//MODIFICARE SURSA PENTRU IMPLEMENTARE 0
/*
__===*@@@ @@@@@ @@@@@
/ ________________________________________ ___ __ _ _
______|^|_ | *** |___ ___ __
/|/~~~~~~~| | *** |____ __ _ __
/ | {_) | | *** My Source(Leo) |__ ___ _ __
____/__|) /~~| |@@@@| ************************************|____ ___ _
/ _____ ~~~~~~~~~|@@@@| ***********************************|___ __ _ __
| / \\ --| |_/~~~~~\_______________________/~~~~~\__|_____ __ _ _
|/ *** \\ |---~|/ *** \_____________________/ *** \_|___ _ __ _ _
` ***** ~~~~===== ***** *****
*** *** ***
------------------------------------------------------------------------------
*/
#include <bits/stdc++.h>
#define INF 0x3f3f3f3f
using namespace std;
//typedef int cost;
//typedef int muchie;
using namespace std;
string fisier = "bellmanford";
const int CMAX = 5e4+15;
struct triplet{
int x , y , c;
};
int muchie , cost , n , m;
int h[CMAX];
int D[CMAX];
int matrice_D[CMAX/5][CMAX/5];
int viz[CMAX];
const long long int oo = 1000*50000;
vector < pair < int , int > > graf[CMAX];
vector < triplet > muchii;
ifstream fin(fisier+".in");
ofstream fout(fisier+".out");
struct comp{
bool operator()(int x, int y){
return D[x] > D[y];
}
};
queue < int > coada;
priority_queue < int , vector < int >, comp > Q;
void citire()
{
int x , y , c;
fin >> n >> m;
for(int i=1;i<=m;i++)
{
fin >> x >> y >> c;
muchii.push_back({x,y,c});
graf[x].push_back({y,c});
}
//sort(muchii.begin(),muchii.end());
//for(int i=0;i<muchii.size();i++)
// cout << muchii[i].x << " " << muchii[i].y << " " << muchii[i].c << '\n';
}
void afisare(vector < pair < int , int > > graf[CMAX]){
for(int i=0;i<=n;i++)
{
cout << "Nodul: " << i << " : ";
for(int j=0;j<graf[i].size();j++)
{
cout << "(" <<graf[i][j].first << "," << graf[i][j].second << ") ";
}
cout << '\n';
}
}
bool BellmanFord(vector<pair<int,int>>graf[CMAX],int start){
for(int i=0;i<=n;i++)
{
viz[i] = 0;
D[i] = oo;
}
D[start] = 0;
coada.push(start);
while(!coada.empty()){
int nodcurent = coada.front();
viz[nodcurent]++;
coada.pop();
if(viz[nodcurent]>=n){
return false;
}
for(int i=0;i<graf[nodcurent].size();i++)
{
int vecin = graf[nodcurent][i].first;
int cost = graf[nodcurent][i].second;
if(D[nodcurent]+cost<D[vecin]){
D[vecin] = D[nodcurent] + cost;
coada.push(vecin);
}
}
}
return true;
}
void Dijkstra(vector<pair<int,int>> graf[CMAX], int start)
{
for(int i=0;i<=n;i++)
D[i] = oo;
//viz[start] = 1;
D[start] = 0;
Q.push(start);
while(!Q.empty()){
int nodcurent = Q.top();
//cout << "nodcurent: " << nodcurent << '\n';
Q.pop();
viz[nodcurent] = 0;
for(int i=0;i<graf[nodcurent].size();i++)
{
int cost, vecin;
vecin = graf[nodcurent][i].first;
cost = graf[nodcurent][i].second;
//cout << "vecini: " << vecin << " ";
//cout << "cost: " << cost << " ";
if(D[nodcurent] + cost < D[vecin]){
//cout << "intrat";
D[vecin] = D[nodcurent] + cost;
if(viz[vecin]==0){
//cout << "bagat in coada";
Q.push(vecin);
viz[vecin] = 1;
}
}
//cout << " |";
}
//cout << '\n';
}
}
int reponderare(int drum, int val_a , int val_b){
return drum + val_a - val_b;
