Dinic'sAlgorithm.cpp

// 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, (int)adj[v].size() };

		// Back edge : 0 flow and 0 capacity
		Edge b{ u, 0, 0, (int)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]{ 0 };

		// 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 Code
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;
}