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#include <iostream>
#include <algorithm>
#include <vector>
using std::vector;
typedef vector<vector<int> > Matrix;
const int INF = 1e9;
Matrix read_data() {
int vertex_count, edge_count;
std::cin >> vertex_count >> edge_count;
Matrix graph(vertex_count, vector<int>(vertex_count, INF));
for (int i = 0; i < edge_count; ++i) {
int from, to, weight;
std::cin >> from >> to >> weight;
--from, --to;
graph[from][to] = graph[to][from] = weight;
}
return graph;
}
std::pair<int, vector<int> > optimal_path_(const Matrix& graph) {
// This solution tries all the possible sequences of stops.
// It is too slow to pass the problem.
// Implement a more efficient algorithm here.
size_t n = graph.size();
vector<int> p(n);
for (size_t i = 0; i < n; ++i)
p[i] = i;
vector<int> best_path;
int best_ans = INF;
do {
int cur_sum = 0;
bool ok = true;
for (size_t i = 1; i < n && ok; ++i)
if (graph[p[i - 1]][p[i]] == INF)
ok = false;
else
cur_sum += graph[p[i - 1]][p[i]];
if (graph[p.back()][p[0]] == INF)
ok = false;
else
cur_sum += graph[p.back()][p[0]];
if (!ok)
continue;
if (cur_sum < best_ans) {
best_ans = cur_sum;
best_path = p;
}
} while (std::next_permutation(p.begin(), p.end()));
if (best_ans == INF)
best_ans = -1;
for (size_t i = 0; i < best_path.size(); ++i)
++best_path[i];
return std::make_pair(best_ans, best_path);
}
struct Memory {
int w; int c; int r;
};
std::pair<int, vector<int> > optimal_path(const Matrix& graph) {
int n = graph.size(); // edges
int m = (1 << n); // max combinations
vector<vector<Memory>> cost(m, vector<Memory>(n, {INF, 0, 0}));
cost[0][0] = {0, -1, -1};
// C(S, i) be the cost of the minimum cost path visiting each vertex in set S exactly once, starting at 1 and ending at i.
// If size of S is 2, then S must be {1, i},
// C(S, i) = dist(1, i)
for (int i = 1; i < n; i++) {
int sid = (1 << i) + 1;
int v = graph[0][i];
if (v != INF) {
cost[sid][i] = {v, 0, 0};
// std::cout << " set : ["<< sid << "][" << i << "] = " << cost[sid][i].w << std::endl;
}
}
// Else if size of S is greater than 2.
// C(S, i) = min { C(S-{i}, j) + dis(j, i)} where j belongs to S, j != i and j != 1.
// Note that 1 must be present in every subset S, so 1 less bit:
m = (1 << (n - 1));
for (int s = 2; s <= n; s++) {
// std::cout << " size : " << s << std::endl;
// loop from 0 ..m, with n=5, s=2 => 110, 101, 011
for (int b = 0; b < m; b++) {
int nb = 0;
int v = b;
while(v) {
nb += (v & 1); // check last bit
v >>= 1; // shift
}
if (nb != s) {
continue;
}
// shift them and add 1 -> 1100, 1010, 0110
int bits = (b << 1);
// std::cout << " bits : " << bits << std::endl;
for (int i = 1; i < n; i++) { // not 0 it's our start
if (bits & (1 << i)) {
for (int j = 0; j < n; j++) {
if (j != i && (bits & (1 << j))) { // do not stay on the same vertex
int k = bits + 1;
int nk = (bits ^ (1 << i)) + 1;
// std::cout << " try : " << nk << "->" << j << "->" << i <<std::endl;
int c = cost[nk][j].w + graph[j][i];
if (c < cost[k][i].w) {
cost[k][i] = {c, nk, j};
// std::cout << " set : ["<< k << "][" << i << "] = " << c << std::endl;
}
}
}
}
}
}
}
// std::cout << std::endl;
// for (auto &row : cost) {
// for(auto &m : row) {
// std::cout << " " << (m.w == INF ? 0 : m.w) << " (" << m.c << ";" << m.r << ") ";
// }
// std::cout << std::endl;
// }
// std::cout << std::endl;
int best = INF;
vector<int> path;
auto &last_row = cost[(1 << n) - 1];
Memory& last_m = cost[0][0];
int j;
for (int i = 0; i < cost[0].size(); i++) {
auto &cell = last_row[i];
int c = cell.w + graph[i][0];
if (c < best) {
j = i;
best = c;
last_m = cell;
}
}
if (best == INF) {
best = -1;
} else {
path.push_back(j + 1);
while(last_m.r > 0) {
// std::cout << last_m.w << " " << last_m.c << " " << last_m.r << std::endl;
path.push_back(last_m.r + 1);
last_m = cost[last_m.c][last_m.r];
}
path.push_back(1);
}
std::reverse(std::begin(path), std::end(path));
return std::make_pair(best, path);
}
void print_answer(const std::pair<int, vector<int> >& answer) {
std::cout << answer.first << "\n";
if (answer.first == -1)
return;
const vector<int>& path = answer.second;
for (size_t i = 0; i < path.size(); ++i)
std::cout << path[i] << " ";
std::cout << "\n";
}
int main() {
print_answer(optimal_path(read_data()));
return 0;
}
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