#include <cstdio> #include <cstdlib> #include <cstdint> #include <vector> struct graph { struct edge { int vert; int next; edge(int vert, int next) : vert(vert), next(next) {} }; std::vector<int> firsts; std::vector<edge> edges; graph(int count) { firsts.resize(count, -1); } graph(graph&&) = default; graph(const graph&) = delete; graph& operator=(graph&&) = default; graph& operator=(const graph&) = delete; void add_edge(int from, int to) { int idx = edges.size(); edges.push_back(edge(to, firsts[from])); firsts[from] = idx; } template<typename F> void for_each_neighbor(int v, F f) const { for (int e = firsts[v]; e != -1; e = edges[e].next) { f(edges[e].vert); } } }; static const uint64_t MODULUS = 1000 * 1000 * 1000 + 7; enum class color : uint8_t { unknown = 0, red = 1, blue = 2, }; std::vector<uint64_t> gen_factorials(uint64_t count) { std::vector<uint64_t> ret; ret.reserve(count); ret.push_back(1); for (uint64_t i = 1; i < count; i++) { ret.push_back((ret.back() * i) % MODULUS); } return ret; } constexpr uint64_t modular_inverse(const int64_t a) { int64_t oldr = a; int64_t r = MODULUS; int64_t olds = 1; int64_t s = 0; while (r != 0) { const int64_t q = oldr / r; const int64_t newr = oldr - q * r; const int64_t news = olds - q * s; oldr = r; olds = s; r = newr; s = news; } return (olds + MODULUS) % MODULUS; } int main() { int n, m; scanf("%d %d", &n, &m); std::vector<bool> lit_status; lit_status.reserve(n); for (int i = 0; i < n; i++) { int x; scanf("%d", &x); lit_status.push_back(x != 0); } graph g(n); for (int i = 0; i < m; i++) { int a, b; scanf("%d %d", &a, &b); a--; b--; g.add_edge(a, b); g.add_edge(b, a); } uint64_t total = 1; auto factorials = gen_factorials(n + 1); auto binomial = [&factorials] (uint64_t n, uint64_t k) -> uint64_t { const uint64_t denominator = (factorials[k] * factorials[n - k]) % MODULUS; return (factorials[n] * modular_inverse(denominator)) % MODULUS; }; std::vector<color> colors(n, color::unknown); std::vector<std::pair<int, color>> component_verts; for (int i = 0; i < n; i++) { if (colors[i] != color::unknown) { continue; } bool colorable = true; component_verts.push_back({i, color::red}); colors[i] = color::red; int pos = 0; while (pos < component_verts.size()) { auto [v, col] = component_verts[pos++]; color other_col = (col == color::red) ? color::blue : color::red; g.for_each_neighbor(v, [&] (int other) { if (colors[other] == color::unknown) { colors[other] = other_col; component_verts.push_back({other, other_col}); } else if (colors[other] != other_col) { colorable = false; } }); } int reds_lit = 0; int reds_total = 0; int blues_lit = 0; int blues_total = 0; int parity = 0; for (auto [v, col] : component_verts) { if (col == color::red) { reds_total++; if (lit_status[v]) { reds_lit++; } } else { blues_total++; if (lit_status[v]) { blues_lit++; } } if (lit_status[v]) { parity = 1 - parity; } } // printf("Partition size: %llu, colorable: %s\n", (unsigned long long int)component_verts.size(), colorable ? "true" : "false"); uint64_t contribution = 0; if (!colorable) { // printf(" parity: %d\n", parity); // All configurations with the right parity are good for (int p = parity; p <= component_verts.size(); p += 2) { // printf(" adding for p = %d: %llu\n", p, binomial(component_verts.size(), p)); contribution = (contribution + binomial(component_verts.size(), p)) % MODULUS; } } else { // printf(" reds lit: %d/%d, blues lit: %d/%d\n", reds_lit, reds_total, blues_lit, blues_total); // The graph is bipartite. Every operation adds or removes a bulb in both parts. // We cannot go below 0 bulbs in either part or go above any part's capacity, // but otherwise configurations are unrestricted. const int begin = -std::min(reds_lit, blues_lit); const int end = std::min(reds_total - reds_lit, blues_total - blues_lit); for (int offp = begin; offp <= end; offp++) { const int r = reds_lit + offp; const int b = blues_lit + offp; // printf(" adding for r=%d/b=%d: %llu/%llu\n", r, b, binomial(reds_total, r), binomial(blues_total, b)); const uint64_t count = (binomial(reds_total, r) * binomial(blues_total, b)) % MODULUS; contribution = (contribution + count) % MODULUS; } } component_verts.clear(); total = (total * contribution) % MODULUS; } printf("%llu\n", total); 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 | #include <cstdio> #include <cstdlib> #include <cstdint> #include <vector> struct graph { struct edge { int vert; int next; edge(int vert, int next) : vert(vert), next(next) {} }; std::vector<int> firsts; std::vector<edge> edges; graph(int count) { firsts.resize(count, -1); } graph(graph&&) = default; graph(const graph&) = delete; graph& operator=(graph&&) = default; graph& operator=(const graph&) = delete; void add_edge(int from, int to) { int idx = edges.size(); edges.push_back(edge(to, firsts[from])); firsts[from] = idx; } template<typename F> void for_each_neighbor(int v, F f) const { for (int e = firsts[v]; e != -1; e = edges[e].next) { f(edges[e].vert); } } }; static const uint64_t MODULUS = 1000 * 1000 * 1000 + 7; enum class color : uint8_t { unknown = 0, red = 1, blue = 2, }; std::vector<uint64_t> gen_factorials(uint64_t count) { std::vector<uint64_t> ret; ret.reserve(count); ret.push_back(1); for (uint64_t i = 1; i < count; i++) { ret.push_back((ret.back() * i) % MODULUS); } return ret; } constexpr uint64_t modular_inverse(const int64_t a) { int64_t oldr = a; int64_t r = MODULUS; int64_t olds = 1; int64_t s = 0; while (r != 0) { const int64_t q = oldr / r; const int64_t newr = oldr - q * r; const int64_t news = olds - q * s; oldr = r; olds = s; r = newr; s = news; } return (olds + MODULUS) % MODULUS; } int main() { int n, m; scanf("%d %d", &n, &m); std::vector<bool> lit_status; lit_status.reserve(n); for (int i = 0; i < n; i++) { int x; scanf("%d", &x); lit_status.push_back(x != 0); } graph g(n); for (int i = 0; i < m; i++) { int a, b; scanf("%d %d", &a, &b); a--; b--; g.add_edge(a, b); g.add_edge(b, a); } uint64_t total = 1; auto factorials = gen_factorials(n + 1); auto binomial = [&factorials] (uint64_t n, uint64_t k) -> uint64_t { const uint64_t denominator = (factorials[k] * factorials[n - k]) % MODULUS; return (factorials[n] * modular_inverse(denominator)) % MODULUS; }; std::vector<color> colors(n, color::unknown); std::vector<std::pair<int, color>> component_verts; for (int i = 0; i < n; i++) { if (colors[i] != color::unknown) { continue; } bool colorable = true; component_verts.push_back({i, color::red}); colors[i] = color::red; int pos = 0; while (pos < component_verts.size()) { auto [v, col] = component_verts[pos++]; color other_col = (col == color::red) ? color::blue : color::red; g.for_each_neighbor(v, [&] (int other) { if (colors[other] == color::unknown) { colors[other] = other_col; component_verts.push_back({other, other_col}); } else if (colors[other] != other_col) { colorable = false; } }); } int reds_lit = 0; int reds_total = 0; int blues_lit = 0; int blues_total = 0; int parity = 0; for (auto [v, col] : component_verts) { if (col == color::red) { reds_total++; if (lit_status[v]) { reds_lit++; } } else { blues_total++; if (lit_status[v]) { blues_lit++; } } if (lit_status[v]) { parity = 1 - parity; } } // printf("Partition size: %llu, colorable: %s\n", (unsigned long long int)component_verts.size(), colorable ? "true" : "false"); uint64_t contribution = 0; if (!colorable) { // printf(" parity: %d\n", parity); // All configurations with the right parity are good for (int p = parity; p <= component_verts.size(); p += 2) { // printf(" adding for p = %d: %llu\n", p, binomial(component_verts.size(), p)); contribution = (contribution + binomial(component_verts.size(), p)) % MODULUS; } } else { // printf(" reds lit: %d/%d, blues lit: %d/%d\n", reds_lit, reds_total, blues_lit, blues_total); // The graph is bipartite. Every operation adds or removes a bulb in both parts. // We cannot go below 0 bulbs in either part or go above any part's capacity, // but otherwise configurations are unrestricted. const int begin = -std::min(reds_lit, blues_lit); const int end = std::min(reds_total - reds_lit, blues_total - blues_lit); for (int offp = begin; offp <= end; offp++) { const int r = reds_lit + offp; const int b = blues_lit + offp; // printf(" adding for r=%d/b=%d: %llu/%llu\n", r, b, binomial(reds_total, r), binomial(blues_total, b)); const uint64_t count = (binomial(reds_total, r) * binomial(blues_total, b)) % MODULUS; contribution = (contribution + count) % MODULUS; } } component_verts.clear(); total = (total * contribution) % MODULUS; } printf("%llu\n", total); return 0; } |