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// Folosind algoritmul pentru flux, adaugam un nod de inceput, un nod de final si capacitate 1 pe muchii
// Retinem muchiile sub forma de pozitii in lista de adiacenta, pentru a avea acces rapid la nodurile adiacente
// retinem pentru fiecare muchie capacitatea, pozitia din lista de adiacenta, nodurile pe care le uneste
//O(n*m^2)
#include <iostream>
#include <bits/stdc++.h>
using namespace std;
using namespace std::chrono;
//ifstream in("maxflow.in");
//ofstream out("maxflow.out");
ifstream in("cuplaj.in");
ofstream out("cuplaj.out");
struct edge{
int n1, n2, cap, pos;
};
vector<vector<int>> adjList;
vector<edge> edges;
vector<bool> visited;
vector<int> parent;
int n,m,e, nrN;
int source,dest;
void addEdge(int x, int y){
int dim = (int)edges.size();
adjList[x].push_back(dim);
adjList[y].push_back(dim+1);
edges.push_back({x,y,1,dim+1});
edges.push_back({y,x,0, dim});
}
void read(){
in >> n >> m >> e;
nrN = n + m + 2;
source = 0;
dest = nrN -1;
adjList.resize(nrN);
int x, y;
for(int i = 0; i < e; ++i)
{
in >> x >> y;
addEdge(x,y + n);
}
for(int i = 1; i <= n; ++i)
{
addEdge(0,i);
}
for(int i = 1; i <= m; ++i)
{
addEdge(i+n, m + n + 1);
}
}
bool BFS()
{
parent.clear();
parent.resize(nrN);
visited.clear();
visited.resize(nrN, false);
visited[source] = true;
queue<int> q;
q.push(source);
while(!q.empty()) {
int pNode = q.front(); //nodul parinte
q.pop();
if(pNode != dest)
// alegem noduri adiacente cu nodul parinte(nodul (0) de start in primul rand)
for (int el: adjList[pNode])
{
// muchia care pleaca din nodul el
edge cEdge = edges[el];
// daca nodul in care ajunge muchia din 'el' nu a fost cuplat
// si mai putem sa trimitem flux, o cuplam cu 'el'
if(!visited[cEdge.n2] && cEdge.cap != 0)
{
parent[cEdge.n2] = el;
//adaugam urmatorul nod ce urmeaza sa fie vizitat
q.push(cEdge.n2);
visited[cEdge.n2] = true;
}
}
}
return visited[dest];
}
int EdmondsKarp(int source, int dest)
{
int mxFlow = 0;
while(BFS()) {
for (int el: adjList[dest]) {
// daca nodul in care ajunge muchia ce pleaca din 'el'
// a fost vizitat si muchia de intoarcere poate intoarce flux
if (visited[edges[el].n2] && edges[edges[el].pos].cap != 0) {
int mnCap = INT_MAX;
edge cEdge = edges[el];
parent[dest] = cEdge.pos;
int cNode = dest;
// parcurgem drumul de crestere de la destinatie spre sursa
while (cNode != source) {
mnCap = min(mnCap, edges[parent[cNode]].cap);
// mergem in nodul dinspre care a venit muchia
cNode = edges[parent[cNode]].n1;
}
cNode = dest;
while (cNode != source){
// pentru muchia reziduala crestem fluxul
// muchia de pe pozitia parintelui nodului curent
edges[edges[parent[cNode]].pos].cap += mnCap;
// pentru muchia normala scadam capacitatea ocupata
edges[parent[cNode]].cap -= mnCap;
cNode = edges[parent[cNode]].n1;
}
mxFlow += mnCap;
}
}
}
return mxFlow;
}
int main() {
auto start = high_resolution_clock::now();
read();
out << EdmondsKarp(0, n + m + 1) << endl;
for(auto edge:edges){
if(edge.n1 < edge.n2 && edge.n1 != 0 && edge.n2!= dest && edge.cap == 0)
out<<edge.n1<<" "<<edge.n2 - n<<endl;
}
auto stop = high_resolution_clock::now();
auto duration = duration_cast<microseconds>(stop - start);
cout << "Durata: " << duration.count();
return 0;
}