maximumflow

int MaximumFlow(const graph& g, int s, int t)
{
	//maximum flow == return value
	int maxflow = 0;

	//res is Residual graph
	vector<vector<int>> res(g.flow.begin(), g.flow.end());
	//parent present where from
	vector<int> parent(g.V, -1);

	//bfs function for search route
	function<bool(int, int)> bfs = [&](int s, int t)->bool{
		//queue for bfs
		queue<int> qu;
		//visited check
		vector<bool> visited(g.V, false);
		//visit function for visit [add queue, visit check, parent check]
		function<void(int, int)> visit = [&](int v, int u)->void {
			qu.push(v);
			visited[v] = true;
			parent[v] = u;
		};

		visit(s, -1);
		while (qu.size())
		{
			int n = qu.front(); qu.pop();

			//for loop n to v
			for (size_t v = 0; v < g.V; v++)
				if (!visited[v] && res[n][v] > 0)
					visit(v, n);
		}

		return visited[t] == true;
	};

	//bfs loop, if (s to t) is true
	while (bfs(s, t))
	{
		//init pathflow INF, for renewal
		int pathflow = INF;
		//renewal pathflow
		for (size_t v = t; v != s; v = parent[v])
			pathflow = min(pathflow, res[parent[v]][v]);

		for (size_t v = t; v != s; v = parent[v])
		{
			res[parent[v]][v] -= pathflow;
			res[v][parent[v]] += pathflow;
		}

		//add pathflow to maxflow
		maxflow += pathflow;
	}

	if (!print)
	{
		vector<size_t> out;
		for (size_t v = t; v + 1;v = parent[v])
			out.push_back(v);
		vector<size_t> rout(out.rbegin(), out.rend());
		for (size_t t : rout)
			cout << t << "->";
		cout << endl;
		print = true;
	}

	//return maxflow
	return maxflow;
}