HDU 1269 迷宫城堡 最大强连通图题解

Posted 2020-09-18 claireyuancy

寻找一个迷宫是否是仅仅有一个最大强连通图。

使用Tarjan算法去求解，经典算法。必需要学习好，要自己创造出来是十分困难的了。

參考资料：https://www.byvoid.com/blog/scc-tarjan/

const int N = 10001;

vector<int> gra[N];
stack<int> stk;
bool inStack[N];
int dfsNum[N];
int backTrackNum[N];
int cur, sum;
int n, m;

void Tarjan(int u)
{
	inStack[u] = true;
	dfsNum[u] = backTrackNum[u] = ++cur;
	stk.push(u);

	for (int i = 0; i < (int)gra[u].size(); i++)
	{
		int v = gra[u][i];
		if (!dfsNum[v]) Tarjan(v), backTrackNum[u] = backTrackNum[v] < backTrackNum[u]? backTrackNum[v] : backTrackNum[u];
		else if (inStack[v]) backTrackNum[u] = backTrackNum[v] < backTrackNum[u]?
 backTrackNum[v] : backTrackNum[u];
	}
	if (backTrackNum[u] == dfsNum[u])
	{
		++sum;
		while (stk.size())
		{
			int v = stk.top(); stk.pop();
			inStack[v] = false;
			if (u == v) break;
		}
	}
}

void solveTarjan()
{
	sum = cur = 0;
	memset(dfsNum, 0, sizeof(dfsNum));
	for (int i = 1; i <= n; i++)
	{
		if (!dfsNum[i]) Tarjan(i);
	}
}

void initGraph()
{
	int a, b;
	for (int i = 1; i <= n; i++) gra[i].clear();//别忘了清空
	for (int i = 0; i < m; i++)
	{
		scanf("%d %d", &a, &b);
		gra[a].push_back(b);
	}
}

int main()
{
	while (scanf("%d %d", &n, &m) && n)
	{
		initGraph();
		solveTarjan();
		if (sum == 1) puts("Yes");
		else puts("No");
	}
	return 0;
}