Edge disjoint paths with Ford-Fulkerson algorithm

////  main.cpp//  Edge Disjoint paths////  Created by Longxiang Lyu on 8/15/16.//  Copyright © 2016 Longxiang Lyu. All rights reserved.//#include <iostream>#include <string>#include <vector>#include <queue>#include <algorithm>#include <stack>using namespace std;bool bfs(vector<vector<int>> &rGraph, vector<int> &parent, int s, int t){    int V = static_cast<int>(rGraph.size());    vector<int> visited(V, 0);      // mark all vertices as unvisited    queue<int> q;    q.push(s);    visited[s] = 1;                 // mark source vertex as visited        parent.clear();    parent.resize(V);    parent[s] = -1;        while (!q.empty())    {        int u = q.front();          // get the first element        q.pop();                for (int v = 0; v != V; ++v)        {            if (visited[v] == 0 && rGraph[u][v] > 0)            {                q.push(v);                parent[v] = u;                visited[v] = 1;            }        }    }    return visited[t] == 1;}void printM(const vector<vector<int>> &M){    for (int i = 0; i != M.size(); ++i)    {        for (int j = 0; j != M[i].size(); ++j)            cout << M[i][j] << " ";        cout << endl;    }}void buildPath(vector<vector<int>> &fGraph, vector<int> &path, int u, int dest){    if (u == dest)        return;    int sz = static_cast<int>(fGraph[u].size());        for (int j = 0; j != sz; ++j)    {        if (fGraph[u][j] > 0)        {            path.push_back(j);            fGraph[u][j] = 0;            buildPath(fGraph, path, j, dest);            break;        }    }    return;}int fordFulkerson(vector<vector<int>> &graph, vector<vector<int>> &paths, int s, int t){    int u, v;            vector<int> parent;        auto rGraph = graph;        int max_flow = 0;               // initially zero flow        while (bfs(rGraph, parent, s, t))    {        int bottleneck = INT_MAX;                // get the bottleneck capacity of the augment path        for (v = t; v != s; v = parent[v])        {            u = parent[v];            bottleneck = min(bottleneck, rGraph[u][v]);        }                for (v = t; v != s; v = parent[v])        {            u = parent[v];            rGraph[u][v] -= bottleneck;            rGraph[v][u] += bottleneck;        }                max_flow += bottleneck;            }        for (int i = 0; i != graph.size(); ++i)    {        for (int j = 0; j != graph.size(); ++j)            graph[i][j] = graph[i][j] - rGraph[i][j] >= 0 ? graph[i][j] - rGraph[i][j] : 0;    }        paths.clear();    paths.resize(max_flow);        for (int i = 0; i != max_flow; ++i)    {        paths[i].push_back(s);        buildPath(graph, paths[i], s, t);    }        return max_flow;}int main(int argc, const char * argv[]){    // insert code here...    vector<vector<int>> graph = {        {0, 1, 1, 1, 0, 0, 0, 0},        {0, 0, 1, 0, 0, 0, 0, 0},        {0, 0, 0, 1, 0, 0, 1, 0},        {0, 0, 0, 0, 0, 0, 1, 0},        {0, 0, 1, 0, 0, 0, 0, 1},        {0, 1, 0, 0, 0, 0, 0, 1},        {0, 0, 0, 0, 0, 1, 0, 1},        {0, 0, 0, 0, 0, 0, 0, 0}    };        vector<vector<int>> paths;        cout << "Number of edge disjoint paths: " << endl << fordFulkerson(graph, paths, 0, 7) << endl;        for (auto a : paths)    {        for (auto b : a)            cout << b << " ";        cout << endl;    }        return 0;}

reference:

http://www.cs.princeton.edu/~wayne/kleinberg-tardos/pdf/07NetworkFlowII-2x2.pdf

http://www.geeksforgeeks.org/find-edge-disjoint-paths-two-vertices/