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#include <bits/stdc++.h>
using namespace std;
ifstream f("maxflow.in");
ofstream g("maxflow.out");
vector<vector<int>> gr;
vector<vector<int>> flow;
bool bfs(int n, int src, int dest, int father[])
{
bool visited[1001];
memset(visited, 0, 1001);
memset(father, 0, 1001);
queue<int> vertexes;
vertexes.push(src);
while(!vertexes.empty())
{
int currentNode = vertexes.front();
vertexes.pop();
for(auto extr2: gr[currentNode])
{
if(extr2!=0)
if(!visited[extr2] and flow[currentNode][extr2]>0) //daca nu am vizitat nodul extr2
//si capacitatea muchiei formata din nodul curent si extremitatea 2 permite trecerea flow-ului
{
father[extr2] = currentNode;
if(extr2 == dest)
return true;
vertexes.push(extr2);
visited[extr2] = true;
}
}
}
return false; //nu am gasit un drum de la sursa la destinatie, inseamna nu mai am drumuri si ca am ajuns la flux maxim
}
int fordFulkerson(int n, int src, int dest)
{
int u, v, max_flow_for_route, currentNode;
int father[1001];
memset(father, 0, 1001);
int srcAux = src, destAux = dest, fNode, finalFlow = 0;
while(bfs(n, src, dest, father))
{
max_flow_for_route = INT_MAX;
srcAux = src;
destAux = dest;
while(destAux!=srcAux)
{
//calculez flow-ul maxim de transmis pe drumul gasit de bfs
max_flow_for_route = min(max_flow_for_route, flow[father[destAux]][destAux]);
destAux = father[destAux];
}
destAux = dest;
srcAux = src;
//acum updatez graful rezidual pe drumul gasit de bfs
while(destAux!=srcAux)
{
fNode = father[destAux];
flow[fNode][destAux] -= max_flow_for_route; //muchia mea pe directia corecta va avea o capacitate mai mica de flow
flow[destAux][fNode] += max_flow_for_route; //muchia pe directia inversa va avea mai mult flow de dat
//logic pt ca voi avea mai mult flow de extras
destAux = fNode;
}
finalFlow += max_flow_for_route; //adun flow-ul drumului la flow-ul final
}
return finalFlow;
}
int main()
{
int n,m,node1,node2,flux;
f>>n>>m;
flow.resize(1002);
gr.resize(1002);
for(int i=1;i<=1002;i++)
flow[i].resize(1002);
for(int i=1;i<=m;i++)
{
f>>node1>>node2>>flux;
gr[node1].push_back(node2);
gr[node2].push_back(node1);
flow[node1][node2] = flux;
}
g<<fordFulkerson(n,1,n);
return 0;
}