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// Algoritmul de flux, adauga un nod de start si un nod final
// Capacitatea pe muchii o sa fie gradul de iesire pe muchiile care pleaca din start si
// gradul de intrare pe muchiile spre nodul final
// O(n * m^2)
#include <iostream>
#include <bits/stdc++.h>
#include <fstream>
using namespace std;
using namespace std::chrono;
//ifstream in("maxflow.in");
//ofstream out("maxflow.out");
ifstream in("harta.in");
ofstream out("harta.out");
vector<vector<int>> adjList;
vector<pair<int,int>> degrees;
unordered_map<int, int> cap[205];
unordered_map<int,int> sol;
vector<int> parents;
struct muchie{
};
int n,m,e;
void read(){
in >> n;
adjList.resize(2 * n + 2);
// cap.resize(n + m + 3, vector<int>(n + m + 3, 0));
int x, y;
degrees.emplace_back(make_pair(0,n));
while(in>>x>>y){
degrees.emplace_back(make_pair(x,y));
}
for(int i = 1; i <= n ;i++)
for(int j = n + 1; j<= n * 2; j++)
{
if(i + n != j){
adjList[i].emplace_back(j);
adjList[j].emplace_back(i);
cap[i][j] = 1;
}
}
for(int i = 1; i <= n; i++)
{
adjList[0].emplace_back(i);
// adjList[i].emplace_back(0);
cap[0][i] = degrees[i].first;
}
for(int i = 1; i + n <= n * 2; i++)
{
adjList[i + n].emplace_back(n * 2 + 1);
adjList[n * 2 + 1].emplace_back(i + n);
cap[i + n][n * 2 + 1] = degrees[i].second;
}
}
int BFS(int source, int dest, vector<int>& parent)
{
fill(parent.begin(), parent.end(), -1);
parent[source] = 0;
queue<int> q;
q.push(source);
while(!q.empty()) {
int pNode = q.front(); //nodul parinte
q.pop();
for (auto el: adjList[pNode])
{
int cNode = el; // copiii nodului parinte actual
if(cNode != pNode && parent[cNode] == -1 && cap[pNode][cNode] > 0)
{
parent[cNode] = pNode;
if(cNode == dest)
{
return 1;
}
//adaugam urmatorul nod ce urmeaza sa fie vizitat
q.push({cNode});
}
}
}
return 0;
}
int EdmondsKarp(int source, int dest)
{
vector<int> parent(n * 2 + 2, -1);
parent[source] = -2;
int mxFlow = 0;
while(BFS(source,dest,parent)) {
for (auto el: adjList[dest]) {
if (parent[el] != -1) {
int mnCap = INT_MAX;
int cNode = dest;
// parent[dest] = el;
while (cNode != source) {
mnCap = min(mnCap, cap[parent[cNode]][cNode]);
cNode = parent[cNode];
}
cNode = dest;
while (cNode != source){
cap[cNode][parent[cNode]] += mnCap;
cap[parent[cNode]][cNode] -= mnCap;
cNode = parent[cNode];
}
mxFlow += mnCap;
}
}
}
return mxFlow;
}
int main()
{
auto start = high_resolution_clock::now();
read();
out<<EdmondsKarp(0, 2*n+1)<<endl;
for(int i = 1; i<=n;i++)
for(int j = n + 1; j<= n * 2; j++){
if(i + n != j && cap[i][j] == 0)
out<<i<<" "<<j - n<<endl;
}
auto stop = high_resolution_clock::now();
auto duration = duration_cast<microseconds>(stop - start);
cout<<"Durata: "<< duration.count();
return 0;
}
//V2
// Acelasi algoritm dar fara sa retinem muchiile sub forma de pozitii in lista de adiacenta,
// Avem doar o lista de adiacenta normala
// 90 de puncte cu unordered_map
/*
#include <iostream>
#include <bits/stdc++.h>
#include <fstream>
using namespace std;
using namespace std::chrono;
//ifstream in("maxflow.in");
//ofstream out("maxflow.out");
ifstream in("cuplaj.in");
ofstream out("cuplaj.out");
vector<int> adjList[20005];
unordered_map<int, int> cap[20005];
unordered_map<int,int> sol;
struct muchie{
};
int n,m,e;
void read(){
in >> n >> m >> e;
// adjList.resize(n + m + 3);
// cap.resize(n + m + 3, vector<int>(n + m + 3, 0));
int x, y;
for(int i = 0; i < e; i++)
{
in >> x >> y;
adjList[x].emplace_back(y+n);
adjList[y + n].emplace_back(x);
cap[x][y+n] = 1;
}
for(int i = 1; i <= n; i++)
{
adjList[0].emplace_back(i);
// adjList[i].emplace_back(0);
cap[0][i] = 1;
}
for(int i = 1; i <= m; i++)
{
adjList[i + n].emplace_back(n + m + 1);
adjList[n + m + 1].emplace_back(i + n);
cap[i + n][n+m+1] = 1;
}
}
int BFS(int source, int dest, vector<int>& parent)
{
fill(parent.begin(), parent.end(), -1);
parent[source] = 0;
queue<int> q;
q.push(source);
while(!q.empty()) {
int pNode = q.front(); //nodul parinte
q.pop();
for (auto el: adjList[pNode])
{
int cNode = el; // copiii nodului parinte actual
if(cNode != pNode && parent[cNode] == -1 && cap[pNode][cNode] > 0)
{
parent[cNode] = pNode;
if(cNode == dest)
{
return 1;
}
//adaugam urmatorul nod ce urmeaza sa fie vizitat
q.push({cNode});
}
}
}
return 0;
}
int EdmondsKarp(int source, int dest)
{
vector<int> parent(n + m + 3, -1);
int mxFlow = 0;
while(BFS(source,dest,parent)) {
for (auto el: adjList[dest]) {
if (parent[el] != -1) {
int mnCap = INT_MAX;
int cNode = dest;
parent[dest] = el;
while (cNode != source) {
mnCap = min(mnCap, cap[parent[cNode]][cNode]);
cNode = parent[cNode];
}
cNode = dest;
while (cNode != source){
cap[cNode][parent[cNode]] += mnCap;
cap[parent[cNode]][cNode] -= mnCap;
if(cap[parent[cNode]][cNode] == 0 && parent[cNode] != 0 && cNode != n + m + 1)
sol[parent[cNode]] = cNode - n;
cNode = parent[cNode];
}
mxFlow += mnCap;
}
}
}
return mxFlow;
}
int main()
{
auto start = high_resolution_clock::now();
read();
out<<EdmondsKarp(0, n + m + 1)<<endl;
for(int i = 1; i <= n; i++)
{
if(sol[i] != 0 && i != 0 && sol[i] != n + m + 1)
out<< i << " "<<sol[i]<<endl;
}
auto stop = high_resolution_clock::now();
auto duration = duration_cast<microseconds>(stop - start);
cout<<"Durata: "<< duration.count();
return 0;
}
*/