#include<bits/stdc++.h>
using namespace std;
#define int int64_t
#define pb push_back
#define pii pair<int, int>
#define st first
#define nd second
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
const int MAXN = 200'009;
const int MOD = 1e9+7;
vector<int> G[MAXN];
int col[MAXN];
int ans = 1;
int type[MAXN];
int fact[MAXN];
int fact_inv[MAXN];
int pow2[MAXN];
bool is2;
vector<int> v;
void dfs(int x, int t) {
type[x] = t;
v.pb(x);
for(int y:G[x]) {
if(type[y]==0) {
dfs(y, 3-t);
} else if(type[y]==t) {
is2 = false;
}
}
}
int C(int a, int b) {
return fact[a]*fact_inv[b]%MOD*fact_inv[a-b]%MOD;
}
int f(int a, int b) {
int c = 1;
while(b) {
if(b%2)
c = c*a%MOD;
a = a*a%MOD;
b/=2;
}
return c;
}
int32_t main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
pow2[0] = 1;
for(int i=1;i<MAXN;i++) pow2[i] = pow2[i-1]*2%MOD;
fact[0] = 1;
for(int i=1;i<MAXN;i++) fact[i] = fact[i-1]*i%MOD;
fact_inv[MAXN-1] = f(fact[MAXN-1], MOD-2);
for(int i=MAXN-2;i>=0;i--) fact_inv[i] = fact_inv[i+1]*(i+1)%MOD;
int n, m;
cin >> n >> m;
for(int i=1;i<=n;i++) {
cin >> col[i];
}
for(int i=0;i<m;i++) {
int a, b;
cin >> a >> b;
G[a].pb(b);
G[b].pb(a);
}
for(int i=1;i<=n;i++) {
if(type[i]) continue;
is2 = true;
v.clear();
dfs(i, 1);
if(is2) {
int res = 0;
int sz1 = 0, sz2 = 0;
int cnt1 = 0, cnt2 = 0;
bool yes = false;
for(int x:v) {
for(int y:G[x]) {
if(col[x]==col[y]) {
yes = true;
}
}
if(type[x]==1) {
sz1++;
if(col[x]) cnt1++;
} else {
sz2++;
if(col[x]) cnt2++;
}
}
if(!yes) continue;
int Min = min(cnt1, cnt2);
cnt1-=Min, cnt2-=Min;
while(cnt1<=sz1&&cnt2<=sz2) {
res += C(sz1, cnt1)*C(sz2, cnt2);
res %= MOD;
cnt1++, cnt2++;
}
ans = ans*res%MOD;
} else {
ans = ans*pow2[sz(v)-1]%MOD;
}
}
cout << ans << "\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 | #include<bits/stdc++.h> using namespace std; #define int int64_t #define pb push_back #define pii pair<int, int> #define st first #define nd second #define sz(x) (int)(x).size() #define all(x) (x).begin(), (x).end() const int MAXN = 200'009; const int MOD = 1e9+7; vector<int> G[MAXN]; int col[MAXN]; int ans = 1; int type[MAXN]; int fact[MAXN]; int fact_inv[MAXN]; int pow2[MAXN]; bool is2; vector<int> v; void dfs(int x, int t) { type[x] = t; v.pb(x); for(int y:G[x]) { if(type[y]==0) { dfs(y, 3-t); } else if(type[y]==t) { is2 = false; } } } int C(int a, int b) { return fact[a]*fact_inv[b]%MOD*fact_inv[a-b]%MOD; } int f(int a, int b) { int c = 1; while(b) { if(b%2) c = c*a%MOD; a = a*a%MOD; b/=2; } return c; } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(NULL); pow2[0] = 1; for(int i=1;i<MAXN;i++) pow2[i] = pow2[i-1]*2%MOD; fact[0] = 1; for(int i=1;i<MAXN;i++) fact[i] = fact[i-1]*i%MOD; fact_inv[MAXN-1] = f(fact[MAXN-1], MOD-2); for(int i=MAXN-2;i>=0;i--) fact_inv[i] = fact_inv[i+1]*(i+1)%MOD; int n, m; cin >> n >> m; for(int i=1;i<=n;i++) { cin >> col[i]; } for(int i=0;i<m;i++) { int a, b; cin >> a >> b; G[a].pb(b); G[b].pb(a); } for(int i=1;i<=n;i++) { if(type[i]) continue; is2 = true; v.clear(); dfs(i, 1); if(is2) { int res = 0; int sz1 = 0, sz2 = 0; int cnt1 = 0, cnt2 = 0; bool yes = false; for(int x:v) { for(int y:G[x]) { if(col[x]==col[y]) { yes = true; } } if(type[x]==1) { sz1++; if(col[x]) cnt1++; } else { sz2++; if(col[x]) cnt2++; } } if(!yes) continue; int Min = min(cnt1, cnt2); cnt1-=Min, cnt2-=Min; while(cnt1<=sz1&&cnt2<=sz2) { res += C(sz1, cnt1)*C(sz2, cnt2); res %= MOD; cnt1++, cnt2++; } ans = ans*res%MOD; } else { ans = ans*pow2[sz(v)-1]%MOD; } } cout << ans << "\n"; } |
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