高斯消元
[HNOI2013]游走 这个的方程比较经典
hdoj 7109 n^3预处理n^2询问修改矩阵最后一列
//#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math") //#pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native") //#include <immintrin.h> //#include <emmintrin.h> #include <bits/stdc++.h> using namespace std; #define rep(i,h,t) for (int i=h;i<=t;i++) #define dep(i,t,h) for (int i=t;i>=h;i--) #define ll long long #define me(x) memset(x,0,sizeof(x)) #define IL inline #define rint register int //unsigned seed = std::chrono::system_clock::now().time_since_epoch().count(); //mt19937 myrand(seed); //uniform_int_distribution<ll>dist(1,10000000); //dist(myrand); inline ll rd(){ ll x=0;char c=getchar();bool f=0; while(!isdigit(c)){if(c=='-')f=1;c=getchar();} while(isdigit(c)){x=(x<<1)+(x<<3)+(c^48);c=getchar();} return f?-x:x; } char ss[1<<26],*A=ss,*B=ss; IL char gc() { return A==B&&(B=(A=ss)+fread(ss,1,1<<26,stdin),A==B)?EOF:*A++; } template<class T>void maxa(T &x,T y) { if (y>x) x=y; } template<class T>void mina(T &x,T y) { if (y<x) x=y; } template<class T>void read(T &x) { int f=1,c; while (c=gc(),c<48||c>57) if (c=='-') f=-1; x=(c^48); while(c=gc(),c>47&&c<58) x=x*10+(c^48); x*=f; } char sr[1<<26],z[20]; int C=-1,Z; template <class T> void wer(T x) { if (x<0) sr[++C]='-',x=-x; while (z[++Z]=x%10+48,x/=10); while (sr[++C]=z[Z],--Z); sr[++C]='\n'; } const int mo=998244353; ll fsp(int x,int y) { if (y==1) return x; ll ans=fsp(x,y/2); ans=ans*ans%mo; if (y%2==1) ans=ans*x%mo; return ans; } struct cp { ll x,y; cp operator +(cp B) { return (cp){x+B.x,y+B.y}; } cp operator -(cp B) { return (cp){x-B.x,y-B.y}; } ll operator *(cp B) { return x*B.y-y*B.x; } int half() { return y < 0 || (y == 0 && x < 0); } }; struct re{ int a,b,c; }; const int N=510; int w[N],siz[N],pp[11]; ll h[N][10],gl[N]; re g[N][N]; int n,m,q; struct gauss{ ll jl[N][N],f[N][N],ans[N]; void Gauss() { n--; rep(i,1,n) jl[i][i]=1; rep(i,1,n) { int kk=fsp(f[i][i],mo-2); rep(j,1,n) if (i!=j) { ll t=-1ll*f[j][i]*kk%mo; rep(k,1,n) (f[j][k]+=t*f[i][k])%=mo; rep(k,1,n) (jl[j][k]+=t*jl[i][k])%=mo; } } rep(i,1,n) { int kk=fsp(-f[i][i],mo-2); rep(j,1,n) jl[i][j]=jl[i][j]*kk%mo; } n++; } inline ll js() { ll anss=0; rep(i,1,n-1) { ans[i]=0; rep(j,1,n-1) (ans[i]+=jl[i][j]*h[j][7])%=mo; } rep(i,1,n-1) rep(j,1,n) if (g[i][j].b) { (anss+=ans[i]*gl[i]%mo*g[i][j].b)%=mo; } return anss; } } M; ll ans=0,ans2=0; inline void cl() { ans=0; ll sum=0; rep(i,1,n) sum+=w[i]; sum=fsp(sum,mo-2); rep(i,1,n) gl[i]=fsp(siz[i],mo-2); rep(i,1,n-1) h[i][0]=w[i]*sum%mo; rep(i,1,7) rep(j,1,n-1) { h[j][i]=0; rep(k,1,n) if (g[j][k].a) (h[j][i]+=h[k][i-1]*gl[k])%=mo; } pp[0]=1; rep(i,1,10) pp[i]=pp[i-1]*2; rep(i,0,6) rep(j,1,n-1) rep(k,1,n) if (g[j][k].a) (ans+=h[j][i]*gl[j]%mo*max(g[j][k].a/pp[i],g[j][k].b))%=mo; } inline void pr() { ll now=((ans+ans2)%mo+mo)%mo; wer(now); } int main() { ios::sync_with_stdio(false); read(n); read(m);read(q); rep(i,1,n-1) read(w[i]); rep(i,1,m) { int x,y,a,b; read(x); read(y); read(a); read(b); siz[x]++; siz[y]++; g[x][y]=(re){a,b}; g[y][x]=(re){a,b}; } cl(); rep(i,1,n-1) { M.f[i][i]=-1; rep(j,1,n-1) if (g[i][j].a) M.f[i][j]=gl[j]; } M.Gauss(); ans2=M.js(); pr(); while (q--) { int kk,x,y,a,b,c; read(kk); if (kk==1) { read(x); read(y); read(a); read(b); if (x!=n) rep(i,0,6) (ans-=h[x][i]*gl[x]%mo*max(g[x][y].a/pp[i],g[x][y].b))%=mo; if (y!=n) rep(i,0,6) (ans-=h[y][i]*gl[y]%mo*max(g[y][x].a/pp[i],g[y][x].b))%=mo; if (x!=n) (ans-=M.ans[x]*gl[x]%mo*g[x][y].b)%=mo; if (y!=n) (ans-=M.ans[y]*gl[y]%mo*g[y][x].b)%=mo; g[x][y]=g[y][x]=(re){a,b}; if (x!=n) rep(i,0,6) (ans+=h[x][i]*gl[x]%mo*max(g[x][y].a/pp[i],g[x][y].b))%=mo; if (y!=n) rep(i,0,6) (ans+=h[y][i]*gl[y]%mo*max(g[y][x].a/pp[i],g[y][x].b))%=mo; if (x!=n) (ans+=M.ans[x]*gl[x]%mo*g[x][y].b)%=mo; if (y!=n) (ans+=M.ans[y]*gl[y]%mo*g[y][x].b)%=mo; } else { read(x); read(c); w[x]=c; cl(); ans2=M.js(); } pr(); } fwrite(sr,1,C+1,stdout); return 0; }
