POJ1151 Atlantis 【扫描线】

Description

Input

Output

Sample Input

2
10 10 20 20
15 15 25 25.5
0

Sample Output

Test case #1
Total explored area: 180.00 

我累个去~~这题从早上8：30一直做到如今22：50，总算是A掉了，上午一直没看懂扫描线，然后看到傍晚总算是有些头目了，结果写的时候非常生疏，等到摸摸索索完全然全地写完已经大半夜了。满心欢喜地提交又各种RE，開始以为是数组开小了，然后翻了倍依然RE，就这样RE了6、7次后猛地发现是freopen忘了凝视掉，o(╯□╰)o...尼玛啊！！总归是在睡觉前找到问题了。

题意：给定n个矩形的对角坐标，各自是左下和右上，浮点型。求矩形覆盖的面积。

题解：扫描线解法，将每一个矩形分别以长宽为直线切割，终于垂直于x轴的割线有2n条，垂直于y轴的割线也有2n条，将这些割线存到两个数组里并排序，建立一个线段树用以维护扫描线当前在y轴方向覆盖的长度。最后，在扫描线从左往右扫描的过程中，一旦经过一条垂直于x轴的割线就立刻将这条割线更新到线段树里，覆盖面积即为两条相邻扫描线的距离乘以左边一条扫描线的长度，累加下去即得终于覆盖面积。x轴割线数组须要记录边是入边还是出边。若是出边则右边的的面积对此出边是不计的，可是存在入边重合的情况，须要详细考虑。

2014-9-23 23:32:51更新

#include <stdio.h>
#include <string.h>
#include <algorithm>
#define maxn 202
#define lson l, mid, rt << 1
#define rson mid, r, rt << 1 | 1
using namespace std;

struct Node {
    double y1, y2, len;
    int covers;
} T[maxn << 2];
struct Node2 {
    double x, y1, y2;
    int isLeft;
} xNode[maxn];
double yNode[maxn];

bool cmp(Node2 a, Node2 b) {
    return a.x < b.x;
}

void pushUp(int l, int r, int rt) {
    if(T[rt].covers > 0)
        T[rt].len = T[rt].y2 - T[rt].y1;
    else if(r - l == 1) T[rt].len = 0.0;
    else T[rt].len = T[rt << 1].len + T[rt << 1 | 1].len;
}

void build(int l, int r, int rt) {
    T[rt].covers = 0;
    T[rt].y1 = yNode[l];
    T[rt].y2 = yNode[r];
    T[rt].len = 0.0;
    if(r - l == 1) return;
    int mid = (l + r) >> 1;
    build(lson);
    build(rson);
}

void update(Node2 x, int l, int r, int rt) {
    if(x.y1 == T[rt].y1 && x.y2 == T[rt].y2) {
        T[rt].covers += x.isLeft;
        pushUp(l, r, rt);
        return;
    }
    int mid = (l + r) >> 1;
    if(x.y2 <= yNode[mid]) update(x, lson);
    else if(x.y1 >= yNode[mid]) update(x, rson);
    else {
        Node2 x1 = x, x2 = x;
        x1.y2 = x2.y1 = yNode[mid];
        update(x1, lson);
        update(x2, rson);
    }
    pushUp(l, r, rt);
}

int main() {
    //freopen("stdin.txt", "r", stdin);
    int n, i, id, cas = 1;
    double x1, y1, x2, y2, sum;
    while(scanf("%d", &n), n) {
        for(i = id = 0; i < n; ++i) {
            scanf("%lf%lf%lf%lf", &x1, &y1, &x2, &y2);
            yNode[id] = y1;
            xNode[id].x = x1;
            xNode[id].y1 = y1;
            xNode[id].y2 = y2;
            xNode[id++].isLeft = 1;

            yNode[id] = y2;
            xNode[id].x = x2;
            xNode[id].y1 = y1;
            xNode[id].y2 = y2;
            xNode[id++].isLeft = -1;
        }
        sort(yNode, yNode + id);
        build(0, id - 1, 1);
        sort(xNode, xNode + id, cmp);
        update(xNode[0], 0, id - 1, 1);
        for(i = 1, sum = 0.0; i < id; ++i) {
            sum += T[1].len * (xNode[i].x - xNode[i-1].x);
            update(xNode[i], 0, id - 1, 1);
        }
        printf("Test case #%d\nTotal explored area: %.2lf\n\n", cas++, sum); 
    }
    return 0;
}

