#include <iostream>
#include <bits/stdc++.h>
#define inf 100000000
#define maxFlow 110000
using namespace std;
class graph
{
// bitul 1 orientat sau neorientat, bitul 2 cost muchie
enum input {orientat = 1, neorientat = 2, cu_cost = 4, fillLat = 8};
struct muchie
{
int from, to, cost;
muchie(int _from, int _to, int _cost = 1):
from(_from), to(_to), cost(_cost)
{
}
};
input tipGraf;
int n,m;
int* extraArgs = nullptr;
vector<int>* la = nullptr;
vector<int>* lat = nullptr;
vector<pair<int,int>>* lac = nullptr;
vector<int> topo;
ifstream f;
ofstream g;
public:
void clearData();
void readData(string nume_fisier, input _tip_graf, int _extra_args_count = 0);
void addEdge(int from, int to, int cost = -1);
//////////////////////////////////////////////////////////////////////////////////
void bfs();
//////////////////////////////////////////////////////////////////////////////////
void dfs();
void dfsTopo(int from, int dist[]);
//////////////////////////////////////////////////////////////////////////////////
void ctc();
void dfsCtc(int nod, vector<vector<int>>& cc, int data[]);
//////////////////////////////////////////////////////////////////////////////////
void sortaret();
//////////////////////////////////////////////////////////////////////////////////
void critice();
void dfsCritice(int from, int parent, vector<pair<int,int>>& mcrit, int lowLink[], int ids[], int id);
//////////////////////////////////////////////////////////////////////////////////
void biconex();
void dfsBiconexe(int from, stack<pair<int,int>>& st, vector<vector<int>>& cb, int lowlink[], int ids[], int id);
//////////////////////////////////////////////////////////////////////////////////
int findParent(int x, int parents[]);
void unite(int x, int y, int parents[], int sizes[]);
void apm();
pair<int,int> getParentAndHeight(int x, int parents[]);
//////////////////////////////////////////////////////////////////////////////////
void disjoint();
//////////////////////////////////////////////////////////////////////////////////
void dijkstra();
//////////////////////////////////////////////////////////////////////////////////
void bellmanford();
//////////////////////////////////////////////////////////////////////////////////
void royfloyd();
//////////////////////////////////////////////////////////////////////////////////
void darb();
int bfs_farthest();
int dist_to_node(int node);
//////////////////////////////////////////////////////////////////////////////////
void maxflow();
void getPath(int parent[], int** fluxLeft);
};
void graph::clearData()
{
if (la != nullptr)
{
delete[] la;
la = nullptr;
}
if (lat != nullptr)
{
delete[] lat;
lat = nullptr;
}
if (lac != nullptr)
{
delete[] lac;
lac = nullptr;
}
if (extraArgs != nullptr)
{
delete[] extraArgs;
extraArgs = nullptr;
}
}
void graph::readData (string nume_fisier, input _tip_graf, int _extra_args_count)
{
tipGraf = _tip_graf;
f.open(nume_fisier + ".in");
g.open(nume_fisier + ".out");
f >> n >> m;
if (_extra_args_count)
{
extraArgs = new int[_extra_args_count];
for (int i = 0; i < _extra_args_count; i++)
f >> extraArgs[i];
}
int x,y,c;
if (_tip_graf & input::orientat)
{
if (_tip_graf & input::cu_cost)
{
lac = new vector<pair<int,int>>[n+1];
for (int i = 1; i <= m; i++)
{
f >> x >> y >> c;
lac[x].push_back({y,c});
}
}
else
{
if (_tip_graf & input::fillLat)
{
la = new vector<int>[n+1];
lat = new vector<int>[n+1];
for (int i = 1; i <= m; i++)
{
f >> x >> y;
// cout << x << ' ' << y << '\n';
la[x].push_back(y);
lat[y].push_back(x);
}
}
else
{
la = new vector<int>[n+1];
for (int i = 1; i <= m; i++)
{
f >> x >> y;
la[x].push_back(y);
}
}
}
}
else if (_tip_graf & input::neorientat)
