题目给出 n 个矩形，要求它们的面积并。具体做法是离散化。先把 2n 个 x 坐标排序去重，然后再把所有水平线段（要记录是矩形上边还是下边）按 y 坐标排序。最后对于每一小段区间 (x[i], x[i + 1]) 扫描所有的水平线段，求出这些水平线段在小区间内覆盖的面积。总的时间复杂度是 O(n^2)。利用线段树，可以优化到 O(nlogn)。
/**//*************************************************************************
Author: WHU_GCC
Created Time: 2007-8-21 15:56:29
File Name: pku1151.cpp
Description:
************************************************************************/
#include <iostream>
#include <cmath>
using namespace std;
#define out(x) (cout << #x << ": " << x << endl)
typedef long long int64;
const int maxint = 0x7FFFFFFF;
const int64 maxint64 = 0x7FFFFFFFFFFFFFFFLL;
template <class T> void show(T a, int n) 
{ for (int i = 0; i < n; ++i) cout << a[i] << ' '; cout << endl; }
template <class T> void show(T a, int r, int l) { for (int i = 0; i < r; ++i) show(a[i], l); cout << endl; }
const int maxn = 1000;
typedef struct line_t
{
double l, r, y;
int flag;
};
bool operator <(const line_t &a, const line_t &b)
{
return a.y < b.y;
}
bool d_equal(const double &a, const double &b)
{
return abs(a - b) < 1e-9;
}
int n;
double x[maxn];
int cnt_x, cnt_line;
line_t line[maxn];
int main()
{
int ca = 1;
while (scanf("%d", &n), n != 0)
{
cnt_x = 0;
cnt_line = 0;
for (int i = 0; i < n; i++)
{
double x1, y1, x2, y2;
scanf("%lf%lf%lf%lf", &x1, &y1, &x2, &y2);
x[cnt_x++] = x1;
x[cnt_x++] = x2;
line[cnt_line].flag = 0;
line[cnt_line].l = x1;
line[cnt_line].r = x2;
line[cnt_line++].y = y1;
line[cnt_line].flag = 1;
line[cnt_line].l = x1;
line[cnt_line].r = x2;
line[cnt_line++].y = y2;
}
sort(line, line + cnt_line);
sort(x, x + cnt_x);
cnt_x = unique(x, x + cnt_x, d_equal) - x;
double area = 0.0;
for (int i = 0; i < cnt_x - 1; i++)
{
int cnt = 0;
double now_y;
for (int j = 0; j < cnt_line; j++) if (line[j].l <= x[i] && line[j].r >= x[i + 1])
{
if (cnt == 0) now_y = line[j].y;
if (line[j].flag == 0) cnt++;
else cnt--;
if (cnt == 0) area += (x[i + 1] - x[i]) * (line[j].y - now_y);
}
}
printf("Test case #%d\n", ca++);
printf("Total explored area: %.2lf\n\n", area);
}
return 0;
}