#include <iostream> #include <algorithm> #include <vector> #include <stack> using namespace std; int n, m; // THE GRAPH struct Gate { short in0, in1; // input lines short out0, out1; // output lines }; struct Line { short source; // gate or (-1) for input short target; // gate or (-1) for output short status; // {-1, 0, 1} }; vector<Gate> G; vector<Line> L; vector<short> O; // indices of output lines vector<short> revO; // revO[line] = output index or -1 void build_graph(const vector<pair<int,int>>& Orders) { G.reserve(m); L.reserve(n+2*m); vector<short>Fronts(n); for (int i=0; i<n; i++) { Fronts[i] = L.size(); L.push_back({.source=-1, .target=-1, .status=-1}); } for (const auto& order : Orders) { short inA = Fronts[order.first]; short inB = Fronts[order.second]; L[inA].target = G.size(); L[inB].target = G.size(); Fronts[order.first] = L.size(); L.push_back({.source=(short)G.size(), .target=-1, .status=-1}); Fronts[order.second] = L.size(); L.push_back({.source=(short)G.size(), .target=-1, .status=-1}); G.push_back({.in0=inA, .in1=inB, .out0=Fronts[order.first], .out1=Fronts[order.second]}); } O = std::move(Fronts); revO.resize(L.size(), -1); for (int i=0; i<n; i++) revO[O[i]] = i; } // THE MAIN RECURSION struct FixedBits { uint64_t zeros; short minone, maxone; }; stack<short> BackStack; stack<FixedBits> FBStack; vector<long long> Results; bool is_gate_non_trivial(int g) { return (L[G[g].out0].status == -1) && (L[G[g].out1].status == -1); } short go_through_gate(short g, short val) { if (val==0) return (L[G[g].out0].status==-1) ? G[g].out0 : G[g].out1; else return (L[G[g].out1].status==-1) ? G[g].out1 : G[g].out0; } short go_and_mark_to_the_output(short l, short val) { while (true) { L[l].status = val; BackStack.push(l); if (L[l].target != -1) l = go_through_gate(L[l].target, val); else break; } short ll = revO[l]; if (L[l].status == 0) FBStack.top().zeros |= (1ull<<ll); else { FBStack.top().minone = min(FBStack.top().minone, ll); FBStack.top().maxone = max(FBStack.top().maxone, ll); } return l; } void clear_lines_from_backstack() { while (true) { short l = BackStack.top(); if (l >= 0) { L[l].status = -1; BackStack.pop(); } else break; } } bool are_fixed_bits_ok() { FixedBits fb = FBStack.top(); if (fb.minone==100 || fb.minone==fb.maxone) return true; return (((1ull<<fb.maxone) - (1ull<<fb.minone)) & fb.zeros) == 0; } void process_minusone_block(int size) { /* cerr << "(-1) block size=" << size << endl; */ for (int sblen=1; sblen<=size; sblen++) Results[sblen] += size-sblen+1; } void process_one_minusone_block(int size, int left, int right) { /* cerr << "1-(-1) block size=" << size << " left=" << left << " right=" << right << endl; */ if (left > right) swap(left, right); // left <= right for (int i=0; i<=left; i++) Results[size+i] += i+1; for (int i=left+1; i<=right; i++) Results[size+i] += left+1; for (int i=right+1; i<=left+right; i++) Results[size+i] += left + right + 1 - i; } void RRR(int g) { // look for non-trivial gate while (g<m && !is_gate_non_trivial(g)) g++; // if at the bottom, add to results and finish if (g==m) { /* cerr << "I'm at the bottom:"; */ /* for (int i=0; i<n; i++) */ /* cerr << ' ' << L[O[i]].status; */ /* cerr << endl; */ FixedBits fb = FBStack.top(); // case 1 - there are no ones if (fb.minone == 100) { for (int i=0; i<n; ) { if (L[O[i]].status == -1) { int j; for (j=i+1; j<n && L[O[j]].status==-1; j++); process_minusone_block(j-i); i = j; } else i++; } } // case 2 - there are some ones else { short minbarrier = fb.minone - 1; while (minbarrier>=0 && (fb.zeros & (1ull<<minbarrier))==0) minbarrier--; short maxbarrier = fb.maxone + 1; while (maxbarrier<n && (fb.zeros & (1ull<<maxbarrier))==0) maxbarrier++; process_one_minusone_block(fb.maxone-fb.minone+1, fb.minone-minbarrier-1, maxbarrier-fb.maxone-1); } return; } // else branch BackStack.push(-1); FBStack.push(FBStack.top()); go_and_mark_to_the_output(G[g].out0, 0); go_and_mark_to_the_output(G[g].out1, 0); if (are_fixed_bits_ok()) RRR(g+1); else { /* cerr << "ER" << endl; */ /* for (int i=0; i<n; i++) */ /* cerr << ' ' << L[O[i]].status; */ /* cerr << endl; */ } clear_lines_from_backstack(); FBStack.pop(); FBStack.push(FBStack.top()); go_and_mark_to_the_output(G[g].out0, 1); go_and_mark_to_the_output(G[g].out1, 1); if (are_fixed_bits_ok()) RRR(g+1); else { /* cerr << "ER" << endl; */ /* for (int i=0; i<n; i++) */ /* cerr << ' ' << L[O[i]].status; */ /* cerr << endl; */ } clear_lines_from_backstack(); FBStack.pop(); BackStack.pop(); } void RRRStart() { FBStack.push({.zeros=0, .minone=100, .maxone=-100}); Results.resize(n+1, 0); RRR(0); } int main() { // full cleanup for testing G.clear(); L.clear(); O.clear(); revO.clear(); while (!BackStack.empty()) BackStack.pop(); while (!FBStack.empty()) FBStack.pop(); Results.clear(); /* cerr << "STARTING" << endl; */ ios::sync_with_stdio(false); cin.tie(nullptr); cin >> n >> m; vector<pair<int,int>> Orders(m); for (auto& ord : Orders) { cin >> ord.first >> ord.second; ord.first--; ord.second--; } build_graph(Orders); RRRStart(); for (int i=1; i<=n; i++) cout << (Results[i]%2) << ' '; cout << '\n'; 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 | #include <iostream> #include <algorithm> #include <vector> #include <stack> using namespace std; int n, m; // THE GRAPH struct Gate { short in0, in1; // input lines short out0, out1; // output lines }; struct Line { short source; // gate or (-1) for input short target; // gate or (-1) for output short status; // {-1, 0, 1} }; vector<Gate> G; vector<Line> L; vector<short> O; // indices of output lines vector<short> revO; // revO[line] = output index or -1 void build_graph(const vector<pair<int,int>>& Orders) { G.reserve(m); L.reserve(n+2*m); vector<short>Fronts(n); for (int i=0; i<n; i++) { Fronts[i] = L.size(); L.push_back({.source=-1, .target=-1, .status=-1}); } for (const auto& order : Orders) { short inA = Fronts[order.first]; short inB = Fronts[order.second]; L[inA].target = G.size(); L[inB].target = G.size(); Fronts[order.first] = L.size(); L.push_back({.source=(short)G.size(), .target=-1, .status=-1}); Fronts[order.second] = L.size(); L.push_back({.source=(short)G.size(), .target=-1, .status=-1}); G.push_back({.in0=inA, .in1=inB, .out0=Fronts[order.first], .out1=Fronts[order.second]}); } O = std::move(Fronts); revO.resize(L.size(), -1); for (int i=0; i<n; i++) revO[O[i]] = i; } // THE MAIN RECURSION struct FixedBits { uint64_t zeros; short minone, maxone; }; stack<short> BackStack; stack<FixedBits> FBStack; vector<long long> Results; bool is_gate_non_trivial(int g) { return (L[G[g].out0].status == -1) && (L[G[g].out1].status == -1); } short go_through_gate(short g, short val) { if (val==0) return (L[G[g].out0].status==-1) ? G[g].out0 : G[g].out1; else return (L[G[g].out1].status==-1) ? G[g].out1 : G[g].out0; } short go_and_mark_to_the_output(short l, short