{
if (_tip_graf & input::cu_cost)
{
lac = new vector<pair<int,int>>[n+1];
for (int i = 1; i <= m; i++)
{
f >> x >> y >> c;
lac[x].push_back({y,c});
lac[y].push_back({x,c});
}
}
else
{
la = new vector<int>[n+1];
for (int i = 1; i <= m; i++)
{
f >> x >> y;
la[x].push_back(y);
la[y].push_back(x);
}
}
}
f.close();
}
void graph::addEdge(int from, int to, int cost)
{
if (tipGraf & input::orientat)
{
if (tipGraf & input::cu_cost)
{
lac[from].push_back({to, cost});
}
else
{
if (tipGraf & input::fillLat)
{
la[from].push_back(to);
lat[to].push_back(from);
}
else
{
la[from].push_back(to);
}
}
}
else if (tipGraf & input::neorientat)
{
if (tipGraf & input::cu_cost)
{
lac[from].push_back({to,cost});
lac[to].push_back({from, cost});
}
else
{
la[from].push_back(to);
la[to].push_back(from);
}
}
}
void graph::bfs()
{
// readData("bfs", input::orientat, 1);
int start = extraArgs[0];
int* dist = new int[n+1];
queue<int> q;
q.push(start);
dist[start] = 0;
while (q.size())
{
for (auto to: la[q.front()])
{
if (dist[to] == -1)
{
q.push(to);
dist[to] = dist[q.front()] + 1;
}
}
q.pop();
}
for (int i = 1; i <= n; i++)
g << dist[i] << ' ';
delete[] dist;
clearData();
}
void graph::dfsTopo(int from, int dist[])
{
dist[from] = 1;
for (auto to: la[from])
{
if (!dist[to])
dfsTopo(to, dist);
}
topo.push_back(from);
}
void graph::dfs()
{
// readData("dfs", input::neorientat);
int* dist = new int[n+1];
int cc = 0;
for (int i = 1; i <= n; i++)
{
if (!dist[i])
{
dfsTopo(i, dist);
cc++;
}
}
g << cc;
delete[] dist;
clearData();
}
void graph::dfsCtc(int nod, vector<vector<int>>& cc, int dist[])
{
dist[nod] = 1;
cc[cc.size() - 1].push_back(nod);
for (auto to: lat[nod])
{
if (!dist[to])
dfsCtc(to, cc, dist);
}
}
void graph::ctc()
{
// readData("ctc", (input)(input::orientat | input::fillLat));
int* dist = new int[n+1];
for (int i = 1; i <= n; i++)
{
if (!dist[i])
dfsTopo(i, dist);
}
reverse(topo.begin(), topo.end());
memset(dist, 0, sizeof(int) * (n+1));
vector<vector<int>> cc;
for (auto nod: topo)
{
if (!dist[nod])
{
cc.push_back(vector<int>());
dfsCtc(nod, cc, dist);
}
}
g << cc.size() << '\n';
for (auto& row: cc)
{
for (auto el: row)
g << el << ' ';
g << '\n';
}
delete[] dist;
clearData();
}
void graph::sortaret()
{
// readData("sortaret", (input)(input::orientat));
int* dist = new int[n+1];
for (int i = 1; i <= n; i++)
{
if (!dist[i])
dfsTopo(i, dist);
}
reverse(topo.begin(), topo.end());
for (auto el: topo)
g << el << ' ';
delete[] dist;
clearData();
}
void graph::dfsCritice(int from, int parent, vector<pair<int,int>>& mcrit, int lowLink[], int ids[], int id)
{
lowLink[from] = id;
ids[from] = id;
id ++;
for (auto to: la[from])
{
if (ids[to] == -1)
{
dfsCritice(to, from, mcrit, lowLink, ids, id);
lowLink[from] = min(lowLink[from], lowLink[to]);
}
else if (to != parent)
lowLink[from] = min(lowLink[from], ids[to]);
}
if (lowLink[from] == ids[from] && parent != 0)
mcrit.push_back({from, parent});
}
void graph::critice()
{
// readData("critice", (input)(input::neorientat));
int* ids = new int[n+1];
for (int i = 1; i <= n; i++)
ids[i] = -1;
int* lowLink = new int[n+1];
for (int i = 1; i <= n; i++)
lowLink[i] = 0;
vector<pair<int, int>> mcrit;
for (int i = 1; i <= n; i++)
{
if (ids[i] == -1)
{
dfsCritice(i, 0, mcrit, lowLink, ids, 0);
}
}
for (auto& per: mcrit)
g << per.first << ' ' << per.second << '\n';
delete[] ids;
delete[] lowLink;
}
void graph::dfsBiconexe(int from, stack<pair<int,int>>& st, vector<vector<int>>& cb, int lowLink[], int ids[], int id)
{
lowLink[from] = ids[from] = id++;
for (auto to: la[from])
{
if (ids[to] != -1)
lowLink[from] = min(lowLink[from], ids[to]);
else
{
st.push({from, to});
