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#include <vector>
#include <queue>
#include <fstream>
#include <climits>
#include <iostream>
using namespace std;
ifstream fileIn("maxflow.in");
ofstream fileOut("maxflow.out");
class Graph {
int N;
int M;
vector<int> prev_in_bfs;
vector<vector<int>> list_adj;
vector<bool> visited;
vector<vector<int>> capacities;
public:
void read();
int bfs(int s, int t);
int maxflow(int source, int target);
int getNoNodes(){
return N;
}
};
void Graph:: read() {
fileIn >> N >> M;
// resize
list_adj.resize(N + 1);
visited.resize(N + 1);
prev_in_bfs.resize(N + 1);
capacities.resize(N+1);
for(int i = 1; i < (int) capacities.size(); i++) {
capacities[i].resize(N + 1, 0);
}
int a, b, c;
for(int i=1; i<= M; i++) {
fileIn >> a >> b >> c;
list_adj[a].push_back(b);
capacities[a][b] = c;
}
}
int Graph::bfs(int s, int t) {
//filling prev and visited vectors with default values
fill(prev_in_bfs.begin(), prev_in_bfs.end(), -1);
fill(visited.begin(), visited.end(), false);
// queue for bfs
queue<pair<int,int>> q_bfs;
//visiting the start node and adding to the queue
q_bfs.push({s, INT_MAX});
visited[s] = true;
int bottleneck;
while(!q_bfs.empty()) {
auto curr = q_bfs.front();
int curr_node = curr.first;
int curr_flow = curr.second;
q_bfs.pop();
for( auto node: list_adj[curr_node]) {
// for every adj node
int flow = capacities[curr_node][node];
if(!visited[node] && flow) { // if the node it s not visited in this bfs and the edge have capacity
//we visit it and set its prev node
visited[node] = true;
prev_in_bfs[node] = curr_node;
//we calculate bottleneck as minimum on the current path from source to target
bottleneck = min(curr_flow, flow);
if (node == t) {
return bottleneck;
}
q_bfs.push({node, bottleneck});
}
}
}
return 0;
}
int Graph::maxflow(int source, int target) {
int flow = 0;
int bottleneck;
bottleneck = bfs(source,target);
while(bottleneck !=0) {
flow += bottleneck;
int curr_node = target; // traverse the path in reverse order to update capacity
for(curr_node; curr_node != source; curr_node = prev_in_bfs[curr_node]) {
capacities[prev_in_bfs[curr_node]][curr_node] -= bottleneck; //decreasing forward edge capacity
capacities[curr_node][prev_in_bfs[curr_node]] += bottleneck; // increasing the reversed edge capacity
}
bottleneck = bfs(source, target);
}
return flow;
}
int main() {
Graph my_graph;
my_graph.read();
fileOut << my_graph.maxflow(1, my_graph.getNoNodes());
return 0;
}