}
int reponderare_inversa(int drum, int val_a , int val_b){
return drum - val_a + val_b;
}
/*
void BFS(int start)
{
queue < int > quada;
bool vizitat[CMAX];
quada.push(start);
while(!quada.empty()){
int nodcurent = quada.front();
quada.pop();
}
}
*/
bool Johnson(){
//Adaugam nodul 0 la graful nostru
vector < pair < int , int > > graf_modif[CMAX];
int h[CMAX];
for(int i=1;i<=n;i++)
{
//Adaugam nodul 0
graf[0].push_back({i,0});
}
if(BellmanFord(graf,0)==false){
return false;
}
else{
for(int i=1;i<=n;i++)
h[i] = D[i];
for(int i=0;i<muchii.size();i++){
//reponderam graful cu ce am gasit dupa executia algoritmului Bellman Ford
graf_modif[muchii[i].x].push_back({muchii[i].y,reponderare(muchii[i].c,D[muchii[i].x],D[muchii[i].y])});
}
/*
cout << "Graf reponderat: \n";
afisare(graf_modif);
*/
/*
cout << "h = ";
for(int i=1;i<=n;i++)
cout << h[i] << " ";
cout << '\n';
*/
for(int j=1;j<=n;j++)
{
memset(viz,0,CMAX);
Dijkstra(graf_modif,j);
/*
cout << "Pentru : " << j << " avem: \n";
//memset(D,0,CMAX);
for(int z=1;z<=n;z++)
cout << D[z] << " ";
cout << '\n';
*/
//cout << "Pentru nodul : " << j << " avem urmatoarele valori: ";
for(int z=1;z<=n;z++){
//facem repondnerarea inversa
matrice_D[j][z] = reponderare_inversa(D[z],h[j],h[z]);
//cout << matrice_D[j][z] << " ";
}
//cout << '\n';
}
}
afisare(graf_modif);
return true;
/*
for(int i=1;i<=n;i++)
cout << D[i] << " ";
cout << '\n';
*/
}
bool Johnson2(){
//Adaugam nodul 0 la graful nostru
vector < pair < int , int > > graf_modif[CMAX];
int h[CMAX];
for(int i=1;i<=n;i++)
{
//Adaugam nodul 0
graf[0].push_back({i,0});
}
if(BellmanFord(graf,0)==false){
return false;
}
else{
for(int i=1;i<=n;i++)
h[i] = D[i];
for(int i=0;i<muchii.size();i++){
//reponderam graful cu ce am gasit dupa executia algoritmului Bellman Ford
graf_modif[muchii[i].x].push_back({muchii[i].y,reponderare(muchii[i].c,D[muchii[i].x],D[muchii[i].y])});
}
/*
cout << "Graf reponderat: \n";
afisare(graf_modif);
*/
/*
cout << "h = ";
for(int i=1;i<=n;i++)
cout << h[i] << " ";
cout << '\n';
*/
for(int j=1;j<=n;j++)
{
memset(viz,0,CMAX);
Dijkstra(graf_modif,j);
/*
cout << "Pentru : " << j << " avem: \n";
//memset(D,0,CMAX);
for(int z=1;z<=n;z++)
cout << D[z] << " ";
cout << '\n';
*/
//cout << "Pentru nodul : " << j << " avem urmatoarele valori: ";
for(int z=1;z<=n;z++){
//facem repondnerarea inversa
matrice_D[j][z] = reponderare_inversa(D[z],h[j],h[z]);
//cout << matrice_D[j][z] << " ";
}
//cout << '\n';
}
}
afisare(graf_modif);
return true;
/*
for(int i=1;i<=n;i++)
cout << D[i] << " ";
cout << '\n';
*/
}
int main(){
citire();
//BellmaFord
if(BellmanFord(graf,1)==true){
for(int i=2;i<=n;i++)
fout << D[i] << " ";
}
else
fout << "Ciclu negativ!";
// resetare vector vizitati
// memset(viz,0,CMAX);
/*
Dijkstra(graf,1);
for(int i=2;i<=n;i++)
if(D[i]!=oo)
fout << D[i] << " ";
else
fout << 0 << " ";
*/
/*
if(Johnson() == false)
{
cout << -1;
}
else{
for(int i=1;i<=n;i++)
{
for(int j=1;j<=n;j++)
cout << matrice_D[i][j] << " ";
cout << '\n';
}
}
*/
//afisare(graf);
return 0;
}