dfsBiconexe(to, st, cb, lowLink, ids, id);
lowLink[from] = min(lowLink[from], lowLink[to]);
if (lowLink[to] >= ids[from])
{
vector<int> comp;
while (st.top().first != from)
{
comp.push_back(st.top().second);
st.pop();
}
comp.push_back(st.top().first);
comp.push_back(st.top().second);
st.pop();
cb.push_back(comp);
}
}
}
}
void graph::biconex()
{
// readData("biconex", (input)(input::neorientat));
int* ids = new int[n+1];
for (int i = 1; i <= n; i++)
ids[i] = -1;
int* lowLink = new int[n+1];
for (int i = 1; i <= n; i++)
lowLink[i] = 0;
vector<vector<int>> cb;
stack<pair<int,int>> st;
for (int i = 1; i <= n; i++)
{
if (ids[i] == -1)
dfsBiconexe(i, st, cb, lowLink, ids, 0);
}
g << cb.size() << '\n';
for (auto& row: cb)
{
for (auto el: row)
g << el << ' ';
g << '\n';
}
delete[] ids;
delete[] lowLink;
}
pair<int,int> graph::getParentAndHeight(int x, int parents[])
{
vector<int> met;
int h = 0;
while (parents[x] != 0)
{
h++;
met.push_back(x);
x = parents[x];
}
for (auto el: met)
parents[el] = x;
return {x, h};
}
int graph::findParent(int x, int parents[])
{
vector<int> met;
while (parents[x] != 0)
{
met.push_back(x);
x = parents[x];
}
for (int nod: met)
parents[nod] = x;
return x;
}
void graph::unite(int x, int y, int parents[], int sizes[])
{
int x_parent = findParent(x, parents);
int y_parent = findParent(y, parents);
if (x_parent == y_parent)
return;
if (sizes[x_parent] > sizes[y_parent])
{
parents[y_parent] = x_parent;
sizes[x_parent] += sizes[y_parent];
}
else
{
parents[x_parent] = y_parent;
sizes[y_parent] += sizes[x_parent];
}
}
void graph::apm()
{
// readData("apm", (input)(input::orientat | input::cu_cost));
int* parents = new int[n+1];
for (int i = 1; i <= n; i++)
parents[i] = 0;
int* sizes = new int[n+1];
for (int i = 1; i <= n; i++)
sizes[i] = 1;
vector<muchie> muchii;
for (int i = 1; i <= n; i++)
{
for (auto per: lac[i])
muchii.push_back({i, per.first, per.second});
}
sort(muchii.begin(), muchii.end(), [](muchie& m1, muchie& m2){ return (m1.cost < m2.cost);});
vector<muchie> sol;
int s = 0;
for (auto& m: muchii)
{
int p1 = findParent(m.from, parents);
int p2 = findParent(m.to, parents);
if (p1 == p2)
continue;
unite(m.from, m.to, parents, sizes);
sol.push_back(m);
s += m.cost;
}
g << s << '\n';
g << sol.size() << '\n';
for (auto& m: sol)
g << m.from << ' ' << m.to << '\n';
delete[] parents;
delete[] sizes;
}
void graph::disjoint()
{
ifstream f("disjoint.in");
ofstream g("disjoint.out");
f >> n >> m;
int* parents = new int[n+1];
for (int i = 1; i <= n; i++)
parents[i] = 0;
int* sizes = new int[n+1];
for (int i = 1; i <= n; i++)
sizes[i] = 1;
for (int i = 1; i <= m; i++)
{
int op, from, to;
f >> op >> from >> to;
int parinte_from = findParent(from, parents);
int parinte_to = findParent(to, parents);
if (op == 1)
{
unite(from, to, parents, sizes);
}
else
{
if (parinte_from == parinte_to)
g << "DA\n";
else
g << "NU\n";
}
}
delete[] parents;
delete[] sizes;
}
void graph::dijkstra()
{
int max_dist = 1e9;
// readData("dijkstra", (input)(input::orientat | input::cu_cost));
int* dist = new int[n+1];
for (int i = 1; i <= n; i++)
dist[i] = max_dist;
int* viz = new int[n+1];
for (int i = 1; i <= n; i++)
viz[i] = 0;
priority_queue<pair<int, int>> q; // cost negativ si nod
q.push({0, 1});
dist[1] = 0;
while (q.size())
{
int top = q.top().second;
q.pop();
if (viz[top])
continue;
viz[top] = 1;
for (auto& per: lac[top])
{
if (dist[per.first] > dist[top] + per.second)
{
dist[per.first] = dist[top] + per.second;
q.push({-dist[per.first], per.first});
}
}
}
for (int i = 2; i <= n; i++)
{
if (dist[i] == max_dist)
{
dist[i] = 0;
}
g << dist[i] << ' ';
}
delete[] dist;
}
void graph::bellmanford()
{
int max_dist = 1e9;
