#include <iostream>
#include <fstream>
#include <vector>
#include <deque>
#include <stack>
#include <tuple>
#include <queue>
#include <list>
using namespace std;
class Graph {
struct nodeStruct {
int node, cost;
bool operator()(nodeStruct const& n1, nodeStruct const& n2) { return n1.cost > n2.cost; }
};
vector<list<nodeStruct>> adjacent;
vector<list<nodeStruct>> transposed() {
vector<list<nodeStruct>> ret(adjacent.size());
for(int i = 0; i < adjacent.size(); i++)
for(nodeStruct node: adjacent[i])
ret[node.node].push_back(nodeStruct({i, node.cost}));
return ret;
}
void dfs(int current, vector<bool> &visited, stack<int> &order) {
visited[current] = true;
for(auto i: adjacent[current])
if(!visited[i.node])
dfs(i.node, visited, order);
order.push(current);
}
void bfs(int current, vector<int> &costs, vector<bool> &visited, deque<int> &queue) {
queue.push_back(current);
visited[current] = true;
costs[current] = 0;
while(queue.empty() != 1) {
int k = queue.front();
for(auto i: adjacent[k])
if(!visited[i.node]) {
costs[i.node] += (costs[k] + 1);
visited[i.node] = true;
queue.push_back(i.node);
}
queue.pop_front();
}
}
void _biconnected(int node, int daddy, vector<bool> &visited, vector<int> &level, vector<int> &minLevel, stack<int> &s, vector<vector<int>> &components, vector<pair<int,int>> &criticalEdges) {
visited[node] = true;
minLevel[node] = level[node] = level[daddy] + 1;
s.push(node);
for (auto x: adjacent[node])
if (x.node != daddy) {
if (visited[x.node])
minLevel[node] = min(minLevel[node], level[x.node]);
else {
_biconnected(x.node, node, visited, level, minLevel, s, components, criticalEdges);
minLevel[node] = min(minLevel[node], minLevel[x.node]);
if(level[node] < minLevel[x.node])
criticalEdges.emplace_back(node, x.node);
if (minLevel[x.node] >= level[node]) {
components.resize(components.size()+1);
while (s.top() != x.node) {
components[components.size()-1].push_back(s.top());
s.pop();
}
components[components.size()-1].push_back(x.node);
s.pop();
components[components.size()-1].push_back(node);
}
}
}
}
void _hardConnected(int node, vector<bool> &visited, vector<vector<int>> &components, vector<list<nodeStruct>> &t) {
visited[node] = false;
components[components.size() - 1].push_back(node);
for(auto j: t[node])
if(visited[j.node])
_hardConnected(j.node, visited, components, t);
}
public:
Graph(vector<tuple<int, int, int>> &data, int nrNodes, bool oriented=true) {
adjacent.resize(nrNodes);
for(auto[node1, node2, cost]: data) {
adjacent[node1].push_back(nodeStruct({node2, cost}));
if(!oriented)
adjacent[node2].push_back(nodeStruct({node1, cost}));
}
}
friend ostream& operator<< (ostream& os, Graph graph) {
os << graph.adjacent.size() << " nodes\n";
for(int i = 0; i < graph.adjacent.size(); i++) {
os << "node " << i << ": ";
for(nodeStruct j: graph.adjacent[i])
os << "(" << j.node << ", " << j.cost << ") ";
os << "\n";
}
return os;
}
int connected() {
vector<bool> visited(adjacent.size());
int nr = 0;
for(int i = 0; i < adjacent.size(); i++)
if(!visited[i]) {
stack<int> _;
nr++;
dfs(i, visited, _);
}
return nr;
}
pair<vector<int>, vector<bool>> costs(int start) {
vector<int> costs(adjacent.size());
vector<bool> visited(adjacent.size());
deque<int> queue;
bfs(start, costs, visited, queue);
return make_pair(costs, visited);
}
stack<int> topologicalSort() {
vector<bool> visited(adjacent.size());
stack<int> order;
for(int i = 0; i < adjacent.size(); i++)
if(!visited[i])
dfs(i, visited, order);
return order;
}
pair<vector<vector<int>>, vector<pair<int,int>>> biconnected(){
stack<int> s;
vector<int> level(adjacent.size()), minLevel(adjacent.size());
vector<bool> visited(adjacent.size());
vector<vector<int>> components;
vector<pair<int,int>> criticalEdges;
for (int i = 0; i < adjacent.size(); i++)
if (visited[i] == 0)
_biconnected(i, 0, visited, level, minLevel, s, components, criticalEdges);
return make_pair(components, criticalEdges);
}
vector<vector<int>> hardConnected() {
stack<int> s;
vector<bool> visited(adjacent.size());
vector<vector<int>> components;
vector<list<nodeStruct>> t = transposed();
for(int i = 0; i < adjacent.size(); i++)
if(!visited[i])
dfs(i, visited, s);
while(!s.empty()){
if(visited[s.top()]){
components.resize(components.size() + 1);
_hardConnected(s.top(), visited, components, t);
}
s.pop();
}
return components;
}
pair<vector<int>, bool> dijkstraBellman(int start) {
const int inf = 250001;
vector<int> visited(adjacent.size()), distance(adjacent.size(), inf);
priority_queue<nodeStruct, vector<nodeStruct>, nodeStruct> costs;
costs.push({start, 0});
distance[start] = 0;
while(costs.empty() != 1) {
int node = costs.top().node;
costs.pop();
for(auto i: adjacent[node]){
if(distance[i.node] == inf || distance[i.node] > i.cost + distance[node]){
distance[i.node] = i.cost + distance[node];
costs.push({i.node, distance[i.node]});
visited[node]++;
if(visited[i.node] >= adjacent.size())
return make_pair(distance, 1);
}
}
visited[node]++;
}
return make_pair(distance, 0);
}
};
int main() {
ifstream in("dijkstra.in");
ofstream out("dijkstra.out");
vector<tuple<int, int, int>> data;
int n, m, start;
in >> n >> m; // >> start;
for(int i = 0; i < m; i++) {
int aux1, aux2, cost;
in >> aux1 >> aux2 >> cost;
data.emplace_back(aux1 - 1, aux2 - 1, cost);
// data.emplace_back(aux2 - 1, aux1 - 1, 0);
}
Graph g(data, n);
auto dijks = g.dijkstraBellman(0);
if(dijks.second)
out << "Ciclu negativ!";
else for(int i = 1; i < dijks.first.size(); i++)
out << dijks.first[i] << " ";
// out << g.connected();
// auto components = g.hardConnected();
// out << components.size() << "\n";
// for(auto j: component)
// out << j + 1 << " ";
// out << "\n";
// }
// auto rez = g.biconnected();
// out << rez.first.size() << "\n";
// for(const auto& connected: rez.first) {
// for(auto node: connected)
// out << node + 1 << " ";
// out << "\n";
// }
// for(auto [x, y] : rez.second)
// cout << "(" << x + 1 << ", " << y + 1 << ") ";
return 0;
}