Dinic Algorithm to solve max flow problem

//
//  main.cpp
//  Dinic
//
//  Created by Longxiang Lyu on 8/12/16.
//  Copyright © 2016 Longxiang Lyu. All rights reserved.
//
// reference:
// https://sites.google.com/site/indy256/algo_cpp/dinic_flow
// the example is from wikipedia page:
// https://en.wikipedia.org/wiki/Dinic%27s_algorithm
// the prove for dinic can be found at:
// http://cseweb.ucsd.edu/classes/sp11/cse202-a/lecture8-final.pdf
// this algorithm is proved to run in O(m*n*n) time


#include 
#include 
#include 
#include 
#include 

using namespace std;



bool dinic_bfs(vector> &graph, vector &dist, int src, int dest)
{
    int V = static_cast(graph.size());
    dist.clear();
    dist.resize(V, -1);
    dist[src] = 0;
    
    queue q;
    q.push(src);
    
    while (!q.empty())
    {
        int u = q.front();
        q.pop();
        
        for (int v = 0; v != V; ++v)
        {
            if (dist[v] < 0 && graph[u][v] > 0)
            {
                dist[v] = dist[u] + 1;
                q.push(v);
            }
        }
        
    }
    
    return dist[dest] >= 0;
}

int dinic_dfs(vector> &graph, vector &dist, int u, int dest, int bottleneck)
{
    if (u == dest)
        return bottleneck;
    
    int V = static_cast(graph.size());
    
    for (int v = 0; v != V; ++v)
    {
        if (dist[v] == dist[u] + 1 && graph[u][v] > 0)
        {
            int _bottleneck = dinic_dfs(graph, dist, v, dest, min(bottleneck, graph[u][v]));
            if (_bottleneck > 0)
            {
                // augment this path
                graph[u][v] -= _bottleneck;
                graph[v][u] += _bottleneck;
                return _bottleneck;
             }
        }
    }
    
    return 0;
    
}

int dinic(vector> &graph, int src, int dest)
{
    int max_flow = 0;
    vector dist;
    
    // ensure dest is reachable from src
    while (dinic_bfs(graph, dist, src, dest))
    {
        // find the blocking flow from current residual graph
        while(int bottleneck = dinic_dfs(graph, dist, 0, 5, INT_MAX))
            max_flow += bottleneck;
    }
    return max_flow;
}




int main(int argc, const char * argv[]) {
    
    vector> graph = {{0, 10, 10, 0, 0, 0},
                                 {0, 0, 2, 4, 8, 0},
                                 {0, 0, 0, 0, 9, 0},
                                 {0, 0, 0, 0, 0, 10},
                                 {0, 0, 0, 6, 0, 10},
                                 {0, 0, 0, 0, 0, 0}};
    
    
    cout << "Max Flow: " << dinic(graph, 0, 5) << endl;

    return 0;
}