// readData("bellmanford", (input)(input::orientat | input::cu_cost));
int* dist = new int[n+1];
for (int i = 1; i <= n; i++)
dist[i] = max_dist;
int* viz = new int[n+1];
for (int i = 1; i <= n; i++)
viz[i] = 0;
queue<int> q; // cost negativ si nod
q.push(1);
dist[1] = 0;
while (q.size())
{
int from = q.front();
q.pop();
viz[from] ++;
if (viz[from] >= n)
{
g << "Ciclu negativ!";
return;
}
for (auto& per: lac[from])
{
if (dist[per.first] > dist[from] + per.second)
{
dist[per.first] = dist[from] + per.second;
q.push(per.first);
}
}
}
for (int i = 2; i <= n; i++)
{
if (dist[i] == max_dist)
{
dist[i] = 0;
}
g << dist[i] << ' ';
}
delete[] dist;
}
void graph::royfloyd()
{
ifstream in("royfloyd.in");
ofstream out("royfloyd.out");
in >> n;
int minDist[100][100];
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
{
in >> minDist[i][j];
if (minDist[i][j] == 0 && i != j)
minDist[i][j] = inf;
}
for (int k = 0; k < n; k++)
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
//minDist[i][j] = min(min(minDist[i][j], minDist[i][k] + dist[k][j]), dist[i][k] + minDist[k][j]);
if (minDist[i][k] + minDist[k][j] < minDist[i][j])
minDist[i][j] = minDist[i][k] + minDist[k][j];
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
if (minDist[i][j] == inf)
{
minDist[i][j] = 0;
}
out << minDist[i][j] << ' ';
}
out << '\n';
}
}
int graph::bfs_farthest()
{
int* viz = new int[n+1];
queue<int> q;
q.push(1);
viz[1] = 1;
while (q.size())
{
int from = q.front();
for (auto& to: la[from])
{
if (!viz[to])
{
viz[to] = 1;
q.push(to);
}
}
if (q.size() == 1)
{
delete[] viz;
return q.front();
}
q.pop();
}
delete[] viz;
return -1;
}
int graph::dist_to_node(int node)
{
int* dist = new int[n+1];
memset(dist, -1, sizeof(int) * (n+1));
queue<int> q;
q.push(node);
dist[node] = 0;
while (q.size())
{
int from = q.front();
for (auto& to: la[from])
{
if (dist[to] == -1)
{
dist[to] = 1 + dist[from];
q.push(to);
}
}
if (q.size() == 1)
{
int d = dist[q.front()];
delete[] dist;
return d;
}
q.pop();
}
delete[] dist;
return -1;
}
void graph::darb()
{
ifstream in("darb.in");
ofstream out("darb.out");
in >> n;
la = new vector<int>[n+1];
int from, to;
while (in >> from >> to)
{
la[from].push_back(to);
la[to].push_back(from);
}
int farthest = bfs_farthest();
out << dist_to_node(farthest) + 1;
}
void graph::getPath(int parent[], int** fluxLeft)
{
memset(parent, 0, sizeof(int) * (n+1));
vector<int> q;
parent[1] = -1;
q.push_back(1);
for (int i = 0; i < q.size() ; i++)
{
if (q[i] == n)
{
continue;
}
for (auto to: la[q[i]])
{
if (fluxLeft[q[i]][to] <= 0 || parent[to] != 0)
continue;
parent[to] = q[i];
q.push_back(to);
}
}
}
void graph::maxflow()
{
ifstream in("maxflow.in");
ofstream out("maxflow.out");
in >> n >> m;
int s = 1, f = n;
la = new vector<int>[n+1];
int* parent = new int[n+1];
int flux = 0;
int** fluxLeft = new int*[n+1];
for (int i = 0; i < n+1; i++)
{
fluxLeft[i] = new int[n+1];
for (int j = 0; j < n+1; j++)
fluxLeft[i][j] = 0;
}
for (int i = 1; i <= m ; ++i)
{
int x,y,c;
in >> x >> y >> c;
la[x].push_back(y);
la[y].push_back(x);
fluxLeft[x][y] = c;
}
getPath(parent, fluxLeft);
while (parent[f] != 0)
{
for (int i = -1; i < (int)la[f].size(); i++)
{
if (i != -1)
{
parent[f] = la[f][i];
}
int minn = maxFlow;
int nod = f;
while (parent[nod] != -1)
{
if (fluxLeft[parent[nod]][nod] < minn)
minn = fluxLeft[parent[nod]][nod];
if (minn <= 0)
break;
nod = parent[nod];
}
if (minn <= 0)
continue;
flux += minn;
nod = f;
while (parent[nod] != -1)
{
fluxLeft[parent[nod]][nod] -= minn;
fluxLeft[nod][parent[nod]] += minn;
nod = parent[nod];
}
}
getPath(parent, fluxLeft);
}
out << flux;
}
int main()
{
graph g;
g.maxflow();
return 0;
}