覆盖的面积（线段树+扫描线）

因为要求覆盖两次的面积，所以可以开二维表示被覆盖1次及以上和被覆盖两次及以上的面积。
主要在up更新上，如果当前区间被标记为一次，二次覆盖的面积就为其儿子面积之和，具体看代码吧。
  1 #include <iostream>
  2 #include<cstdio>
  3 #include<cstring>
  4 #include<algorithm>
  5 #include<stdlib.h>
  6 #include<vector>
  7 #include<cmath>
  8 #include<queue>
  9 #include<set>
 10 #include<map>
 11 using namespace std;
 12 #define N 4010
 13 #define LL long long
 14 #define INF 0xfffffff
 15 const double eps = 1e-8;
 16 const double pi = acos(-1.0);
 17 const double inf = ~0u>>2;
 18 map<double,int>f;
 19 double s[N<<2],res[N<<2];
 20 int fs[N<<2];
 21 double val[N],que[N];
 22 struct node
 23 {
 24     double x1,x2,y;
 25     int f;
 26     node(){}
 27     node(double x1,double x2,double y,int f):x1(x1),x2(x2),y(y),f(f){}
 28     bool operator < (const node &s) const
 29     {
 30         return y <s.y;
 31     }
 32 }p[N];
 33 void up(int w,int l,int r)
 34 {
 35     if(fs[w]>1)
 36     {
 37         s[w] = val[r+1]-val[l];
 38         res[w] = s[w];
 39     }
 40     else if(fs[w]==1)
 41     {
 42         if(l==r)
 43         s[w] = 0;
 44         else
 45         s[w] = res[w<<1]+res[w<<1|1];
 46         res[w] = val[r+1]-val[l];
 47     }
 48     else
 49     {
 50         if(l==r)
 51         {
 52             s[w] = 0;
 53             res[w] = 0;
 54         }
 55         else
 56         {
 57             s[w] = s[w<<1]+s[w<<1|1];
 58         res[w] = res[w<<1]+res[w<<1|1];
 59         }
 60     }
 61 }
 62 void build(int l,int r,int w)
 63 {
 64     fs[w] = 0;
 65     res[w] = s[w] = 0;
 66     if(l==r)
 67     {
 68         return ;
 69     }
 70     int m = (l+r)>>1;
 71     build(l,m,w<<1);
 72     build(m+1,r,w<<1|1);
 73     up(w,l,r);
 74 }
 75 void update(int a,int b,int d,int l,int r,int w)
 76 {
 77     if(a<=l&&b>=r)
 78     {
 79         fs[w]+=d;
 80         up(w,l,r);
 81         return ;
 82     }
 83     int m = (l+r)>>1;
 84     if(a<=m) update(a,b,d,l,m,w<<1);
 85     if(b>m) update(a,b,d,m+1,r,w<<1|1);
 86     up(w,l,r);
 87 }
 88 int main()
 89 {
 90     int t,i,n;
 91     scanf("%d",&t);
 92     while(t--)
 93     {
 94         scanf("%d",&n);
 95         f.clear();
 96         int g = 0;
 97         for(i = 1; i <=n ;i++)
 98         {
 99             double x1,x2,y1,y2;
100             scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2);
101             p[++g] = node(x1,x2,y1,1);
102             que[g] = x1;
103             p[++g] = node(x1,x2,y2,-1);
104             que[g] = x2;
105         }
106         sort(p+1,p+g+1);
107         sort(que+1,que+g+1);
108         int o = 0;
109         f[que[1]] = ++o;
110         val[o] = que[1];
111         for(i = 2; i <= g; i++)
112         {
113             if(fabs(que[i]-que[i-1])>0)
114             {
115                 f[que[i]] = ++o;
116                 val[o] = que[i];
117             }
118         }
119         double ans = 0;
120         build(1,o-1,1);
121         for(i = 1; i < g ; i++)
122         {
123             int l = f[p[i].x1];
124             int r = f[p[i].x2]-1;
125             if(l<=r)
126             {
127                 update(l,r,p[i].f,1,o-1,1);
128             }
129             double sum = s[1]*(p[i+1].y-p[i].y);
130            // cout<<sum<<endl;
131             ans+=sum;
132         }
133         printf("%.2f
",ans);
134     }
135     return 0;
136 }
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