// Arti1990, II UWr #include <bits/stdc++.h> #define forr(i, n) for(int i=0; i<n; i++) #define FOREACH(iter, coll) for(auto iter = coll.begin(); iter != coll.end(); ++iter) #define FOREACHR(iter, coll) for(auto iter = coll.rbegin(); iter != coll.rend(); ++iter) #define lbound(P,K,FUN) ({auto SSS=P, PPP = P-1, KKK=(K)+1; while(PPP+1!=KKK) {SSS = (PPP+(KKK-PPP)/2); if(FUN(SSS)) KKK = SSS; else PPP = SSS;} PPP;}) #define testy() int _tests; cin>>_tests; FOR(_test, 1, _tests) #define CLEAR(tab) memset(tab, 0, sizeof(tab)) #define CONTAIN(el, coll) (coll.find(el) != coll.end()) #define FOR(i, a, b) for(int i=a; i<=b; i++) #define FORD(i, a, b) for(int i=a; i>=b; i--) #define MP make_pair #define PB push_back #define ff first #define ss second #define deb(X) X; #define SIZE(coll) ((int)coll.size()) #define M 1000000007 #define INF 1000000007LL using namespace std; int n, m, a, b; long long silnia[1000007], odwr[1000007]; long long suma[2], ile[2], dwudzielny; struct wierzch { int kolor; int byl; int val; vector <int> l; }; wierzch tab[1000007]; /* int licz_brut() { vector <int> v; FOR(i, 1, n) v.PB(tab[i].kolor); set <vector<int>> s; deque <vector<int>> q; s.insert(v); q.PB(v); while(!q.empty()) { v = q.front(); q.pop_front(); for(auto el : v) cout << el << " "; cout << '\n'; FOR(i, 1, n) for(auto el : tab[i].l) { if(el > i) { if(v[i-1] == v[el-1]) { v[i-1] ^= 1; v[el-1] ^= 1; if(s.count(v) == 0) { s.insert(v); q.PB(v); } v[i-1] ^= 1; v[el-1] ^= 1; } } } } return s.size(); } */ long long pot(int n) { long long res = 1; forr(i, n) res = (res*2)%M; return res; } pair <long long, long long> euklid(long long a, long long b) { if(b == 0) return make_pair(1, 0); pair <long long, long long> p = euklid(b, a%b); return make_pair(p.second, p.first - p.second * (a/b)); } long long odwrotnosc(long long a, long long mod) { long long e = euklid(a, mod).first; return (e < 0 ? mod-((-e) % mod) : (e % mod)); } long long binom(int n, int k) { return silnia[n] * odwr[k] % M * odwr[n-k] % M; } void init() { silnia[0] = 1; odwr[0] = 1; FOR(i, 1, 200007) { silnia[i] = (silnia[i-1]*i) % M; odwr[i] = odwrotnosc(silnia[i], M); } } void dfs(int nr, int kolor) { //cout << "odwiedza " << nr << " z kolorem " << kolor << '\n'; tab[nr].byl = 1; ile[kolor]++; tab[nr].kolor = kolor; suma[kolor] += tab[nr].val; for(auto el : tab[nr].l) if(!tab[el].byl) { dfs(el, 1-kolor); } else if(tab[el].kolor == kolor) dwudzielny = 0; } long long licz() { long long res = 1; FOR(i, 1, n) if(!tab[i].byl) { ile[0] = ile[1] = 0; suma[0] = suma[1] = 0; dwudzielny = 1; dfs(i, 0); if(!dwudzielny) { //cout << "dodaje potege " << ile[0] + ile[1] - 1 << '\n'; res = (res*pot(ile[0]+ile[1]-1)) % M; } else { long long r = 0; int minn = min(suma[0], suma[1]); suma[0] -= minn; suma[1] -= minn; int dl = min(ile[0] - suma[0], ile[1] - suma[1]); FOR(d, 0, dl) { //cout << "dodaje kombinacje " << suma[0]+d << " z " << ile[0] << " razy " << suma[1]+d << " z " << ile[1] << '\n'; r = (r + binom(ile[0], suma[0]+d) * binom(ile[1], suma[1]+d)) % M; } res = res * r % M; } //cout << "res: " << res << '\n'; } return res; } int solve() { init(); cin >> n >> m; FOR(i, 1, n) cin >> tab[i].val; forr(i, m) { cin >> a >> b; tab[a].l.PB(b); tab[b].l.PB(a); } cout << licz() << '\n'; //cout << licz_brut() << '\n'; return 0; } int main() { //std::ios_base::sync_with_stdio(0); //cin.tie(0); //cout.tie(0); solve(); 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 | // Arti1990, II UWr #include <bits/stdc++.h> #define forr(i, n) for(int i=0; i<n; i++) #define FOREACH(iter, coll) for(auto iter = coll.begin(); iter != coll.end(); ++iter) #define FOREACHR(iter, coll) for(auto iter = coll.rbegin(); iter != coll.rend(); ++iter) #define lbound(P,K,FUN) ({auto SSS=P, PPP = P-1, KKK=(K)+1; while(PPP+1!