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#include<iostream> #include<queue> #include<limits.h> #include<vector> #include <map> #include <utility> #include <algorithm> #include <cassert> #include <optional> using namespace std; using MaxFlow = int; using VertexId = int; void fulkerson(map<VertexId, vector<pair<VertexId, MaxFlow>>> graph) { using Flow = int; VertexId maxInd = max_element(graph.cbegin(), graph.cend(), [](auto x, auto y) { return x.first < y.first; })->first; map<VertexId, vector<pair<VertexId, Flow>>> flowInGraph; for (auto const&[vertId, edges] : graph) { vector<pair<VertexId, Flow>> flow; for (auto& edge : edges) { flow.push_back({edge.first,Flow{0}}); } flowInGraph[vertId] = flow; } vector<VertexId> chain; bool found = false; auto recurseSearch = [&](VertexId id, auto recurse) { if (id == maxInd) { found = true; return; } for (auto& nextVertflowToNext : flowInGraph[id]) { auto nextVert = nextVertflowToNext.first; auto flowToNext = nextVertflowToNext.second; MaxFlow maxFlow; auto find = find_if(graph[id].cbegin(), graph[id].cend(), [&](pair<VertexId, MaxFlow> x) { return x.first == nextVert; }); assert(find != graph[id].cend()); maxFlow = find->second; if (flowToNext < maxFlow) { recurse(nextVert, recurse); if (found) { chain.push_back(nextVert); return; } } } }; recurseSearch(VertexId{1}, recurseSearch); reverse(chain.begin(), chain.end()); // find min flow //VertexId curr = 1; //for (auto next : chain) //{ // auto find = find_if(graph[id].cbegin(), graph[id].cend(), [&](pair<VertexId, MaxFlow> x) // { // return x.first == nextVert; // }); // assert(find != graph[id].cend()); // // //} for (auto i : chain) cout << " " << i << " "; } //int main() //{ //map<VertexId, vector<pair<VertexId, MaxFlow>>> graph; //graph[1] = {{2,1},{4,4}}; //graph[2] = {{3,2},{5,3},{4,2}}; //graph[3] = {{6,2}}; //graph[4] = {{3,3}}; //graph[5] = {{6,1}}; //graph[6] = {}; // //fulkerson(graph); //constexpr int nodes = 6; // //int mat[nodes][nodes] = { // {0, 1, 0, 4, 0, 0}, // {0, 0, 2, 2, 3, 0}, // {0, 0, 0, 0, 0, 2}, // {0, 0, 3, 0, 0, 0}, // {0, 0, 0, 0, 0, 1}, // {0, 0, 0, 0, 0, 0} //}; //cout << "Max flow = " << ford_fulkerson_compute<nodes>(mat, 0, 5) << endl; //return 0; //} constexpr int V = 6; /* Returns true if there is a path from source 's' to sink 't' in residual graph. Also fills parent[] to store the path */ bool bfs(int rGraph[V][V], int s, int t, int parent[]) { // Create a visited array and mark all vertices as not visited bool visited[V]; memset(visited, 0, sizeof(visited)); // Create a queue, enqueue source vertex and mark source vertex // as visited queue <int> q; q.push(s); visited[s] = true; parent[s] = -1; // Standard BFS Loop while (!q.empty()) { int u = q.front(); q.pop(); for (int v = 0; v < V; v++) { if (visited[v] == false && rGraph[u][v] > 0) { q.push(v); parent[v] = u; visited[v] = true; } } } // If we reached sink in BFS starting from source, then return // true, else false return (visited[t] == true); } // Returns the maximum flow from s to t in the given graph int fordFulkerson(int graph[V][V], int s, int t) { int u, v; // Create a residual graph and fill the residual graph with // given capacities in the original graph as residual capacities // in residual graph int rGraph[V][V]; // Residual graph where rGraph[i][j] indicates // residual capacity of edge from i to j (if there // is an edge. If rGraph[i][j] is 0, then there is not) for (u = 0; u < V; u++) for (v = 0; v < V; v++) rGraph[u][v] = graph[u][v]; int parent[V]; // This array is filled by BFS and to store path int max_flow = 0; // There is no flow initially // Augment the flow while tere is path from source to sink while (bfs(rGraph, s, t, parent)) { // Find minimum residual capacity of the edges along the // path filled by BFS. Or we can say find the maximum flow // through the path found. int path_flow = INT_MAX; for (v = t; v != s; v = parent[v]) { u = parent[v]; path_flow = min(path_flow, rGraph[u][v]); } // update residual capacities of the edges and reverse edges // along the path for (v = t; v != s; v = parent[v]) { u = parent[v]; rGraph[u][v] -= path_flow; rGraph[v][u] += path_flow; } // Add path flow to overall flow max_flow += path_flow; } // Return the overall flow return max_flow; } // Driver program to test above functions int main() { int graph[V][V] = { {0, 1, 0, 4, 0, 0}, {0, 0, 2, 2, 3, 0}, {0, 0, 0, 0, 0, 2}, {0, 0, 3, 0, 0, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0} }; cout << "The maximum possible flow is " << fordFulkerson(graph, 0, 5); return 0; }
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