#include <stdio.h>
#include <algorithm>
#define maxn 202
#define lson l, mid, rt << 1
#define rson mid, r, rt << 1 | 1
using std::sort;

struct Node{
	double y1, y2, height; //y1, y2记录y坐标离散前的值
	int coverTimes;
} tree[maxn << 2]; //区间树
double yArr[maxn]; //垂直于Y轴的割线
struct node{
	double x, y1, y2;
	int isLeftEdge;
} xArr[maxn]; //垂直于X轴的割线

bool cmp(node a, node b){ return a.x < b.x; }

void build(int l, int r, int rt)
{
	tree[rt].coverTimes = 0;
	tree[rt].height = 0;
	tree[rt].y1 = yArr[l];
	tree[rt].y2 = yArr[r];
	if(r - l == 1) return;
	
	int mid = (l + r) >> 1;
	build(lson);
	build(rson);
}

void getSweepLinesHeight(int l, int r, int rt)
{//因为存在线段覆盖的情况，所以长线段结束并不能代表扫描线长度为0
	if(tree[rt].coverTimes > 0){ 
		tree[rt].height = tree[rt].y2 - tree[rt].y1;
	}else if(r - l == 1){
		tree[rt].height = 0;
	}else tree[rt].height = tree[rt << 1].height + tree[rt << 1 | 1].height;
}

void update(node xNode, int l, int r, int rt)
{
	if(xNode.y1 == tree[rt].y1 && xNode.y2 == tree[rt].y2){
		tree[rt].coverTimes += xNode.isLeftEdge;
		getSweepLinesHeight(l, r, rt);
		return;
	} //include r - l == 1
	
	int mid = (l + r) >> 1;	
	if(xNode.y2 <= yArr[mid]) update(xNode, lson);
	else if(xNode.y1 >= yArr[mid]) update(xNode, rson);
	else{
		node temp = xNode;
		temp.y2 = yArr[mid];
		update(temp, lson);
		temp = xNode; temp.y1 =yArr[mid];
		update(temp, rson);
	}
	
	getSweepLinesHeight(l, r, rt); //Attention!	
}

int main()
{
	//freopen("stdin.txt", "r", stdin);
	int n, i, cas = 1, id;
	double x1, y1, x2, y2, sum;
	while(scanf("%d", &n), n){
		for(i = id = 0; i < n; ++i){
			scanf("%lf%lf%lf%lf", &x1, &y1, &x2, &y2);
			yArr[id] = y1; xArr[id].x = x1;
			xArr[id].isLeftEdge = 1; //1表示左。-1表示右
			xArr[id].y1 = y1; xArr[id++].y2 = y2;
			
			yArr[id] = y2; xArr[id].x = x2;
			xArr[id].isLeftEdge = -1;
			xArr[id].y1 = y1; xArr[id++].y2 = y2;
		}
		
		sort(yArr, yArr + id);
		sort(xArr, xArr + id, cmp);
		build(0, id - 1, 1);		
				
		update(xArr[0], 0, id - 1, 1);
		for(i = 1, sum = 0; i < id; ++i){
			sum += tree[1].height * (xArr[i].x - xArr[i - 1].x);
			update(xArr[i], 0, id - 1, 1);
		}
		
		printf("Test case #%d\nTotal explored area: %.2lf\n\n", cas++, sum);
	}
	return 0;
}