P3387 【模板】缩点

强连通分量

缩点

拓扑排序

DAG dp

#include 
#include 
#include 
#include 
#include 
#include 

using namespace std;

const int MAXN = 10001;

vector Edge[MAXN];
vector NewEdge[MAXN];

int PreWeight[MAXN] = {0};
int NewWeight[MAXN] = {0};

int DP[MAXN];

int DFN[MAXN];
int Low[MAXN];
bool Vis[MAXN];
int Belong[MAXN];
stack Stack;
int idx = 0;
int Color = 0;
int N,M;

void AddEdge(int u,int v)
{
	Edge[u].push_back(v);
} 

void AddNewEdge(int u,int v)
{
	NewEdge[u].push_back(v);
}

void Tarjan(int u)
{
	DFN[u] = Low[u] = ++idx;
	Stack.push(u);
	
	Vis[u] = true;
	
	int size = Edge[u].size();
	for(int i = 0;i < size;i++)
	{
		int v = Edge[u][i];
		if(!DFN[v])
		{
			Tarjan(v);
			Low[u] = min(Low[u],Low[v]);
		}
		else if(Vis[v])
		{
			Low[u] = min(Low[u],DFN[v]);
		}
	}
	
	if(DFN[u] == Low[u])
	{
		Color++;
		int cur = -1;
		while(cur != u)
		{
			cur = Stack.top();
			Stack.pop();
			Belong[cur] = Color;
			Vis[cur] = 0;
			//获得强联通块的权值 
			NewWeight[Color] += PreWeight[cur];
		}
	}
}

inline int Topo(void)
{
	queue Que;
	int In[MAXN] = {0};
	
	for(int i = 1;i <= Color;i++)
	{
		for(int j = 0;j < NewEdge[i].size();j++)
		{
			int v = NewEdge[i][j];
			In[v]++;
		}
	}
	for(int i = 1;i <= Color;i++)
	{
		if(In[i] == 0)
		{
			Que.push(i);
            //DP初始值
			DP[i] = NewWeight[i];
		}
	}
	int ans = 0;
	while(Que.size())
	{
		int v = Que.front();
		Que.pop();
		
		for(int i = 0;i < NewEdge[v].size();i++)
		{
			int Now = NewEdge[v][i];
			
			DP[Now] = max(DP[Now],DP[v]+NewWeight[Now]);
			In[Now]--;
			if(In[Now] == 0)
			{
				Que.push(Now);
			}
		}
	}
	for(int i = 1;i <= Color;i++)
	{
		ans = max(ans,DP[i]);
	}
	return ans;
}

int main(void)
{
	cin >> N >> M;
	
	for(int i = 1;i <= N;i++)
	{
		cin >> PreWeight[i];
	}
	
	for(int i = 1;i <= M;i++)
	{
		int u,v;
		cin >> u >> v; 
		AddEdge(u,v);
	}
	
	for(int i = 1;i <= N;i++)
	{
		if(!DFN[i])
		{
			Tarjan(i);
		}
	}
	
	for(int u = 1;u <= N;u++)
	{
		int size = Edge[u].size();
		for(int j = 0;j < size;j++)
		{
			int v = Edge[u][j];
			if(Belong[u] != Belong[v])
			{
				AddNewEdge(Belong[u],Belong[v]);
			}
		}
	}
	
	int res = 0;
	res = Topo();
	cout << res << endl;
	return 0;
}