C/C++，图算法——Dinic最大流量算法

1 文本格式

// C++ implementation of Dinic's Algorithm 
#include<bits/stdc++.h> 
using namespace std;

// A structure to represent a edge between 
// two vertex 
struct Edge
{
    int v;  // Vertex v (or "to" vertex) 
    // of a directed edge u-v. "From" 
    // vertex u can be obtained using 
    // index in adjacent array.

int flow; // flow of data in edge

int C;    // capacity

int rev; // To store index of reverse 
    // edge in adjacency list so that 
    // we can quickly find it. 
};

// Residual Graph 
class Graph
{
    int V; // number of vertex 
    int* level; // stores level of a node 
    vector< Edge >* adj;
public:
    Graph(int V)
    {
        adj = new vector<Edge>[V];
        this->V = V;
        level = new int[V];
    }

// add edge to the graph 
    void addEdge(int u, int v, int C)
    {
        // Forward edge : 0 flow and C capacity 
        Edge a{ v, 0, C, adj[v].size() };

// Back edge : 0 flow and 0 capacity 
        Edge b{ u, 0, 0, adj[u].size() };

adj[u].push_back(a);
        adj[v].push_back(b); // reverse edge 
    }

bool BFS(int s, int t);
    int sendFlow(int s, int flow, int t, int ptr[]);
    int DinicMaxflow(int s, int t);
};

// Finds if more flow can be sent from s to t. 
// Also assigns levels to nodes. 
bool Graph::BFS(int s, int t)
{
    for (int i = 0; i < V; i++)
        level[i] = -1;

level[s] = 0;  // Level of source vertex

// Create a queue, enqueue source vertex 
    // and mark source vertex as visited here 
    // level[] array works as visited array also. 
    list< int > q;
    q.push_back(s);

vector<Edge>::iterator i;
    while (!q.empty())
    {
        int u = q.front();
        q.pop_front();
        for (i = adj[u].begin(); i != adj[u].end(); i++)
        {
            Edge& e = *i;
            if (level[e.v] < 0 && e.flow < e.C)
            {
                // Level of current vertex is, 
                // level of parent + 1 
                level[e.v] = level[u] + 1;

q.push_back(e.v);
            }
        }
    }

// IF we can not reach to the sink we 
    // return false else true 
    return level[t] < 0 ? false : true;
}

// A DFS based function to send flow after BFS has 
// figured out that there is a possible flow and 
// constructed levels. This function called multiple 
// times for a single call of BFS. 
// flow : Current flow send by parent function call 
// start[] : To keep track of next edge to be explored. 
//           start[i] stores  count of edges explored 
//           from i. 
//  u : Current vertex 
//  t : Sink 
int Graph::sendFlow(int u, int flow, int t, int start[])
{
    // Sink reached 
    if (u == t)
        return flow;

// Traverse all adjacent edges one -by - one. 
    for (; start[u] < adj[u].size(); start[u]++)
    {
        // Pick next edge from adjacency list of u 
        Edge& e = adj[u][start[u]];

if (level[e.v] == level[u] + 1 && e.flow < e.C)
        {
            // find minimum flow from u to t 
            int curr_flow = min(flow, e.C - e.flow);

int temp_flow = sendFlow(e.v, curr_flow, t, start);

// flow is greater than zero 
            if (temp_flow > 0)
            {
                // add flow  to current edge 
                e.flow += temp_flow;

// subtract flow from reverse edge 
                // of current edge 
                adj[e.v][e.rev].flow -= temp_flow;
                return temp_flow;
            }
        }
    }

return 0;
}

// Returns maximum flow in graph 
int Graph::DinicMaxflow(int s, int t)
{
    // Corner case 
    if (s == t)
        return -1;

int total = 0;  // Initialize result

// Augment the flow while there is path 
    // from source to sink 
    while (BFS(s, t) == true)
    {
        // store how many edges are visited 
        // from V { 0 to V } 
        int* start = new int[V + 1];

// while flow is not zero in graph from S to D 
        while (int flow = sendFlow(s, INT_MAX, t, start))

// Add path flow to overall flow 
            total += flow;
    }

// return maximum flow 
    return total;
}

// Driver program to test above functions 
int main()
{
    Graph g(6);
    g.addEdge(0, 1, 16);
    g.addEdge(0, 2, 13);
    g.addEdge(1, 2, 10);
    g.addEdge(1, 3, 12);
    g.addEdge(2, 1, 4);
    g.addEdge(2, 4, 14);
    g.addEdge(3, 2, 9);
    g.addEdge(3, 5, 20);
    g.addEdge(4, 3, 7);
    g.addEdge(4, 5, 4);

// next exmp 
    /*g.addEdge(0, 1, 3 );
      g.addEdge(0, 2, 7 ) ;
      g.addEdge(1, 3, 9);
      g.addEdge(1, 4, 9 );
      g.addEdge(2, 1, 9 );
      g.addEdge(2, 4, 9);
      g.addEdge(2, 5, 4);
      g.addEdge(3, 5, 3);
      g.addEdge(4, 5, 7 );
      g.addEdge(0, 4, 10);

// next exp
     g.addEdge(0, 1, 10);
     g.addEdge(0, 2, 10);
     g.addEdge(1, 3, 4 );
     g.addEdge(1, 4, 8 );
     g.addEdge(1, 2, 2 );
     g.addEdge(2, 4, 9 );
     g.addEdge(3, 5, 10 );
     g.addEdge(4, 3, 6 );
     g.addEdge(4, 5, 10 ); */

cout << "Maximum flow " << g.DinicMaxflow(0, 5);
    return 0;
}

2 代码格式

// C++ implementation of Dinic's Algorithm 
#include<bits/stdc++.h> 
using namespace std;