=KKK) {SSS = (PPP+(KKK-PPP)/2); if(FUN(SSS)) KKK = SSS; else PPP = SSS;} PPP;}) #define testy() int _tests; cin>>_tests; FOR(_test, 1, _tests) #define CLEAR(tab) memset(tab, 0, sizeof(tab)) #define CONTAIN(el, coll) (coll.find(el) != coll.end()) #define FOR(i, a, b) for(int i=a; i<=b; i++) #define FORD(i, a, b) for(int i=a; i>=b; i--) #define MP make_pair #define PB push_back #define ff first #define ss second #define deb(X) X; #define SIZE(coll) ((int)coll.size()) #define M 1000000007 #define INF 1000000007LL using namespace std; int n, m, a, b; long long silnia[1000007], odwr[1000007]; long long suma[2], ile[2], dwudzielny; struct wierzch { int kolor; int byl; int val; vector <int> l; }; wierzch tab[1000007]; /* int licz_brut() { vector <int> v; FOR(i, 1, n) v.PB(tab[i].kolor); set <vector<int>> s; deque <vector<int>> q; s.insert(v); q.PB(v); while(!q.empty()) { v = q.front(); q.pop_front(); for(auto el : v) cout << el << " "; cout << '\n'; FOR(i, 1, n) for(auto el : tab[i].l) { if(el > i) { if(v[i-1] == v[el-1]) { v[i-1] ^= 1; v[el-1] ^= 1; if(s.count(v) == 0) { s.insert(v); q.PB(v); } v[i-1] ^= 1; v[el-1] ^= 1; } } } } return s.size(); } */ long long pot(int n) { long long res = 1; forr(i, n) res = (res*2)%M; return res; } pair <long long, long long> euklid(long long a, long long b) { if(b == 0) return make_pair(1, 0); pair <long long, long long> p = euklid(b, a%b); return make_pair(p.second, p.first - p.second * (a/b)); } long long odwrotnosc(long long a, long long mod) { long long e = euklid(a, mod).first; return (e < 0 ? mod-((-e) % mod) : (e % mod)); } long long binom(int n, int k) { return silnia[n] * odwr[k] % M * odwr[n-k] % M; } void init() { silnia[0] = 1; odwr[0] = 1; FOR(i, 1, 200007) { silnia[i] = (silnia[i-1]*i) % M; odwr[i] = odwrotnosc(silnia[i], M); } } void dfs(int nr, int kolor) { //cout << "odwiedza " << nr << " z kolorem " << kolor << '\n'; tab[nr].byl = 1; ile[kolor]++; tab[nr].kolor = kolor; suma[kolor] += tab[nr].val; for(auto el : tab[nr].l) if(!tab[el].byl) { dfs(el, 1-kolor); } else if(tab[el].kolor == kolor) dwudzielny = 0; } long long licz() { long long res = 1; FOR(i, 1, n) if(!tab[i].byl) { ile[0] = ile[1] = 0; suma[0] = suma[1] = 0; dwudzielny = 1; dfs(i, 0); if(!dwudzielny) { //cout << "dodaje potege " << ile[0] + ile[1] - 1 << '\n'; res = (res*pot(ile[0]+ile[1]-1)) % M; } else { long long r = 0; int minn = min(suma[0], suma[1]); suma[0] -= minn; suma[1] -= minn; int dl = min(ile[0] - suma[0], ile[1] - suma[1]); FOR(d, 0, dl) { //cout << "dodaje kombinacje " << suma[0]+d << " z " << ile[0] << " razy " << suma[1]+d << " z " << ile[1] << '\n'; r = (r + binom(ile[0], suma[0]+d) * binom(ile[1], suma[1]+d)) % M; } res = res * r % M; } //cout << "res: " << res << '\n'; } return res; } int solve() { init(); cin >> n >> m; FOR(i, 1, n) cin >> tab[i].val; forr(i, m) { cin >> a >> b; tab[a].l.PB(b); tab[b].l.PB(a); } cout << licz() << '\n'; //cout << licz_brut() << '\n'; return 0; } int main() { //std::ios_base::sync_with_stdio(0); //cin.tie(0); //cout.tie(0); solve(); return 0; } |