Problem Link : http://www.lightoj.com/volume_showproblem.php?problem=1108
Algorithm:
1. Make a graph by reverse the edge direction.
2. Run Bellman Ford in reverse Graph and check if there exist a negative weight cycle. Reversing edge doesn’t affect in cycle because if we reverse the edge direction then cycle remain unchanged.
3. If exist a negative cycle then run a DFS on the reverse graph for finding the nodes which are reachable from negative cycle and store them in a vector and after sorting the vector print them.
4. If there is no negative cycle then print impossible.
/* +-+ +-+ +-+ |R| |.| |S| +-+ +-+ +-+ */ #include <bits/stdc++.h> #define pii pair <int,int> #define sc scanf #define pf printf #define Pi 2*acos(0.0) #define ms(a,b) memset(a, b, sizeof(a)) #define pb(a) push_back(a) #define MP make_pair #define db double #define ll long long #define EPS 10E-10 #define ff first #define ss second #define sqr(x) (x)*(x) #define D(x) cout<<#x " = "<<(x)<<endl #define VI vector <int> #define DBG pf("Hi\n") #define MOD 100007 #define MAX 1005 #define CIN ios_base::sync_with_stdio(0); cin.tie(0) #define SZ(a) (int)a.size() #define sf(a) scanf("%d",&a) #define sff(a,b) scanf("%d%d",&a,&b) #define sfff(a,b,c) scanf("%d%d%d",&a,&b,&c) #define loop(i,n) for(int i=0;i<n;i++) #define REP(i,a,b) for(int i=a;i<b;i++) #define TEST_CASE(t) for(int z=1;z<=t;z++) #define PRINT_CASE printf("Case %d: ",z) #define all(a) a.begin(),a.end() #define intlim 2147483648 #define inf 1000000 #define ull unsigned long long using namespace std; struct data { int u,v,w; data(int x, int y, int z) { u=x,v=y,w=z; } }; int n,m,total_edge; vector<data> graph; vector<int>ans,reverse_graph[MAX]; map<int,bool>mp; int d[MAX]; bool visited[MAX]; void dfs(int u) { mp[u]=1; ans.pb(u); loop(i,SZ(reverse_graph[u])) { int v=reverse_graph[u][i]; if(!mp[v]) dfs(v); } } bool bellmanford() { for(int i=1;i<n;i++) { loop(i,m) { int u=graph[i].u; int v=graph[i].v; if(d[u]+graph[i].w<d[v]) { d[v]=d[u]+graph[i].w; } } } bool negative_cycle=0; loop(i,m) { int u=graph[i].u; int v=graph[i].v; if(d[u]+graph[i].w<d[v]) { negative_cycle=1; d[v]=d[u]+graph[i].w; if(!mp[u]) dfs(u); } } return negative_cycle; } void allclear() { graph.clear(); ans.clear(); mp.clear(); loop(i,n+2) {d[i]=inf;reverse_graph[i].clear();} } int main() { ///freopen("in.txt","r",stdin); ///freopen("out.txt","w",stdout); int t; sf(t); TEST_CASE(t) { int u,v,w; sff(n,m); allclear(); loop(i,m) { sfff(u,v,w); graph.pb(data(v,u,w));//reversing graph reverse_graph[v].pb(u); } PRINT_CASE; if(bellmanford()) { sort(all(ans)); pf("%d",ans[0]); REP(i,1,SZ(ans)) pf(" %d",ans[i]); pf("\n"); } else pf("impossible\n"); } return 0; }