// A structure to represent a edge between 
// two vertex 
struct Edge
{
	int v;  // Vertex v (or "to" vertex) 
	// of a directed edge u-v. "From" 
	// vertex u can be obtained using 
	// index in adjacent array. 

	int flow; // flow of data in edge 

	int C;    // capacity 

	int rev; // To store index of reverse 
	// edge in adjacency list so that 
	// we can quickly find it. 
};

// Residual Graph 
class Graph
{
	int V; // number of vertex 
	int* level; // stores level of a node 
	vector< Edge >* adj;
public:
	Graph(int V)
	{
		adj = new vector<Edge>[V];
		this->V = V;
		level = new int[V];
	}

	// add edge to the graph 
	void addEdge(int u, int v, int C)
	{
		// Forward edge : 0 flow and C capacity 
		Edge a{ v, 0, C, adj[v].size() };

		// Back edge : 0 flow and 0 capacity 
		Edge b{ u, 0, 0, adj[u].size() };

		adj[u].push_back(a);
		adj[v].push_back(b); // reverse edge 
	}

	bool BFS(int s, int t);
	int sendFlow(int s, int flow, int t, int ptr[]);
	int DinicMaxflow(int s, int t);
};

// Finds if more flow can be sent from s to t. 
// Also assigns levels to nodes. 
bool Graph::BFS(int s, int t)
{
	for (int i = 0; i < V; i++)
		level[i] = -1;

	level[s] = 0;  // Level of source vertex 

	// Create a queue, enqueue source vertex 
	// and mark source vertex as visited here 
	// level[] array works as visited array also. 
	list< int > q;
	q.push_back(s);

	vector<Edge>::iterator i;
	while (!q.empty())
	{
		int u = q.front();
		q.pop_front();
		for (i = adj[u].begin(); i != adj[u].end(); i++)
		{
			Edge& e = *i;
			if (level[e.v] < 0 && e.flow < e.C)
			{
				// Level of current vertex is, 
				// level of parent + 1 
				level[e.v] = level[u] + 1;

				q.push_back(e.v);
			}
		}
	}

	// IF we can not reach to the sink we 
	// return false else true 
	return level[t] < 0 ? false : true;
}

// A DFS based function to send flow after BFS has 
// figured out that there is a possible flow and 
// constructed levels. This function called multiple 
// times for a single call of BFS. 
// flow : Current flow send by parent function call 
// start[] : To keep track of next edge to be explored. 
//           start[i] stores  count of edges explored 
//           from i. 
//  u : Current vertex 
//  t : Sink 
int Graph::sendFlow(int u, int flow, int t, int start[])
{
	// Sink reached 
	if (u == t)
		return flow;

	// Traverse all adjacent edges one -by - one. 
	for (; start[u] < adj[u].size(); start[u]++)
	{
		// Pick next edge from adjacency list of u 
		Edge& e = adj[u][start[u]];

		if (level[e.v] == level[u] + 1 && e.flow < e.C)
		{
			// find minimum flow from u to t 
			int curr_flow = min(flow, e.C - e.flow);

			int temp_flow = sendFlow(e.v, curr_flow, t, start);

			// flow is greater than zero 
			if (temp_flow > 0)
			{
				// add flow  to current edge 
				e.flow += temp_flow;

				// subtract flow from reverse edge 
				// of current edge 
				adj[e.v][e.rev].flow -= temp_flow;
				return temp_flow;
			}
		}
	}

	return 0;
}

// Returns maximum flow in graph 
int Graph::DinicMaxflow(int s, int t)
{
	// Corner case 
	if (s == t)
		return -1;

	int total = 0;  // Initialize result 

	// Augment the flow while there is path 
	// from source to sink 
	while (BFS(s, t) == true)
	{
		// store how many edges are visited 
		// from V { 0 to V } 
		int* start = new int[V + 1];

		// while flow is not zero in graph from S to D 
		while (int flow = sendFlow(s, INT_MAX, t, start))

			// Add path flow to overall flow 
			total += flow;
	}

	// return maximum flow 
	return total;
}

// Driver program to test above functions 
int main()
{
	Graph g(6);
	g.addEdge(0, 1, 16);
	g.addEdge(0, 2, 13);
	g.addEdge(1, 2, 10);
	g.addEdge(1, 3, 12);
	g.addEdge(2, 1, 4);
	g.addEdge(2, 4, 14);
	g.addEdge(3, 2, 9);
	g.addEdge(3, 5, 20);
	g.addEdge(4, 3, 7);
	g.addEdge(4, 5, 4);

	// next exmp 
	/*g.addEdge(0, 1, 3 );
	  g.addEdge(0, 2, 7 ) ;
	  g.addEdge(1, 3, 9);
	  g.addEdge(1, 4, 9 );
	  g.addEdge(2, 1, 9 );
	  g.addEdge(2, 4, 9);
	  g.addEdge(2, 5, 4);
	  g.addEdge(3, 5, 3);
	  g.addEdge(4, 5, 7 );
	  g.addEdge(0, 4, 10);

	 // next exp
	 g.addEdge(0, 1, 10);
	 g.addEdge(0, 2, 10);
	 g.addEdge(1, 3, 4 );
	 g.addEdge(1, 4, 8 );
	 g.addEdge(1, 2, 2 );
	 g.addEdge(2, 4, 9 );
	 g.addEdge(3, 5, 10 );
	 g.addEdge(4, 3, 6 );
	 g.addEdge(4, 5, 10 ); */

	cout << "Maximum flow " << g.DinicMaxflow(0, 5);
	return 0;
}