Codeforces Round #524 (Div. 2) C. Masha and two friends 几何：判断矩形是否相交以及相交矩形坐标

题意 ：给出一个初始的黑白相间的棋盘  有两个人  第一个人先用白色染一块矩形区域

第二个人再用黑色染一块矩形区域 问最后黑白格子各有多少个

思路：这题的关键在于求相交的矩形区间

给出一个矩形的左下和右上角  则相交的条件为 max(X1,X3)<=min(X2,X4)&&max(Y1,Y3)<=min(Y2,Y4)  这里可以用线和线有公共区间的条件来推 矩形就是两个线

还有就是如果相交则求 相交的矩形的 左下和右上的坐标 ll xa=max(X1,X3),ya=max(Y1,Y3),xb=min(X4,X2),yb=min(Y2,Y4);

然后就是简单的容斥正常做就行了

 #include<bits/stdc++.h>
 #define FOR(i,f_start,f_end) for(int i=f_start;i<=f_end;i++)
 #define MS(arr,arr_value) memset(arr,arr_value,sizeof(arr))
 #define F first
 #define S second
 #define pii pair<int ,int >
 #define mkp make_pair
 #define pb push_back
 #define arr(zzz) array<ll,zzz>
 using namespace std;
 #define ll long long
 #define int long long
 const int maxn=3e5+;
 const int inf=0x3f3f3f3f;
 ll count(int x1,int y1,int x2,int y2,int o){//return black
     ll n=x2-x1+;
     ll m=y2-y1+;
     ll white=,black=;
         if(n&){
             if(m&){
                 white=(n+)/+1ll*(n/+(n+)/)*(m/);
                 black=1ll*m*n-white;
             }
             else {
                 white=black=1ll*n*m/;
             }
         }
         else {
             white=black=1ll*n*m/;
         }
         if(o==){
             return white;
         }
         else return black;

 }
 void exchange(ll &x,ll&y){
     ll tmp=x;
     x=y;
     y=tmp;
 }
 int32_t main(){
     int t;
     scanf("%lld",&t);
     int n,m;
     while(t--){
         ll black=,white=;
         int X1,Y1,X2,Y2,X3,Y3,X4,Y4;
         scanf("%lld%lld",&n,&m);
         scanf("%lld%lld%lld%lld%lld%lld%lld%lld",&X1,&Y1,&X2,&Y2,&X3,&Y3,&X4,&Y4);
         if(n&){
             if(m&){
                 white=(n+)/+  (n/+(n+)/)*(m/);
                 black=1ll*m*n-white;
             }
             else {
                 white=black=1ll*n*m/;
             }
         }
         else {
             white=black=1ll*n*m/;
         }
         ll tmp1=count(X1,Y1,X2,Y2,(X1+Y1)%==);
         white-=1ll*(X2-X1+)*(Y2-Y1+)-tmp1;
         white+=1ll*(X2-X1+)*(Y2-Y1+);
         black-=tmp1;
         ll tmp2=count(X3,Y3,X4,Y4,(X3+Y3)%==);
         white-=1ll*(X4-X3+)*(Y4-Y3+)-tmp2;
         black-=tmp2;
         black+=1ll*(X4-X3+)*(Y4-Y3+);
         /*if(X1<=X3){
             exchange(X1,X3);
             exchange(X2,X4);
             exchange(Y1,Y3);
             exchange(Y2,Y4);
         }
         if(){

         }*/
         ll minx=min(X1,X3);
         ll miny=min(Y1,Y3);
         if(max(X1,X3)<=min(X2,X4)&&max(Y1,Y3)<=min(Y2,Y4)){
             ll xa=max(X1,X3),ya=max(Y1,Y3),xb=min(X4,X2),yb=min(Y2,Y4);
             ll tmp=count(xa,ya,xb,yb,(xa+ya)%==);
             //cout<<xa<<" "<<ya<<" "<<xb<<""<<yb<<" fuck"<<tmp<<endl;
             black+=tmp;
             white-=1ll*(xb-xa+)*(ya-yb+);
             white+=1ll*(xb-xa+)*(ya-yb+)-tmp;

         }
          cout<<white<<" "<<black<<endl;
     }

     return ;
 }