Atlantis

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 16222		Accepted: 6172

There are several ancient Greek texts that contain descriptions of the fabled island Atlantis. Some of these texts even include maps of parts of the island. But unfortunately, these maps describe different regions of Atlantis. Your friend Bill has to know the total area for which maps exist. You (unwisely) volunteered to write a program that calculates this quantity.

The input consists of several test cases. Each test case starts with a line containing a single integer n (1 <= n <= 100) of available maps. The n following lines describe one map each. Each of these lines contains four numbers x1;y1;x2;y2 (0 <= x1 < x2 <= 100000;0 <= y1 < y2 <= 100000), not necessarily integers. The values (x1; y1) and (x2;y2) are the coordinates of the top-left resp. bottom-right corner of the mapped area. 
The input file is terminated by a line containing a single 0. Don't process it.

For each test case, your program should output one section. The first line of each section must be "Test case #k", where k is the number of the test case (starting with 1). The second one must be "Total explored area: a", where a is the total explored area (i.e. the area of the union of all rectangles in this test case), printed exact to two digits to the right of the decimal point. 
Output a blank line after each test case.

2

10 10 20 20

15 15 25 25.5

0

Test case #1

Total explored area: 180.00 

思路：首先将横坐标离散化，再对纵坐标排序，然后根据y轴从下往上扫描，每次的高度就是seg[i].y-seg[i-1].y，这就相当于分矩形的宽，然后要做的事就是查询x轴（矩形长）的有效长度，这就要交给线段树了。

AC代码：

 /*************************************************************************

     > File Name:        area.cpp

     > Author:         wangzhili

     > Mail:           wangstdio.h@gmail.com

     > Created Time:   2014/3/1 星期六 16:06:57

  ************************************************************************/

 #include<iostream>

 #include<algorithm>

 #include<cstdio>

 #define MAX 1000

 using namespace std;

 class TreeNode

 {

     public:

         int left;

         int right;

         int mid;

         int cover;

         int flag;

         double length;

 };

 typedef struct

 {

     double xl, xr, y;

     int flag;

 }Line;

 TreeNode node[*MAX];

 Line seg[MAX];

 double x[MAX];

 double length;

 bool cmp(Line a, Line b)

 {

     return a.y < b.y;

 }

 void BuildTree(int k, int l, int r)

 {

     node[k].left = l;

     node[k].right = r;

     node[k].mid = (l + r) >> ;

     node[k].cover = ;

     node[k].flag = ;

     if(l +  == r)

     {

         node[k].flag = ;

         return ;

     }

     int mid = (l + r) >> ;

     BuildTree(k << , l, mid);

     BuildTree(k << |, mid, r);

 }

 void UpdateTree(int k, int l, int r, int flag)

 {

     if(node[k].left == l && node[k].right == r)

     {

         node[k].cover += flag;

         node[k].length = x[r-] - x[l-];

         return ;

     }

     if(node[k].flag)

         return ;

     if(node[k].mid <= l)

         UpdateTree(k << |, l, r, flag);

     else if(node[k].mid >= r)

         UpdateTree(k << , l, r, flag);

     else

     {

         UpdateTree(k << , l, node[k].mid, flag);

         UpdateTree(k << |, node[k].mid, r, flag);

     }

 }

 void GetLength(int k)

 {

     if(node[k].cover > )

     {

         length += node[k].length;

         return ;

     }

     if(node[k].flag)

         return;

     GetLength(k << );

     GetLength(k << |);

 }

 int GetIndex(double num, int length)

 {

     int l, r, mid;

     l = , r = length-;

     while(l <= r)

     {

         mid = (l + r) >> ;

         if(x[mid] == num)

             return mid;

         else if(x[mid] > num)

             r = mid - ;

         else

             l = mid + ;

     }

 }

 int main(int argc, char const *argv[])

 {

     int n, i, j, k, cnt;

     int xl, xr;

     double ans;

     double x1, y1, x2, y2;

     cnt = ;

     BuildTree(, , );

    // freopen("in.c", "r", stdin);

     while(~scanf("%d", &n) && n)

     {

         j = ;

         ans = .;

         for(i = ; i < ; i ++)

         {

             node[i].cover = ;

         }

         for(i = ; i < n; i ++)

         {

             scanf("%lf%lf%lf%lf", &x1, &y1, &x2, &y2);

             seg[j].xl = x1;

             seg[j].xr = x2;

             seg[j].y = y1;

             x[j] = x1;

             seg[j ++].flag = ;

             seg[j].xl = x1;

             seg[j].xr = x2;

             seg[j].y = y2;

             x[j] = x2;

             seg[j ++].flag = -;

         }

         sort(x, x+j);

         sort(seg, seg+j, cmp);

         k = ;

         for(i = ; i < j; i ++)

         {

             if(x[i] != x[i-])

                 x[k ++] = x[i];

         }

         xl = GetIndex(seg[].xl, k) + ;

         xr = GetIndex(seg[].xr, k) + ;

         UpdateTree(, xl, xr, seg[].flag);

         length = ;

         GetLength();

         for(i = ; i < j; i ++)

         {

             ans += (seg[i].y-seg[i-].y)*length;

             xl = GetIndex(seg[i].xl, k)+;

             xr = GetIndex(seg[i].xr, k)+;

             UpdateTree(, xl, xr, seg[i].flag);

             length = .;

             GetLength();

         }

         printf("Test case #%d\nTotal explored area: %.2lf\n\n", ++cnt, ans);

     }

     return ;

 }