atlantis解题报告
算法：线段树+离散化+扫描线
思想：把矩形的两条侧边存起来，然后排序，所有的y坐标存起来，也排序。映射到一个整数值。
每次遇到一个边先求面积，如果是左边的话插入其y方向的测度，如果是右侧边的话删除y方向的测度。不断的向右扫描。
线段树优化保存y方向的测度。使询问由o(n)变为o(logn)
#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
using namespace std;
#define LEFT(i) (i * 2)
#define RIGHT(i) (i * 2 + 1)
const int SIZE_OF_ARR = 256;
struct Edge
{
double x, y1, y2;
bool flag;
bool operator<(const Edge a) const
{
return x < a.x;
}
} edge[SIZE_OF_ARR];
double arry[SIZE_OF_ARR];
class segment_tree
{
private:
const static int SIZE = 1001 * 8;
int left[SIZE], right[SIZE], cnt[SIZE];
double m[SIZE];
void build(int l, int r, int n);
public:
void initialize(int n);
void insert(int l, int r, int n);
void del(int l, int r, int n);
double queury();
void update(int n);
};
void segment_tree::del(int l, int r, int n)
{
int mid = (right[n] + left[n]) / 2;
if (l == left[n] && r == right[n])
cnt[n]--;
else
{
if (mid <= l)
del(l, r, RIGHT(n));
else if (r <= mid)
del(l, r, LEFT(n));
else
{
del(l, mid, LEFT(n));
del(mid, r, RIGHT(n));
}
}
update(n);
}
void segment_tree::update(int n)
{
if (cnt[n])
m[n] = arry[right[n]] - arry[left[n]];
else
{
if (right[n] - left[n] == 1)
m[n] = 0;
else
m[n] = m[LEFT(n)] + m[RIGHT(n)];
}
}
void segment_tree::insert(int l, int r, int n)
{
int mid = (right[n] + left[n]) / 2;
if (l == left[n] && r == right[n])
cnt[n]++;
else
{
if (mid <= l)
insert(l, r, RIGHT(n));
else if (r <= mid)
insert(l, r, LEFT(n));
else
{
insert(l, mid, LEFT(n));
insert(mid, r, RIGHT(n));
}
}
update(n);
}
double segment_tree::queury()
{
return m[1];
}
void segment_tree::initialize(int n)
{
memset(m, 0, sizeof (m));
memset(cnt, 0, sizeof (cnt));
memset(left, 0, sizeof (left));
memset(right, 0, sizeof (right));
build(0, n, 1);
}
void segment_tree::build(int l, int r, int n)
{
left[n] = l;
right[n] = r;
m[n] = 0;
int mid = (l + r) / 2;
if (r - l <= 1)
return;
build(l, mid, LEFT(n));
build(mid, r, RIGHT(n));
}
segment_tree tree;
int main()
{
int n, cs = 1;
while (scanf("%d", &n) == 1 && n)
{
double x1, x2, y1, y2;
for (int i = 0; i < n; i++)
{
scanf("%lf %lf %lf %lf", &x1, &y1, &x2, &y2);
edge[i * 2].x = x1;
edge[i * 2 + 1].y1 = edge[i * 2].y1 = min(y1, y2);
edge[i * 2 + 1].x = x2;
edge[i * 2 + 1].y2 = edge[i * 2].y2 = max(y1,y2);
arry[i * 2] = y1;
arry[i * 2 + 1] = y2;
if (x1 > x2)
{
edge[i * 2].flag = true;
edge[i * 2 + 1].flag = false;
}
else
{
edge[i * 2].flag = false;
edge[i * 2 + 1].flag = true;
}
}
sort(edge, edge + n * 2);
sort(arry, arry + n * 2);
tree.initialize(n * 2);
double area = 0;
for (int i = 0; i < 2 * n; i++)
{
int a = lower_bound(arry, arry + 2 * n, edge[i].y1) - arry;
int b = lower_bound(arry, arry + 2 * n, edge[i].y2) - arry;
if (a == b)
continue;
if (i == 0)
{
tree.insert(a, b, 1);
continue;
}
area += (edge[i].x - edge[i - 1].x) * tree.queury();
if (edge[i].flag)
tree.del(a, b, 1);
else
tree.insert(a, b, 1);
}
printf("Test case #%d\nTotal explored area: %0.2lf\n\n", cs++, area);
}
return 0;
}