Dinic's Algorithm (maxflow)

vector<int> level, edge_begin;
vector<vector<edge>> edges;

// Simple BFS calculating distance of each vertex from the source
bool level_bfs(int s, int t)
{
    fill(level.begin(), level.end(), -1);
    level[s] = 0;

    queue<int> Q;
    Q.push(s);

    while (!Q.empty())
    {
        int from = Q.front();
        Q.pop();

        for (edge& e : edges[from])
            if (level[e.to] < 0 && e.flow < e.capacity)
            {
                level[e.to] = level[from] + 1;
                Q.push(e.to);
            }
    }

    // Return true if the target is reachable from the source
    return level[t] != -1;
}

// Recursion to push flow from a parent vertex to the target
int push_flow(int from, int t, int flow)
{
    if (from == t)
        return flow;

    // Iterate untraversed edges to find a subpath to the target with positive capacity
    for (; edge_begin[from] < edges[from].size(); edge_begin[from]++)
    {
        edge& e = edges[from][edge_begin[from]];

        // Ascertain foward motion and sufficient capcity
        if (level[e.to] == level[from] + 1 && e.flow < e.capacity)
        {
            int subpath_flow = push_flow(e.to, t, min(flow, e.capacity - e.flow));

            // Update the flow with the positive capacity subpath, if such has been found
            if (subpath_flow > 0)
            {
                e.flow += subpath_flow;
                edges[e.to][e.rev].flow -= subpath_flow;
                return subpath_flow;
            }
        }
    }

    // No positive capacity subpath found
    return 0;
}

// Find the maximum flow of a directed graph
int Dinic(int s, int t)
{
    // Assumes source can't be the target
    int result = 0;

    // Keep pushing flows until unable to reach the target from the source
    while (level_bfs(s, t))
    {
        // Reset current edge iteration for all vertexes
        fill(edge_begin.begin(), edge_begin.end(), 0);

        while (int flow = push_flow(s, t, INT_MAX))
            result += flow;
    }

    return result;
}