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#include <cstring>
#include <fstream>
#include <vector>
using namespace std;
const int MAXN = 20;
const int MAXCONF = (1 << 18) + 1;
const int INF = 1e9;
int N, M, cost_ham;
vector<int> pred[MAXN];
int Cost[MAXN][MAXN];
int cd[MAXCONF][MAXN];
int cost_drum(int conf, int ultim) {
if (cd[conf][ultim] == -1) { // Trebuie calculat.
cd[conf][ultim] = INF; // Initializam un minim.
for (int nod : pred[ultim])
if (conf & (1 << nod)) // nod se afla in configuratie
if (nod != 0 or ((conf ^ (1 << ultim)) == 1)) {
int cost_nod = cost_drum(conf ^ (1 << ultim), nod);
if (cd[conf][ultim] > cost_nod + Cost[nod][ultim])
cd[conf][ultim] = cost_nod + Cost[nod][ultim];
}
}
return cd[conf][ultim];
}
int main() {
ifstream fin("hamilton.in");
ofstream fout("hamilton.out");
fin >> N >> M;
memset(Cost, 127, sizeof(Cost)); // 2.139.062.143
for (int i = 1; i <= M; i++) {
int x, y, c;
fin >> x >> y >> c;
pred[y].push_back(x); // arcul invers
Cost[x][y] = c;
}
cost_ham = INF;
memset(cd, -1, sizeof(cd));
cd[1][0] = 0;
for (int nod : pred[0]) {
int cost_vecin = cost_drum((1 << N) - 1, nod);
if (cost_ham > cost_vecin + Cost[nod][0])
cost_ham = cost_vecin + Cost[nod][0];
}
if (cost_ham != INF)
fout << cost_ham << '\n';
else
fout << "Nu exista solutie" << '\n';
return 0;
}
/*
10000
1111
3210
1110
1000
----
0110
15
14
12
8
12
4
14
10
8
10
2
14
6
4
6
2
15
13
12
8
12
4
13
9
8
9
1
13
5
4
5
1
15
11
10
8
10
2
11
9
8
9
1
11
3
2
3
1
15
7
6
4
6
2
7
5
4
5
1
7
3
2
3
1
11010111 ^
01000000
--------
10010111
*/