Picture

Time Limit: 6000/2000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 4795 Accepted Submission(s): 2339

Problem Description

A number of rectangular posters, photographs and other pictures of the same shape are pasted on a wall. Their sides are all vertical or horizontal. Each rectangle can be partially or totally covered by the others. The length of the boundary of the union of all rectangles is called the perimeter.

Write a program to calculate the perimeter. An example with 7 rectangles is shown in Figure 1.

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The corresponding boundary is the whole set of line segments drawn in Figure 2.

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The vertices of all rectangles have integer coordinates.

Input

Your program is to read from standard input. The first line contains the number of rectangles pasted on the wall. In each of the subsequent lines, one can find the integer coordinates of the lower left vertex and the upper right vertex of each rectangle. The values of those coordinates are given as ordered pairs consisting of an x-coordinate followed by a y-coordinate.

0 <= number of rectangles < 5000
All coordinates are in the range [-10000,10000] and any existing rectangle has a positive area.

Please process to the end of file.

Output

Your program is to write to standard output. The output must contain a single line with a non-negative integer which corresponds to the perimeter for the input rectangles.

Sample Input

7 -15 0 5 10 -5 8 20 25 15 -4 24 14 0 -6 16 4 2 15 10 22 30 10 36 20 34 0 40 16

Sample Output

228

Source

IOI 1998

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  1 //#pragma comment(linker, "/STACK:1024000000,1024000000")
  2 #include<cstdio>
  3 #include<iostream>
  4 #include<cstring>
  5 #include<algorithm>
  6 #include<cmath>
  7 #define clr(x) memset(x,0,sizeof(x))
  8 #define MAXN 50010
  9 using namespace std;
 10 struct edgx
 11 {
 12     int l,u,x;
 13     int d;
 14 }edgex[MAXN];
 15 struct edgy
 16 {
 17     int l,r,y;
 18     int d;
 19 }edgey[MAXN];
 20 struct seg
 21 {
 22     int l,r,cov,len;
 23 }segt[MAXN<<2];
 24 int cntx,cnty;
 25 int x[MAXN],y[MAXN],vec[MAXN];
 26 bool cmpy(edgy a,edgy b)
 27 {
 28     if(a.y==b.y) return a.d>b.d;
 29     return a.y<b.y;
 30 }
 31 bool cmpx(edgx a,edgx b)
 32 {
 33     if(a.x==b.x) return a.d>b.d;
 34     return a.x<b.x;
 35 }
 36 void init(int i,int l,int r)
 37 {
 38     segt[i]=(seg){l,r,0,0};
 39     if(l==r)
 40         return ;
 41     int mid=(l+r)>>1;
 42     init(i<<1,l,mid);
 43     init(i<<1|1,mid+1,r);
 44     return ;
 45 }
 46 void pushup(int i)
 47 {
 48     if(segt[i].cov)
 49     {
 50         segt[i].len=vec[segt[i].r+1]-vec[segt[i].l];
 51     }
 52     else if(segt[i].l==segt[i].r)
 53     {
 54         segt[i].len=0;
 55     }
 56     else
 57     {
 58         segt[i].len=segt[i<<1].len+segt[i<<1|1].len;
 59     }
 60     return ;
 61 }
 62 void update(int i,int l,int r,int value)
 63 {
 64     if(segt[i].l>=l && segt[i].r<=r)
 65     {
 66         segt[i].cov+=value;
 67         pushup(i);
 68         return ;
 69     }
 70     int mid=(segt[i].l+segt[i].r)>>1;
 71     if(mid>=r)
 72     {
 73         update(i<<1,l,r,value);
 74     }
 75     else if(mid<l)
 76     {
 77         update(i<<1|1,l,r,value);
 78     }
 79     else
 80     {
 81         update(i<<1,l,r,value);
 82         update(i<<1|1,l,r,value);
 83     }
 84     pushup(i);
 85     return ;
 86 }
 87 int main()
 88 {
 89     int x1,x2,y1,y2,n,m,T,ans,l,r,k;
 90     while(scanf("%d",&n)!=EOF)
 91     {
 92         cntx=0;
 93         cnty=0;
 94         for(int i=1;i<=n;i++)
 95         {
 96             scanf("%d%d%d%d",&x1,&y1,&x2,&y2);
 97             edgex[++cntx]=(edgx){y1,y2,x1,1};
 98             x[cntx]=x1;
 99             edgex[++cntx]=(edgx){y1,y2,x2,-1};
100             x[cntx]=x2;
101             edgey[++cnty]=(edgy){x1,x2,y1,1};
102             y[cnty]=y1;
103             edgey[++cnty]=(edgy){x1,x2,y2,-1};
104             y[cnty]=y2;
105         }
106         n<<=1;
107         ans=0;
108         memcpy(vec,x,sizeof(x));
109         sort(vec+1,vec+n+1);
110         m=unique(vec+1,vec+n+1)-vec-1;
111         sort(edgey+1,edgey+n+1,cmpy);
112         init(1,1,m);
113         for(int i=1;i<=n;i++)
114             if(edgey[i].l<edgey[i].r)
115             {
116                 k=segt[1].len;
117                 l=lower_bound(vec+1,vec+m+1,edgey[i].l)-vec;
118                 r=lower_bound(vec+1,vec+m+1,edgey[i].r)-vec;
119                 update(1,l,r-1,edgey[i].d);
120                 ans+=abs(segt[1].len-k);
121             }
122         memcpy(vec,y,sizeof(y));
123         sort(vec+1,vec+n+1);
124         m=unique(vec+1,vec+n+1)-vec-1;
125         sort(edgex+1,edgex+n+1,cmpx);
126         init(1,1,m);
127         for(int i=1;i<=n;i++)
128             if(edgex[i].l<edgex[i].u)
129             {
130                 k=segt[1].len;
131                 l=lower_bound(vec+1,vec+m+1,edgex[i].l)-vec;
132                 r=lower_bound(vec+1,vec+m+1,edgex[i].u)-vec;
133                 update(1,l,r-1,edgex[i].d);
134                 ans+=abs(segt[1].len-k);
135             }
136         printf("%d\n",ans);
137     }
138     return 0;
139 }

hdu 1255 矩阵面积并

覆盖的面积

Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 5718 Accepted Submission(s): 2854

Problem Description

给定平面上若干矩形,求出被这些矩形覆盖过至少两次的区域的面积.

技术分享

Input

输入数据的第一行是一个正整数T(1<=T<=100),代表测试数据的数量.每个测试数据的第一行是一个正整数N(1<=N<=1000),代表矩形的数量,然后是N行数据,每一行包含四个浮点数,代表平面上的一个矩形的左上角坐标和右下角坐标,矩形的上下边和X轴平行,左右边和Y轴平行.坐标的范围从0到100000.

注意:本题的输入数据较多,推荐使用scanf读入数据.

Output

对于每组测试数据,请计算出被这些矩形覆盖过至少两次的区域的面积.结果保留两位小数.

Sample Input

2 5 1 1 4 2 1 3 3 7 2 1.5 5 4.5 3.5 1.25 7.5 4 6 3 10 7 3 0 0 1 1 1 0 2 1 2 0 3 1

Sample Output

7.63 0.00

Author

Ignatius.L & weigang Lee

扫描线三巨头 hdu1928&&hdu 1255 && hdu 1542 [POJ 1151]

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扫描线三巨头 hdu1928&&hdu 1255 && hdu 1542 [POJ 1151]

Picture

覆盖的面积

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