// Potyczki Algorytmiczne 2015 // runda 5 // KONtrmanifestacja // Tomasz Pastusiak #include <iostream> #include <algorithm> #include <functional> #include <stack> #include <set> #include <cmath> #include <vector> #include <string> using namespace std; // cities are numbered 1 ... n #define MAXN 500001 //#define MAXM 1000000 #define LL long long int int n,m; vector<int> g[MAXN]; vector<int> gt[MAXN]; int p[MAXN]; // parent int scc_id[MAXN]; //strongly connected component ID for city int scc_id_t[MAXN]; int sccs_size[MAXN]; int processedOrder[MAXN]; int cycleLen; int cycleVerts[MAXN]; int t[MAXN]; // used in topo sort bool mandatory[MAXN]; // SCC start (Stańczyk) int nr; void SccSDfs(vector<int> *graph, int *t, int v){ if(t[v] == -1){ t[v] = nr; for(int i=0; i<graph[v].size() ;++i){ SccSDfs(graph, t, graph[v][i]); } // for each child if(nr < 0) t[v] = -(--nr) - 3; } // if not visited yet } void SccS(){ for(int i=1; i <= n ;++i){ scc_id[i] = scc_id_t[i] = -1; for(int v=0; v<g[i].size(); ++v) gt[v].push_back(i); } nr = -2; for(int i=1; i <= n; ++i){ SccSDfs(gt, scc_id_t, i); processedOrder[scc_id_t[i]] = i; } nr = 0; for(int i=n-1; i>=0; --i){ SccSDfs(g, scc_id, processedOrder[i]); nr++; } } // SCC end int cycleSCC; int cycleStart; void getCycleR(int v){ for(int i=0; i<g[v].size() ;++i){ int child = g[v][i]; if(p[child] == -1){ p[child] = v; if(child == cycleStart){ return; } if(scc_id[child] == cycleSCC){ getCycleR(child); } } // if child not visited yet } // for each child } void getCycle(int v){ cycleStart = v; cycleSCC = scc_id[v]; for(int i=1; i<= n; ++i) p[i] = -1; getCycleR(cycleStart); cycleVerts[0] = cycleStart; cycleLen = 1; int currentVert = p[cycleStart]; while(currentVert != cycleStart){ cycleVerts[cycleLen++] = currentVert; currentVert = p[currentVert]; } } // TOPO begin int topo; int topoSCC; void TopoDfs(int v){ if(!t[v] && scc_id[v] == topoSCC){ t[v] = 1; for(int i=0; i<g[v].size() ;++i){ TopoDfs(g[v][i]); } t[v] = --topo; } } void TopoSort(int scc){ topoSCC = scc; for(int i=1; i<=n ;++i){ t[i] = 0; } topo = n; for(int i=n; i>=1; --i){ TopoDfs(i); } } bool AcyclicD(int scc){ TopoSort(scc); for(int i=1; i <= n; ++i){ for(int v=0; v<g[i].size() ;++v){ if(scc_id[i] != scc || scc_id[g[i][v]] != scc) continue; if(t[i] >= t[g[i][v]]) return false; } } return true; } // TOPO end int main(){ ios_base::sync_with_stdio(false); int a,b; cin >> n >> m; for(int i=0; i<m ; ++i){ cin >> a >> b; g[a].push_back(b); } // DATA LOADED SccS(); /* for(int i=1; i <= n ; ++i){ cout << "City: " << i << " scc ID: " << scc_id[i] << endl; } cout << "--------" << endl; */ for(int i=0; i<n+1 ; ++i){ sccs_size[i] = 0; mandatory[i] = false; } for(int i=1; i<=n ; ++i){ sccs_size[scc_id[i]]++; } int numberOfProperSccs = 0; // "proper" Scc contains at least 2 cities int sccNoticed = -1; for(int i=0; i<n+1 ; ++i){ if(sccs_size[i] >= 2){ numberOfProperSccs++; sccNoticed = i; } } if(numberOfProperSccs == 0){ cout << "NIE" << endl; // no sccs mean no cycles at all return 0; } else if(numberOfProperSccs > 1){ cout << 0 << endl << endl; // if there are at least 2 sccs, there are at least 2 independent cycles return 0; } // if there is only one scc, we don't know... // lets do some brute force // find a cycle in scc (the smaller the better) // for every city in this cycle.... remove it, check if there are any cycles in scc without this city, if there are: city is NOT mandatory, if there is no cycle, city is MANDATORY // another (heuristic?) // until there are not marked cities: // start at some not marked city, do DFS search for cycle but favorizing edges to not-marked cities // when cycle found, mark every it's city.. // it is almost 100% wrong algo.... int cycleStartingPoint; for(int i=1; i<=n ; ++i){ if(scc_id[i] == sccNoticed) cycleStartingPoint = i; } getCycle(cycleStartingPoint); /* cout << "Suspicious cycle: " << endl; for(int i=0; i<cycleLen; ++i){ cout << cycleVerts[i] << ' '; } cout << endl; cout << "--------" << endl; */ int mandatoryVertsCount = 0; for(int i=0; i < cycleLen; ++i){ scc_id[cycleVerts[i]] = -1; // remove it from scc temporarily if(AcyclicD(sccNoticed)) { mandatory[cycleVerts[i]] = true; // if removing vert made graph acyclic, this vert is mandatory mandatoryVertsCount++; } scc_id[cycleVerts[i]] = sccNoticed; // put it back } cout << mandatoryVertsCount << endl; for(int i=1; i<=n; ++i){ if(mandatory[i]) cout << i << ' '; } cout << endl; return 0; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 | // Potyczki Algorytmiczne 2015 // runda 5 // KONtrmanifestacja // Tomasz Pastusiak #include <iostream> #include <algorithm> #include <functional> #include <stack> #include <set> #include <cmath> #include <vector> #include <string> using namespace std; // cities are numbered 1 ... n #define MAXN 500001 //#define MAXM 1000000 #define LL long long int int n,m; vector<int> g[MAXN]; vector<int> gt[MAXN]; int p[MAXN]; // parent int scc_id[MAXN]; //strongly connected component ID for city int scc_id_t[MAXN]; int sccs_size[MAXN]; int processedOrder[MAXN]; int cycleLen; int cycleVerts[MAXN]; int t[MAXN]; // used in topo sort bool mandatory[MAXN]; // SCC start (Stańczyk) int nr; void SccSDfs(vector<int> *graph, int *t, int v){ if(t[v] == -1){ t[v] = nr; for(int i=0; i<graph[v].size() ;++i){ SccSDfs(graph, t, graph[v][i]); } // for each child if(nr < 0) t[v] = -(--nr) - 3; } // if not visited yet } void SccS(){ for(int i=1; i <= n ;++i){ scc_id[i] = scc_id_t[i] = -1; for(int v=0; v<g[i].size(); ++v) gt[v].push_back(i); } nr = -2; for(int i=1; i <= n; ++i){ SccSDfs(gt, scc_id_t, i); processedOrder[scc_id_t[i]] = i; } nr = 0; for(int i=n-1; i>=0; --i){ SccSDfs(g, scc_id, processedOrder[i]); nr++; } } // SCC end int cycleSCC; int cycleStart; void getCycleR(int v){ for(int i=0; i<g[v].size() ;++i){ int child = g[v][i]; if(p[child] == -1){ p[child] = v; if(child == cycleStart){ return; } if(scc_id[child] == cycleSCC){ getCycleR(child); } } // if child not visited yet } // for each child } void getCycle(int v){ cycleStart = v; cycleSCC = scc_id[v]; for(int i=1; i<= n; ++i) p[i] = -1; getCycleR(cycleStart); cycleVerts[0] = cycleStart; cycleLen = 1; int currentVert = p[cycleStart]; while(currentVert != cycleStart){ cycleVerts[cycleLen++] = currentVert; currentVert = p[currentVert]; } } // TOPO begin int topo; int topoSCC; void TopoDfs(int v){ if(!t[v] && scc_id[v] == topoSCC){ t[v] = 1; for(int i=0; i<g[v].size() ;++i){ TopoDfs(g[v][i]); } t[v] = --topo; } } void TopoSort(int scc){ topoSCC = scc; for(int i=1; i<=n ;++i){ t[i] = 0; } topo = n; for(int i=n; i>=1; --i){ TopoDfs(i); } } bool AcyclicD(int scc){ TopoSort(scc); for(int i=1; i <= n; ++i){ for(int v=0; v<g[i].size() ;++v){ if(scc_id[i] != scc || scc_id[g[i][v]] != scc) continue; if(t[i] >= t[g[i][v]]) return false; } } return true; } // TOPO end int main(){ ios_base::sync_with_stdio(false); int a,b; cin >> n >> m; for(int i=0; i<m ; ++i){ cin >> a >> b; g[a].push_back(b); } // DATA LOADED SccS(); /* for(int i=1; i <= n ; ++i){ cout << "City: " << i << " scc ID: " << scc_id[i] << endl; } cout << "--------" << endl; */ for(int i=0; i<n+1 ; ++i){ sccs_size[i] = 0; mandatory[i] = false; } for(int i=1; i<=n ; ++i){ sccs_size[scc_id[i]]++; } int numberOfProperSccs = 0; // "proper" Scc contains at least 2 cities int sccNoticed = -1; for(int i=0; i<n+1 ; ++i){ if(sccs_size[i] >= 2){ numberOfProperSccs++; sccNoticed = i; } } if(numberOfProperSccs == 0){ cout << "NIE" << endl; // no sccs mean no cycles at all return 0; } else if(numberOfProperSccs > 1){ cout << 0 << endl << endl; // if there are at least 2 sccs, there are at least 2 independent cycles return 0; } // if there is only one scc, we don't know... // lets do some brute force // find a cycle in scc (the smaller the better) // for every city in this cycle.... remove it, check if there are any cycles in scc without this city, if there are: city is NOT mandatory, if there is no cycle, city is MANDATORY // another (heuristic?) // until there are not marked cities: // start at some not marked city, do DFS search for cycle but favorizing edges to not-marked cities // when cycle found, mark every it's city.. // it is almost 100% wrong algo.... int cycleStartingPoint; for(int i=1; i<=n ; ++i){ if(scc_id[i] == sccNoticed) cycleStartingPoint = i; } getCycle(cycleStartingPoint); /* cout << "Suspicious cycle: " << endl; for(int i=0; i<cycleLen; ++i){ cout << cycleVerts[i] << ' '; } cout << endl; cout << "--------" << endl; */ int mandatoryVertsCount = 0; for(int i=0; i < cycleLen; ++i){ scc_id[cycleVerts[i]] = -1; // remove it from scc temporarily if(AcyclicD(sccNoticed)) { mandatory[cycleVerts[i]] = true; // if removing vert made graph acyclic, this vert is mandatory mandatoryVertsCount++; } scc_id[cycleVerts[i]] = sccNoticed; // put it back } cout << mandatoryVertsCount << endl; for(int i=1; i<=n; ++i){ if(mandatory[i]) cout << i << ' '; } cout << endl; return 0; } |