#ifdef DEBUG
#define _GLIBCXX_DEBUG
#endif
//#pragma GCC optimize("O3")
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
typedef long long ll;
typedef long double ld;
int n, m;
const int maxN = 200'005;
const int maxM = 400'005;
int c[maxN];
vector<int> g[maxN];
int clr[maxN];
int C[2] = {0, 0};
const int mod = (int)1e9 + 7;
int mult(int a, int b) {
return (1LL * a * b) % mod;
}
int sub(int a, int b) {
int s = a - b;
if (s < 0) {
s += mod;
}
return s;
}
int fact[maxN], invfact[maxN], inv[maxN];
bool HAS_CYC = false;
int pw2[maxN];
bool used[maxN];
void dfs(int v) {
C[clr[v] ^ c[v]]++;
used[v] = true;
for (int to : g[v]) {
if (!used[to]) {
clr[to] = clr[v] ^ 1;
dfs(to);
}
else if (clr[to] != (clr[v] ^ 1)) {
HAS_CYC = true;
}
}
}
int cnk(int n, int k) {
if (n < k || k < 0) return 0;
return mult(fact[n], mult(invfact[k], invfact[n - k]));
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
#ifdef DEBUG
freopen("input.txt", "r", stdin);
#endif
cin >> n >> m;
fact[1] = invfact[1] = inv[1] = fact[0] = invfact[0] = 1;
pw2[0] = 1;
pw2[1] = 2;
for (int i = 2; i < maxN; i++) {
pw2[i] = mult(2, pw2[i - 1]);
fact[i] = mult(i, fact[i - 1]);
inv[i] = mult(inv[mod % i], sub(0, mod / i));
invfact[i] = mult(invfact[i - 1], inv[i]);
}
for (int i = 1; i <= n; i++) {
clr[i] = -1;
cin >> c[i];
}
for (int i = 1; i <= m; i++) {
int a, b;
cin >> a >> b;
g[a].emplace_back(b);
g[b].emplace_back(a);
}
int ans = 1;
for (int i = 1; i <= n; i++) {
if (!used[i]) {
C[0] = C[1] = 0;
HAS_CYC = false;
clr[i] = 0;
dfs(i);
if (HAS_CYC) {
ans = mult(ans, pw2[C[0] + C[1] - 1]);
}
else {
ans = mult(ans, cnk(C[0] + C[1], C[0]));
}
}
}
cout << ans;
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 | #ifdef DEBUG #define _GLIBCXX_DEBUG #endif //#pragma GCC optimize("O3") #include<bits/stdc++.h> using namespace std; #define pb push_back typedef long long ll; typedef long double ld; int n, m; const int maxN = 200'005; const int maxM = 400'005; int c[maxN]; vector<int> g[maxN]; int clr[maxN]; int C[2] = {0, 0}; const int mod = (int)1e9 + 7; int mult(int a, int b) { return (1LL * a * b) % mod; } int sub(int a, int b) { int s = a - b; if (s < 0) { s += mod; } return s; } int fact[maxN], invfact[maxN], inv[maxN]; bool HAS_CYC = false; int pw2[maxN]; bool used[maxN]; void dfs(int v) { C[clr[v] ^ c[v]]++; used[v] = true; for (int to : g[v]) { if (!used[to]) { clr[to] = clr[v] ^ 1; dfs(to); } else if (clr[to] != (clr[v] ^ 1)) { HAS_CYC = true; } } } int cnk(int n, int k) { if (n < k || k < 0) return 0; return mult(fact[n], mult(invfact[k], invfact[n - k])); } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); #ifdef DEBUG freopen("input.txt", "r", stdin); #endif cin >> n >> m; fact[1] = invfact[1] = inv[1] = fact[0] = invfact[0] = 1; pw2[0] = 1; pw2[1] = 2; for (int i = 2; i < maxN; i++) { pw2[i] = mult(2, pw2[i - 1]); fact[i] = mult(i, fact[i - 1]); inv[i] = mult(inv[mod % i], sub(0, mod / i)); invfact[i] = mult(invfact[i - 1], inv[i]); } for (int i = 1; i <= n; i++) { clr[i] = -1; cin >> c[i]; } for (int i = 1; i <= m; i++) { int a, b; cin >> a >> b; g[a].emplace_back(b); g[b].emplace_back(a); } int ans = 1; for (int i = 1; i <= n; i++) { if (!used[i]) { C[0] = C[1] = 0; HAS_CYC = false; clr[i] = 0; dfs(i); if (HAS_CYC) { ans = mult(ans, pw2[C[0] + C[1] - 1]); } else { ans = mult(ans, cnk(C[0] + C[1], C[0])); } } } cout << ans; return 0; } |
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