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- #include <iostream>
- #include <queue>
- #include <vector>
- using namespace std;
- const int INF = 1e9;
- class Graph {
- private:
- vector<vector<int>> adj_list;
- public:
- Graph() {}
- Graph(int n) {
- adj_list.resize(n);
- }
- void add_edge(int a, int b) {
- adj_list[a].push_back(b);
- }
- vector<int> get_neighbours(int x) {
- return adj_list[x];
- }
- };
- class FordFulkerson {
- private:
- int n;
- vector<vector<int>> capacity;
- Graph adj;
- public:
- FordFulkerson(int n, vector<vector<int>> capacity, Graph adj) {
- this->n = n;
- this->capacity = capacity;
- this->adj = adj;
- }
- bool dfs(int S, int E, vector<bool> & visited, vector<int> & path) {
- visited[S] = true;
- path.push_back(S);
- if(S == E) {
- return true;
- }
- for(int neighbour : adj.get_neighbours(S)) {
- if(!visited[neighbour] and capacity[S][neighbour] > 0) {
- if(dfs(neighbour, E, visited, path)) {
- return true;
- }
- }
- }
- path.pop_back();
- return false;
- }
- int ford_fulkerson(int S, int E) {
- int flow = 0;
- vector<bool> visited(n, false);
- vector<int> path;
- while(true) {
- int path_flow = INF;
- fill(visited.begin(), visited.end(), false);
- path.clear();
- if(!dfs(S, E, visited, path)) {
- break;
- }
- for(int i = 0; i < path.size() - 1; i++) {
- int a = path[i];
- int b = path[i + 1];
- path_flow = min(path_flow, capacity[a][b]);
- }
- for(int i = 0; i < path.size() - 1; i++) {
- int a = path[i];
- int b = path[i + 1];
- capacity[a][b] -= path_flow;
- capacity[b][a] += path_flow;
- }
- flow += path_flow;
- }
- return flow;
- }
- };
- int main() {
- int V = 6;
- int graph[6][6] = { {0, 16, 13, 0, 0, 0},
- {0, 0, 10, 12, 0, 0},
- {0, 4, 0, 0, 14, 0},
- {0, 0, 9, 0, 0, 20},
- {0, 0, 0, 7, 0, 4},
- {0, 0, 0, 0, 0, 0}
- };
- Graph adj(6);
- vector<vector<int>> capacity(6, vector<int>(6, 0));
- for(int i = 0; i < 6; i++) {
- for(int j = 0; j < 6; j++) {
- capacity[i][j] = graph[i][j];
- if(graph[i][j] != 0) {
- adj.add_edge(i, j);
- }
- }
- }
- FordFulkerson ff(6, capacity, adj);
- cout << ff.ford_fulkerson(0, 5) << endl;
- return 0;
- }
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