矩形的面积并

const int N = 100; //矩形的最大个数
typedef double typev;
struct seg{
	int l, r;
	int c;    //覆盖数
	typev m;  //覆盖长度
}segs[N<<3];
struct li{
	typev x, ly, hy; //ly为小的，hy为大的
	void set(typev x, typev ly, typev hy){
		this->x = x, this->ly = ly, this->hy = hy;
	}
	bool is_l;   //标记是否是左边的线段
}lis[N*2];
//左下角是(x1,y1)，右上角是(x2,y2), x1<x2,y1<y2的矩形
struct rect{
	typev x1, x2, y1, y2;
	void read(){
		scanf("%lf%lf%lf%lf", &x1, &y1, &x2, &y2);
	}
}rs[N<<1];
typev y[N<<1];
int n, cnt;
bool cmp(li l1, li l2){
	return l1.x < l2.x;
}
void build(int id, int l, int r){
	segs[id].l = l, segs[id].r = r, segs[id].m = segs[id].c = 0;
	if(l < r - 1){
		int mid = (l+r)>>1;
		build(2*id+1, l, mid);
		build(2*id+2, mid, r);
	}
}
int binary(int l, int r, typev k){
	int mid;
	while(l <= r){
		mid = (l+r)>>1;
		if(y[mid] >= k) r = mid-1;
		else l = mid+1;
	}
	return r+1;
}
void renew(int id){
	if(segs[id].c > 0) segs[id].m = y[segs[id].r] - y[segs[id].l];
	else if(segs[id].l == segs[id].r - 1) segs[id].m = 0;
	else{
		segs[id].m = segs[2*id+1].m + segs[2*id+2].m;
	}
}
// 可以把insert和del合为一个函数
void modify(int id, int l, int r, int k){
	if(segs[id].l >= l && segs[id].r <= r){
		segs[id].c += k;
		renew(id);
	}else if(segs[id].l < segs[id].r - 1){
		int mid = (segs[id].l + segs[id].r)>>1;
		if(l < mid) modify(2*id+1, l, r, k);
		if(r > mid) modify(2*id+2, l, r, k);
		renew(id);
	}
}
//n个矩形的面积并
typev unionArea(rect* rs, int n){
	int i;
	typev x1, y1, x2, y2, py1, py2, area;
	for(i = 0; i < n; i++){
		x1 = rs[i].x1; y1 = rs[i].y1;
		x2 = rs[i].x2; y2 = rs[i].y2;
		lis[2*i].set(x1, y1, y2);
		lis[2*i].is_l = true;
		lis[2*i+1].set(x2, y1, y2);
		y[2*i] = y1;
		y[2*i+1] = y2;
		lis[2*i+1].is_l = false;
	}
	n <<= 1;
	sort(y, y + n);
	sort(lis, lis+n, cmp);
	cnt = unique(y, y + n) - y;
	build(0, 0, cnt-1);
	area = 0;
	for(i = 0; i < n-1; i++){
		py1 = binary(0, cnt-1, lis[i].ly);
		py2 = binary(0, cnt-1, lis[i].hy);
		if(lis[i].is_l) modify(0, py1, py2, 1);
		else modify(0, py1, py2, -1);
		area += (lis[i+1].x - lis[i].x) * (segs[0].m);
	}
	return area;
}