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 <iostream>#include <vector>#include <algorithm>#include <queue>#include <stack>using namespace std;bool dinic_bfs(vector<vector<int>> &graph, vector<int> &dist, int src, int dest){    int V = static_cast<int>(graph.size());    dist.clear();    dist.resize(V, -1);    dist[src] = 0;        queue<int> 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<vector<int>> &graph, vector<int> &dist, int u, int dest, int bottleneck){    if (u == dest)        return bottleneck;        int V = static_cast<int>(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<vector<int>> &graph, int src, int dest){    int max_flow = 0;    vector<int> 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<vector<int>> 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;}