[BZOJ2877][NOI2012]魔幻棋盘(二维线段树)

https://blog.sengxian.com/solutions/bzoj-2877

注意二维线段树的upd()也是一个O(log n)的函数（pushdown()应该也是但没写过）。

 #include<cstdio>
 #include<algorithm>
 #define Ls (x<<1)
 #define Rs (Ls|1)
 #define Lson Ls,L,mid
 #define Rson Rs,mid+1,R
 #define lson ls[x],L,mid
 #define rson rs[x],mid+1,R
 #define rep(i,l,r) for (int i=(l); i<=(r); i++)
 typedef long long ll;
 using namespace std;

 const int N=,M=;
 ll c,sm[M],a[N];
 int n,m,x,y,T,nd,op,x1,x2,y1,y2,rt[N<<],ls[M],rs[M];

 int F(int x,int y){ return (x-)*m+y; }
 ll gcd(ll a,ll b){ return b ? gcd(b,a%b) : a; }

 void mdfy(int &x,int L,int R,int pos,ll k){
     if (!x) x=++nd;
     if (L==R){ sm[x]+=k; return; }
     int mid=(L+R)>>;
     if (pos<=mid) mdfy(lson,pos,k); else mdfy(rson,pos,k);
     sm[x]=gcd(sm[ls[x]],sm[rs[x]]);
 }

 void upd(int &x,int L,int R,int pos,int lp,int rp){
     if (!x) x=++nd;
     if (L==R){ sm[x]=gcd(sm[lp],sm[rp]); return; }
     int mid=(L+R)>>;
     if (pos<=mid) upd(lson,pos,ls[lp],ls[rp]); else upd(rson,pos,rs[lp],rs[rp]);
     sm[x]=gcd(sm[ls[x]],sm[rs[x]]);
 }

 void mdfx(int x,int L,int R,int x1,int y1,ll k){
     if (L==R){ mdfy(rt[x],,m,y1,k); return; }
     int mid=(L+R)>>;
     if (x1<=mid) mdfx(Lson,x1,y1,k); else mdfx(Rson,x1,y1,k);
     upd(rt[x],,m,y1,rt[Ls],rt[Rs]);
 }

 ll quey(int x,int L,int R,int l,int r){
     if (L==l && r==R) return sm[x];
     int mid=(L+R)>>;
     if (r<=mid) return quey(lson,l,r);
     else if (l>mid) return quey(rson,l,r);
         else return gcd(quey(lson,l,mid),quey(rson,mid+,r));
 }

 ll quex(int x,int L,int R,int l,int r,int y1,int y2){
     if (L==l && r==R) return quey(rt[x],,m,y1,y2);
     int mid=(L+R)>>;
     if (r<=mid) return quex(Lson,l,r,y1,y2);
     else if (l>mid) return quex(Rson,l,r,y1,y2);
         else return gcd(quex(Lson,l,mid,y1,y2),quex(Rson,mid+,r,y1,y2));
 }

 int main(){
     freopen("chess.in","r",stdin);
     freopen("chess.out","w",stdout);
     scanf("%d%d%d%d%d",&n,&m,&x,&y,&T); int r1=(n+)*+,r2=r1+;
     rep(i,,n) rep(j,,m) scanf("%lld",&a[F(i,j)]);
     rep(i,,n-) rep(j,,m-) mdfx(,,n,i,j,a[F(i+,j+)]-a[F(i+,j)]-a[F(i,j+)]+a[F(i,j)]);
     rep(i,,n-) mdfy(rt[r1],,n,i,a[F(i+,y)]-a[F(i,y)]);
     rep(i,,m-) mdfy(rt[r2],,m,i,a[F(x,i+)]-a[F(x,i)]);
     while (T--){
         scanf("%d%d%d%d%d",&op,&x1,&y1,&x2,&y2);
         if (op==){
             ll t1=(x1+x2) ? quey(rt[r1],,n,x-x1,x+x2-) : ;
             ll t2=(y1+y2) ? quey(rt[r2],,m,y-y1,y+y2-) : ;
             ll t3=((x1+x2)&&(y1+y2)) ? quex(,,n,x-x1,x+x2-,y-y1,y+y2-) : ;
             printf("%lld\n",abs(gcd(gcd(t1,t2),gcd(t3,a[F(x,y)]))));
         }else{
             scanf("%lld",&c);
             mdfx(,,n,x1-,y1-,c); mdfx(,,n,x1-,y2,-c);
             mdfx(,,n,x2,y1-,-c); mdfx(,,n,x2,y2,c);
             if (y1<=y && y2>=y) mdfy(rt[r1],,n,x1-,c),mdfy(rt[r1],,n,x2,-c);
             if (x1<=x && x2>=x) mdfy(rt[r2],,m,y1-,c),mdfy(rt[r2],,m,y2,-c);
             if (x1<=x && x2>=x && y1<=y && y2>=y) a[F(x,y)]+=c;
         }
     }
     return ;
 }