class Graph  
{  
public:  
int vertex;//总结点数  
int edge;//总边数  
int SCC;//强联通分量数  
vector<vector<int> >adjList;//邻接表  
vector<int>represent_SCC;//每个强联通分量的代表元素  
map<int, int>SCcomponents;//强连同分量  
Graph()  
{  
vertex = edge = SCC = 0;  
}  
//curpath表示搜索的时间  
void tarjan_sub(vector<int>&depth, vector<int>&ancestor, stack<int>&Stack, vector<bool>&visited, vector<bool>&inStack, const int &curvertex, int &time)  
{  
visited[curvertex] = true;  
inStack[curvertex] = true;  
depth[curvertex] = ancestor[curvertex] = time++;  
Stack.push(curvertex);  
for (size_t i = 0; i < adjList[curvertex].size(); i++)  
{  
if (!visited[adjList[curvertex][i]])//如果邻接点没被访问过  
{  
tarjan_sub(depth, ancestor, Stack, visited, inStack, adjList[curvertex][i], time);  
ancestor[curvertex] = std::min(ancestor[curvertex], ancestor[adjList[curvertex][i]]);  
}  
else if (inStack[adjList[curvertex][i]])//如果邻接点在之前已经被加入堆栈中  
{  
ancestor[curvertex] = std::min(ancestor[curvertex], depth[adjList[curvertex][i]]);  
}  
}  
if (ancestor[curvertex] == depth[curvertex])  
{  
SCC++;  
represent_SCC.push_back(curvertex);  
while (true)  
{  
inStack[Stack.top()] = false;  
SCcomponents.insert({ Stack.top(),curvertex });  
if (curvertex == Stack.top())  
{  
Stack.pop();  
break;  
}  
Stack.pop();  
}  
}  
}  
void tarjan_main()  
{  
vector<int>depth(vertex + 1, 0), ancestor(vertex + 1, 0);  
stack<int>Stack;  
vector<bool>inStack(vertex + 1, false);  
vector<bool>visited(vertex + 1, false);  
int time = 1;  
for (int curvertex = 1; curvertex <= vertex; curvertex++)  
{  
if (!visited[curvertex])  
{  
tarjan_sub(depth, ancestor, Stack, visited, inStack, curvertex, time);  
}  
}  
}  
pair<int, int>getDegree()  
{  
if (SCC == 1)  
{  
return{ 1,0 };  
}  
vector<pair<int, int> >degree(vertex + 1);//first为出度，second为入度  
set<pair<int, int> >Set;  
for (size_t i = 1; i < adjList.size(); i++)  
{  
for (size_t j = 0; j < adjList[i].size(); j++)  
{  
int initial = SCcomponents.find(i)->second;  
int terminal = SCcomponents.find(adjList[i][j])->second;  
if (initial != terminal&&Set.find({ initial,terminal }) == Set.end())//如果该边的两个点处于两个不同的强联通量中  
{  
Set.insert({ initial,terminal });  
degree[initial].first++;  
degree[terminal].second++;  
}  
}  
}  
int noOutDegree = 0, noInDegree = 0;  
for (size_t i = 0; i < represent_SCC.size(); i++)  
{  
if (!degree[represent_SCC[i]].first)  
{  
noOutDegree++;  
}  
if (!degree[represent_SCC[i]].second)  
{  
noInDegree++;  
}  
}  
return{ noInDegree,std::max(noInDegree,noOutDegree) };  
}  
};  
int main()  
{  
//freopen("input.txt", "r", stdin);  
//freopen("output.txt", "w", stdout);  
int n;  
while (cin >> n)  
{  
Graph graph;  
graph.vertex = n;  
graph.adjList.resize(n + 1);  
for (int i = 1; i <= n; i++)  
{  
while (1)  
{  
int vertex; cin >> vertex; if (!vertex) { break; }  
graph.edge++;  
graph.adjList[i].push_back(vertex);  
}  
}  
graph.tarjan_main();//得到图的几个强联通子图  
pair<int, int> result = graph.getDegree();  
cout << result.first << endl;  
cout << result.second << endl;  
}  
return 0;  
}