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/* Algoritmul lui Prim
* O(m * log m)
*
* Se alege un nod arbitrar S si se introduce in arbore.
* Se asociaza fiecarui nod x, cate o cheie key[x] = oo
* key[S] = 0;
*
* La fiecare pas, se examineaza fiecare muchie incidenta arborelui,
* si se alege "muchia usoara", adica muchia de cost (cheie) minim
* care are un capat in arbore
*/
#include <fstream>
#include <algorithm>
#include <vector>
#include <queue>
#include <bitset>
#include <tuple>
using namespace std;
ifstream fin("apm.in");
ofstream fout("apm.out");
const int Inf = 0x3f3f3f3f,
MaxN = 200001;
struct Edge {
Edge() : node {0}, key {0}
{}
Edge(int node, int key) :
node {node}, key {key}
{}
bool operator < (const Edge& e) const
{
return key > e.key;
}
int node, key;
};
using VI = vector<int>;
using VP = vector<pair<int, int>>;
using VVP = vector<VP>;
int n;
bitset<MaxN> v; // v[x] = 1 (daca nodul x
// a fost adaugat la arbore
// deci daca a iesit din coada
VVP G; // graful
VP apm; // retine muchiile APM-ului
VI key;
long long cost_apm;
void ReadGraph();
void Prim(int x);
void WriteAPM();
int main()
{
ReadGraph();
Prim(1);
WriteAPM();
}
void ReadGraph()
{
int a, b, w, m;
fin >> n >> m;
G = VVP(n + 1);
while (m--)
{
fin >> a >> b >> w;
G[a].emplace_back(b, w);
G[b].emplace_back(a, w);
}
}
void Prim(int x)
{
priority_queue<Edge> Q;
key = VI(n + 1, Inf);
VI t = VI(n + 1); // retine APM
int y, ky; // ky = cheia lui y
key[x] = 0;
Q.emplace(x, 0);
while (!Q.empty())
{
x = Q.top().node;
v[x] = 1;
for (auto& p : G[x])
{
tie(y, ky) = p;
if (v[y]) continue;
if (key[y] > ky)
{
key[y] = ky;
t[y] = x;
Q.emplace(y, key[y]);
}
}
apm.emplace_back(x, t[x]);
cost_apm += key[x];
while (!Q.empty() && v[Q.top().node])
Q.pop();
}
}
void WriteAPM()
{
fout << cost_apm << '\n'
<< apm.size() - 1 << '\n';
for (size_t i = 1; i < apm.size(); ++i)
fout << apm[i].first << ' ' << apm[i].second << '\n';
}