poj_1151 线段树

#define _CRT_SECURE_NO_WARNINGS
#include<stdio.h>
#include<algorithm>
#include<string.h>
#include<vector>
using namespace std;
#define MAX_RECT_NUM 1000
#define MAX_SEG_NUM MAX_RECT_NUM * 2
#define MAX_NODE_NUM 4*MAX_SEG_NUM
#define MAX(a, b) a > b? a :b
#define MIN(a, b) a < b? a :b
//根据矩形的上下边在y方向上划分区间单元（长度不固定），每个矩形占据y方向上的连续的几个单元，形成区间
struct Rect{
	double top_left_x;
	double top_left_y;
	double bottom_right_x;
	double bottom_right_y;

	int interval_beg;	//在y轴上，该矩形所占据区间的起始单元序号
	int interval_end;	//在y轴上，该矩形所占据区间的结束单元序号（从下向上）  inteval_beg 和 interval_end为 闭区间
};

Rect gRects[MAX_RECT_NUM];
vector<double> gPartPoint;		//用于离散化的点纵坐标
vector<double> gSegs;			//离散化之后的段单元长度

struct Node{
	int beg;		//在y轴方向离散化之后，节点所代表区间的起始块号
	int end;		//节点所代表区间的终止块号
	double length;	//节点所代表区间的长度（y轴方向）
	int covered_num;	//扫描线被多少个矩形覆盖
};
Node gNodes[MAX_NODE_NUM];

//对矩形进行x坐标从小到大排序，便于进行扫描
bool CmpToSortRect(const Rect& rect1, const Rect& rect2){
	if (rect1.top_left_x == rect2.top_left_x)
		return rect1.bottom_right_x < rect2.bottom_right_x;
	return rect1.top_left_x < rect2.top_left_x;
}

void BuildTree(int beg, int end, int index){
	gNodes[index].beg = beg;
	gNodes[index].end = end;
	gNodes[index].covered_num = 0;
	if (beg == end){
		gNodes[index].length = gSegs[beg];
		return;
	}
	int left = 2 * index + 1;
	int right = 2 * index + 2;
	int mid = (beg + end) / 2;
	BuildTree(beg, mid, left);
	BuildTree(mid + 1, end, right);
	//由子节点长度得到父节点代表区间的长度
	gNodes[index].length = gNodes[left].length + gNodes[right].length;
}

//向下更新
void PushDown(int index){
	if (gNodes[index].covered_num){
		int left = 2 * index + 1, right = 2 * index + 2;
		gNodes[left].covered_num += gNodes[index].covered_num;
		gNodes[right].covered_num += gNodes[index].covered_num;
	}
	gNodes[index].covered_num = 0;
}

//向上更新
void PushUp(int index){
	int left = 2 * index + 1, right = 2 * index + 2;
	int min = MIN(gNodes[left].covered_num, gNodes[right].covered_num);
	gNodes[index].covered_num = min;
	gNodes[left].covered_num -= min;
	gNodes[right].covered_num -= min;
}

//当扫描线进入矩形区域时step_in = true, 否则为false
void Update(int beg, int end, int index, bool step_in){
	if (gNodes[index].beg >= beg && gNodes[index].end <= end){
		if (step_in){
			gNodes[index].covered_num++;
		}
			
		else{
			gNodes[index].covered_num--;
		}
		return;
	}
	if (gNodes[index].end < beg || gNodes[index].beg > end){
		return;
	}
	if (beg > end){
		return;
	}
	int left = 2 * index + 1, right = 2 * index + 2;
	int mid = (gNodes[index].beg + gNodes[index].end) / 2;
	//向下递归时，先pushdown 向下更新
	PushDown(index);
	Update(beg, MIN(mid, end), left, step_in);
	Update(MAX(mid + 1, beg), end, right, step_in);
	//递归返回进行 向上更新
	PushUp(index);
}

//查询，查询当前情况下，扫描线占据的矩形y方向长度
double Query(int index){
	if (gNodes[index].covered_num > 0){
		return gNodes[index].length;
	}
	if (gNodes[index].beg == gNodes[index].end){
		return 0;
	}
	int left = 2 * index + 1, right = 2 * index + 2;
	return Query(left) + Query(right);
}

bool DoubleEqual(double d1, double d2){
	if (abs(d1 - d2) < 1e-7){
		return true;
	}
	return false;
}
int main(){
	int n, cas = 1;
	while (true){
		scanf("%d", &n);
		if (n == 0){
			break;
		}
		gPartPoint.clear();
		for (int i = 0; i < n; i++){
			scanf("%lf %lf %lf %lf", &gRects[i].top_left_x, &gRects[i].top_left_y, &gRects[i].bottom_right_x, &gRects[i].bottom_right_y);
			gPartPoint.push_back(gRects[i].top_left_y);		 //得到y方向上的各个离散的分界点
			gPartPoint.push_back(gRects[i].bottom_right_y);
		}
		//对分界点进行排序，去重
		sort(gPartPoint.begin(), gPartPoint.end());
		vector<double>::iterator it = unique(gPartPoint.begin(), gPartPoint.end());
		gPartPoint.erase(it, gPartPoint.end());

		//根据分界点，得到离散化之后的区间长度
		gSegs.clear();
		gSegs.reserve(gPartPoint.size());
		for (int i = 0; i < gPartPoint.size() - 1; i++){
			double len = gPartPoint[i + 1] - gPartPoint[i];
			gSegs.push_back(len);
		}

		//得到每个矩形在y方向上占据的离散化之后的区间的  beg和end（闭区间）
		for (int i = 0; i < n; i++){
			vector<double>::iterator it = find(gPartPoint.begin(), gPartPoint.end(), gRects[i].top_left_y);
			gRects[i].interval_beg = it - gPartPoint.begin();
			it = find(gPartPoint.begin(), gPartPoint.end(), gRects[i].bottom_right_y);
			gRects[i].interval_end = it - gPartPoint.begin() - 1;
		}
		
		BuildTree(0, gSegs.size() - 1, 0);

		//将x方向的各个分割点进行排序，去重
		gPartPoint.clear();
		for (int i = 0; i < n; i++){
			gPartPoint.push_back(gRects[i].top_left_x);
			gPartPoint.push_back(gRects[i].bottom_right_x);
		}
		sort(gPartPoint.begin(), gPartPoint.end());
		it = unique(gPartPoint.begin(), gPartPoint.end());
		gPartPoint.erase(it, gPartPoint.end());


		int seg_num = gSegs.size();
		double sum_area = 0;
		double height = 0;
		int beg, end;
		for (int i = 0; i < gPartPoint.size() - 1; i++){
		
			for (int r = 0; r < n; r++){
				if (DoubleEqual(gRects[r].top_left_x, gPartPoint[i])){ //扫描线进入矩形					
					Update(gRects[r].interval_beg, gRects[r].interval_end, 0, true);
				}
				if (DoubleEqual(gRects[r].bottom_right_x, gPartPoint[i])){//扫描线离开矩形
					Update(gRects[r].interval_beg, gRects[r].interval_end, 0, false);
				}

			}
			height = Query(0);
			sum_area += height*(gPartPoint[i + 1] - gPartPoint[i]);
		}
		printf("Test case #%d\n", cas ++);
		printf("Total explored area: %.2lf\n\n", sum_area);
	}
	return 0;
}