POJ_3694_Network

最新推荐文章于 2020-09-18 11:42:25 发布

原创最新推荐文章于 2020-09-18 11:42:25 发布 · 220 阅读

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#poj #cut point and bridge

本文深入解析桥连图算法的核心原理及其实现细节，通过具体代码实例展示了如何利用该算法识别图中的桥边和割点，进而解决相关问题。详细介绍了算法的递归过程和关键步骤，旨在帮助开发者理解和应用这一经典算法于实际场景。

#include<iostream>
#include<sstream>
#include<vector>
#include<string>
#include<map>
#include<algorithm>
#pragma warning(disable:4996)
#include<cmath>
#include<ctime>
using std::cin;
using std::cout;
using std::endl;
using std::stringstream;
using std::vector;
using std::string;
using std::map;
using std::sort;
//对于每个连同块取一个点x调用cur_bridge(x,-1,0,邻接矩阵，桥，割点，祖先，深度，访问)
void cut_bridge(int curvex, int parvex, int curdepth, const vector<vector<bool>>&matrix, vector<vector<bool>>&bridge, vector<bool>&cut, vector<int>&ancestor, vector<int>&depth, vector<int>&vis)
{
	vis[curvex] = 1;
	depth[curvex] = ancestor[curvex] = curdepth;
	int children = 0;
	for (size_t i = 1; i < matrix.size(); i++)
	{
		if (matrix[curvex][i])
		{
			if (i != parvex && 1 == vis[i])
			{
				if (depth[i] < ancestor[curvex])
				{
					ancestor[curvex] = depth[i];
				}
			}
			if (!vis[i])
			{
				cut_bridge(i, curvex, curdepth + 1, matrix, bridge, cut, ancestor, depth, vis);
				children++;
				if (ancestor[i] < ancestor[curvex])
				{
					ancestor[curvex] = ancestor[i];
				}
				if ((parvex == -1 && children>1) || (parvex != -1 && ancestor[i] >= depth[curvex]))
				{
					cut[curvex] = true;
				}
				if (ancestor[i] > depth[curvex])
				{
					bridge[curvex][i] = bridge[i][curvex] = true;
				}
			}
		}
	}
	vis[curvex] = 2;
}
int main()
{
	//freopen("input.txt", "r", stdin);
	//freopen("output.txt", "w", stdout);
	int n;
	while (cin >> n)
	{
		if (!n)
		{
			break;
		}
		vector<vector<bool>>matrix(n + 1, (vector<bool>)(n + 1));
		vector<vector<bool>>bridge(n + 1, (vector<bool>)(n + 1));
		vector<bool>cut(n + 1);
		vector<int>ancestor(n + 1), depth(n + 1), vis(n + 1);
		while (cin >> n)
		{
			if (!n)
			{
				break;
			}
			string str; getline(cin, str);
			stringstream stream; stream << str;
			int m;
			while (stream >> m)
			{
				matrix[n][m] = matrix[m][n] = true;
			}
		}
		cut_bridge(1, -1, 0, matrix, bridge, cut, ancestor, depth, vis);
		int count = 0;
		for (size_t i = 0; i < cut.size(); i++)
		{
			if (cut[i])
			{
				count++;
			}
		}
		cout << count << endl;
	}
	return 0;
}