大意:给定字符串$s$, 保证长度为偶数, 给定q个询问, 每次询问给定两个位置$x$,$y$, 可以任意交换字符, 要求所有字符$s[x],s[y]$在同一半边, 剩余所有同种字符在同一半边的方案数
假设两半的字符种类已经定好, 那么种类数就为$2\frac{(n/2)!^2}{\prod_i c_i!}$.
这里要求字符$s[x],s[y]$在同一侧, 所以可以求出除去$s[x],s[y]$后, 剩余字符分成$\frac{n}{2}$的方案, 这个可以用可逆背包预处理出来, 复杂度$O(52^2n)-O(q)$
#include <iostream> #include <algorithm> #include <cstdio> #include <math.h> #include <set> #include <map> #include <queue> #include <string> #include <string.h> #define REP(i,a,n) for(int i=a;i<=n;++i) #define PER(i,a,n) for(int i=n;i>=a;--i) #define hr putchar(10) #define pb push_back #define lc (o<<1) #define rc (lc|1) #define mid ((l+r)>>1) #define ls lc,l,mid #define rs rc,mid+1,r #define x first #define y second #define io std::ios::sync_with_stdio(false) #define endl '\n' using namespace std; typedef long long ll; typedef pair<int,int> pii; const int P = 1e9+7, INF = 0x3f3f3f3f; ll gcd(ll a,ll b) {return b?gcd(b,a%b):a;} ll qpow(ll a,ll n) {ll r=1%P;for (a%=P;n;a=a*a%P,n>>=1)if(n&1)r=r*a%P;return r;} ll inv(ll x){return x<=1?1:inv(P%x)*(P-P/x)%P;} //head const int N = 1e5+10; int n, m, q; char s[N]; int a[N], b[N], c[N]; int f[N], F[60][N], ans[60][60]; ll fac[N]; int main() { scanf("%s", s+1); n = strlen(s+1), m = n/2; REP(i,1,n) a[i]=b[i]=s[i]; sort(b+1,b+1+n),*b=unique(b+1,b+1+n)-b-1; REP(i,1,n) ++c[a[i]=lower_bound(b+1,b+1+*b,a[i])-b]; REP(i,1,*b) if (c[i]>m) { scanf("%d", &q); while (q--) puts("0"); return 0; } fac[0]=fac[1]=1; REP(i,1,n) fac[i]=fac[i-1]*i%P; ll C = 2*fac[m]%P*fac[m]%P; REP(i,1,*b) C = C*inv(fac[c[i]])%P; f[0] = 1; REP(i,1,*b) PER(j,c[i],m) (f[j]+=f[j-c[i]])%=P; REP(i,1,*b) { REP(j,0,c[i]-1) F[i][j]=f[j]; REP(j,c[i],m) { F[i][j]=f[j]-F[i][j-c[i]]; if (F[i][j]<0) F[i][j]+=P; } ans[i][i] = F[i][m]; } REP(i,1,*b) REP(ii,i+1,*b) { REP(j,0,c[ii]-1) f[j]=F[i][j]; REP(j,c[ii],m) { f[j]=F[i][j]-f[j-c[ii]]; if (f[j]<0) f[j]+=P; } ans[i][ii] = f[m]; } scanf("%d", &q); REP(i,1,q) { int x, y; scanf("%d%d", &x, &y); x = a[x], y = a[y]; if (x>y) swap(x,y); printf("%d\n",int(C*ans[x][y]%P)); } }