#include <bits/stdc++.h> using namespace std; #define debug if (0) typedef long long lld; const lld MOD = 1e9 + 7; int n, m; lld fpw(lld x, lld k) { lld res = 1; for (; k > 0; k >>= 1, x = x * x % MOD) if (k & 1) res = res * x % MOD; return res; } struct component { int sz = 0; bool bipartite = true; pair<int, int> l, r; }; component make_component(const vector<vector<int>> &v, vector<int> &visited, const vector<int> &col, int start) { component res; queue<int> q; visited[start] = 1; q.push(start); res.sz++; res.l.first++; res.l.second += col[start]; while (!q.empty()) { int x = q.front(); q.pop(); for (int u : v[x]) { if (visited[u] == visited[x]) res.bipartite = false; if (visited[u] != 0) continue; visited[u] = 3 - visited[x]; q.push(u); pair<int, int> &part = (visited[u] == 1 ? res.l : res.r); res.sz++; part.first++; part.second += col[u]; } } return res; } vector<component> get_connected(const vector<vector<int>> &v, const vector<int> &col) { vector<int> visited(n, 0); vector<component> cc; for (int i = 0; i < n; ++i) if (visited[i] == 0) cc.push_back(make_component(v, visited, col, i)); return cc; } bool frozen(const vector<int> &cc, const vector<vector<int>> &v, const vector<int> &col) { for (const int x : cc) for (const int u : v[x]) if (col[x] == col[u]) return false; return true; } lld calc(const pair<int, int> &l, const pair<int, int> &r) { lld x = l.first, y = r.first; lld ldif = max(0, l.second - r.second); lld rdif = max(0, r.second - l.second); debug { cout << "CALC(" << x << ", " << y << " | " << ldif << ", " << rdif << ")\n"; } int k1 = 0, k2 = 0; lld lbinom = 1, rbinom = 1; for (; k1 < ldif; ++k1) lbinom = lbinom * (x - k1) % MOD * fpw(k1 + 1, MOD - 2) % MOD; for (; k2 < rdif; ++k2) rbinom = rbinom * (y - k2) % MOD * fpw(k2 + 1, MOD - 2) % MOD; lld res = 0; for (; k1 <= x && k2 <= y; ++k1, ++k2) { res += lbinom * rbinom % MOD; if (res >= MOD) res -= MOD; lbinom = lbinom * (x - k1) % MOD * fpw(k1 + 1, MOD - 2) % MOD; rbinom = rbinom * (y - k2) % MOD * fpw(k2 + 1, MOD - 2) % MOD; } debug { cout << "CALCED: " << res << endl; } return res; } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cin >> n >> m; vector<int> init(n); for (int &i : init) cin >> i; vector<vector<int>> v(n); for (int i = 0; i < m; ++i) { int x, y; cin >> x >> y; v[--x].push_back(--y); v[y].push_back(x); } vector<component> components = get_connected(v, init); lld res = 1; for (auto &[sz, bip, l, r] : components) { debug { cout << "RES -> " << res << endl; } if (!bip) { res = res * fpw(2, sz - 1) % MOD; continue; } res = res * calc(l, r) % MOD; } cout << res << '\n'; }
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 | #include <bits/stdc++.h> using namespace std; #define debug if (0) typedef long long lld; const lld MOD = 1e9 + 7; int n, m; lld fpw(lld x, lld k) { lld res = 1; for (; k > 0; k >>= 1, x = x * x % MOD) if (k & 1) res = res * x % MOD; return res; } struct component { int sz = 0; bool bipartite = true; pair<int, int> l, r; }; component make_component(const vector<vector<int>> &v, vector<int> &visited, const vector<int> &col, int start) { component res; queue<int> q; visited[start] = 1; q.push(start); res.sz++; res.l.first++; res.l.second += col[start]; while (!q.empty()) { int x = q.front(); q.pop(); for (int u : v[x]) { if (visited[u] == visited[x]) res.bipartite = false; if (visited[u] != 0) continue; visited[u] = 3 - visited[x]; q.push(u); pair<int, int> &part = (visited[u] == 1 ? res.l : res.r); res.sz++; part.first++; part.second += col[u]; } } return res; } vector<component> get_connected(const vector<vector<int>> &v, const vector<int> &col) { vector<int> visited(n, 0); vector<component> cc; for (int i = 0; i < n; ++i) if (visited[i] == 0) cc.push_back(make_component(v, visited, col, i)); return cc; } bool frozen(const vector<int> &cc, const vector<vector<int>> &v, const vector<int> &col) { for (const int x : cc) for (const int u : v[x]) if (col[x] == col[u]) return false; return true; } lld calc(const pair<int, int> &l, const pair<int, int> &r) { lld x = l.first, y = r.first; lld ldif = max(0, l.second - r.second); lld rdif = max(0, r.second - l.second); debug { cout << "CALC(" << x << ", " << y << " | " << ldif << ", " << rdif << ")\n"; } int k1 = 0, k2 = 0; lld lbinom = 1, rbinom = 1; for (; k1 < ldif; ++k1) lbinom = lbinom * (x - k1) % MOD * fpw(k1 + 1, MOD - 2) % MOD; for (; k2 < rdif; ++k2) rbinom = rbinom * (y - k2) % MOD * fpw(k2 + 1, MOD - 2) % MOD; lld res = 0; for (; k1 <= x && k2 <= y; ++k1, ++k2) { res += lbinom * rbinom % MOD; if (res >= MOD) res -= MOD; lbinom = lbinom * (x - k1) % MOD * fpw(k1 + 1, MOD - 2) % MOD; rbinom = rbinom * (y - k2) % MOD * fpw(k2 + 1, MOD - 2) % MOD; } debug { cout << "CALCED: " << res << endl; } return res; } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cin >> n >> m; vector<int> init(n); for (int &i : init) cin >> i; vector<vector<int>> v(n); for (int i = 0; i < m; ++i) { int x, y; cin >> x >> y; v[--x].push_back(--y); v[y].push_back(x); } vector<component> components = get_connected(v, init); lld res = 1; for (auto &[sz, bip, l, r] : components) { debug { cout << "RES -> " << res << endl; } if (!bip) { res = res * fpw(2, sz - 1) % MOD; continue; } res = res * calc(l, r) % MOD; } cout << res << '\n'; } |