val) { while (true) { L[l].status = val; BackStack.push(l); if (L[l].target != -1) l = go_through_gate(L[l].target, val); else break; } short ll = revO[l]; if (L[l].status == 0) FBStack.top().zeros |= (1ull<<ll); else { FBStack.top().minone = min(FBStack.top().minone, ll); FBStack.top().maxone = max(FBStack.top().maxone, ll); } return l; } void clear_lines_from_backstack() { while (true) { short l = BackStack.top(); if (l >= 0) { L[l].status = -1; BackStack.pop(); } else break; } } bool are_fixed_bits_ok() { FixedBits fb = FBStack.top(); if (fb.minone==100 || fb.minone==fb.maxone) return true; return (((1ull<<fb.maxone) - (1ull<<fb.minone)) & fb.zeros) == 0; } void process_minusone_block(int size) { /* cerr << "(-1) block size=" << size << endl; */ for (int sblen=1; sblen<=size; sblen++) Results[sblen] += size-sblen+1; } void process_one_minusone_block(int size, int left, int right) { /* cerr << "1-(-1) block size=" << size << " left=" << left << " right=" << right << endl; */ if (left > right) swap(left, right); // left <= right for (int i=0; i<=left; i++) Results[size+i] += i+1; for (int i=left+1; i<=right; i++) Results[size+i] += left+1; for (int i=right+1; i<=left+right; i++) Results[size+i] += left + right + 1 - i; } void RRR(int g) { // look for non-trivial gate while (g<m && !is_gate_non_trivial(g)) g++; // if at the bottom, add to results and finish if (g==m) { /* cerr << "I'm at the bottom:"; */ /* for (int i=0; i<n; i++) */ /* cerr << ' ' << L[O[i]].status; */ /* cerr << endl; */ FixedBits fb = FBStack.top(); // case 1 - there are no ones if (fb.minone == 100) { for (int i=0; i<n; ) { if (L[O[i]].status == -1) { int j; for (j=i+1; j<n && L[O[j]].status==-1; j++); process_minusone_block(j-i); i = j; } else i++; } } // case 2 - there are some ones else { short minbarrier = fb.minone - 1; while (minbarrier>=0 && (fb.zeros & (1ull<<minbarrier))==0) minbarrier--; short maxbarrier = fb.maxone + 1; while (maxbarrier<n && (fb.zeros & (1ull<<maxbarrier))==0) maxbarrier++; process_one_minusone_block(fb.maxone-fb.minone+1, fb.minone-minbarrier-1, maxbarrier-fb.maxone-1); } return; } // else branch BackStack.push(-1); FBStack.push(FBStack.top()); go_and_mark_to_the_output(G[g].out0, 0); go_and_mark_to_the_output(G[g].out1, 0); if (are_fixed_bits_ok()) RRR(g+1); else { /* cerr << "ER" << endl; */ /* for (int i=0; i<n; i++) */ /* cerr << ' ' << L[O[i]].status; */ /* cerr << endl; */ } clear_lines_from_backstack(); FBStack.pop(); FBStack.push(FBStack.top()); go_and_mark_to_the_output(G[g].out0, 1); go_and_mark_to_the_output(G[g].out1, 1); if (are_fixed_bits_ok()) RRR(g+1); else { /* cerr << "ER" << endl; */ /* for (int i=0; i<n; i++) */ /* cerr << ' ' << L[O[i]].status; */ /* cerr << endl; */ } clear_lines_from_backstack(); FBStack.pop(); BackStack.pop(); } void RRRStart() { FBStack.push({.zeros=0, .minone=100, .maxone=-100}); Results.resize(n+1, 0); RRR(0); } int main() { // full cleanup for testing G.clear(); L.clear(); O.clear(); revO.clear(); while (!BackStack.empty()) BackStack.pop(); while (!FBStack.empty()) FBStack.pop(); Results.clear(); /* cerr << "STARTING" << endl; */ ios::sync_with_stdio(false); cin.tie(nullptr); cin >> n >> m; vector<pair<int,int>> Orders(m); for (auto& ord : Orders) { cin >> ord.first >> ord.second; ord.first--; ord.second--; } build_graph(Orders); RRRStart(); for (int i=1; i<=n; i++) cout << (Results[i]%2) << ' '; cout << '\n'; return 0; } |