#include <iostream>
#include <map>
#include <vector>
#include <bitset>
using namespace std;
const int MAX_N = 200'007;
const long long mod = 1'000'000'007;
vector<int>adj[MAX_N];
int col[MAX_N], state[MAX_N];
void dfs(int x, vector<int>&v) {
v.push_back(x);
for(int y : adj[x]) {
if(col[y] == -1) {
col[y] = 1 - col[x];
dfs(y, v);
}
}
}
long long fact[MAX_N];
long long bpow(long long x, long long exp) {
if(exp == 0)
return 1;
long long r = bpow(x, exp / 2);
r = r * r % mod;
if(exp % 2 == 1)
r = r * x % mod;
return r;
}
long long choose(int n, int k) {
long long ans = fact[n] * bpow(fact[k], mod - 2) % mod;
return ans * bpow(fact[n - k], mod - 2) % mod;
}
int main() {
fact[0] = 1;
for(int i = 1; i < MAX_N; i++)
fact[i] = fact[i - 1] * i % mod;
int n, m; cin >> n >> m;
for(int i = 0; i < n; i++) {
cin >> state[i];
col[i] = -1;
}
for(int i = 0; i < m; i++) {
int x, y;
cin >> x >> y;
x--; y--;
adj[x].push_back(y);
adj[y].push_back(x);
}
long long result = 1;
for(int i = 0; i < n; i++) {
if(col[i] == -1) {
vector<int>v;
col[i] = 0;
dfs(i, v);
bool bipart = true;
for(int x : v) {
for(int y : adj[x]) {
if(col[x] == col[y]) {
bipart = false;
}
}
}
if(!bipart) {
result = result * bpow(2, v.size() - 1) % mod;
} else {
// cout << "bipart\n";
int left = 0, right = 0, lone = 0, rone = 0;
for(int x : v) {
if(col[x] == 0) {
left++;
lone += state[x];
} else {
right++;
rone += state[x];
}
}
// cout << "left = " << left << " right = " << right << "\n";
// cout << "lone = " << lone << ", rone = " << rone << "\n";
long long local = 0;
for(int i = -min(left - lone, right - rone); i <= min(lone, rone); i++) {
local = (local + choose(left, lone - i) * choose(right, rone - i)) % mod;
}
// cout << "local = " << local << "\n";
result = result * local % mod;
}
}
}
cout << result << "\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 | #include <iostream> #include <map> #include <vector> #include <bitset> using namespace std; const int MAX_N = 200'007; const long long mod = 1'000'000'007; vector<int>adj[MAX_N]; int col[MAX_N], state[MAX_N]; void dfs(int x, vector<int>&v) { v.push_back(x); for(int y : adj[x]) { if(col[y] == -1) { col[y] = 1 - col[x]; dfs(y, v); } } } long long fact[MAX_N]; long long bpow(long long x, long long exp) { if(exp == 0) return 1; long long r = bpow(x, exp / 2); r = r * r % mod; if(exp % 2 == 1) r = r * x % mod; return r; } long long choose(int n, int k) { long long ans = fact[n] * bpow(fact[k], mod - 2) % mod; return ans * bpow(fact[n - k], mod - 2) % mod; } int main() { fact[0] = 1; for(int i = 1; i < MAX_N; i++) fact[i] = fact[i - 1] * i % mod; int n, m; cin >> n >> m; for(int i = 0; i < n; i++) { cin >> state[i]; col[i] = -1; } for(int i = 0; i < m; i++) { int x, y; cin >> x >> y; x--; y--; adj[x].push_back(y); adj[y].push_back(x); } long long result = 1; for(int i = 0; i < n; i++) { if(col[i] == -1) { vector<int>v; col[i] = 0; dfs(i, v); bool bipart = true; for(int x : v) { for(int y : adj[x]) { if(col[x] == col[y]) { bipart = false; } } } if(!bipart) { result = result * bpow(2, v.size() - 1) % mod; } else { // cout << "bipart\n"; int left = 0, right = 0, lone = 0, rone = 0; for(int x : v) { if(col[x] == 0) { left++; lone += state[x]; } else { right++; rone += state[x]; } } // cout << "left = " << left << " right = " << right << "\n"; // cout << "lone = " << lone << ", rone = " << rone << "\n"; long long local = 0; for(int i = -min(left - lone, right - rone); i <= min(lone, rone); i++) { local = (local + choose(left, lone - i) * choose(right, rone - i)) % mod; } // cout << "local = " << local << "\n"; result = result * local % mod; } } } cout << result << "\n"; } |
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