hdu 4629 Burning （扫描线）

Problem - 4629

　　以前写过PSLG模拟的版本，今天写了一下扫描线做这题。

　　其实这题可以用set存线段来做，类似于判断直线交的做法。不过实现起来有点麻烦，于是我就直接暴力求交点了。

代码如下：

#include <set>
#include <queue>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <algorithm>

using namespace std;

const double EPS = 1e-10;
inline int sgn(double x) { return (x > EPS) - (x < -EPS);}
typedef pair<double, double> Point;
#define x first
#define y second
Point operator + (Point a, Point b) { return Point(a.x + b.x, a.y + b.y);}
Point operator - (Point a, Point b) { return Point(a.x - b.x, a.y - b.y);}
Point operator * (Point a, double p) { return Point(a.x * p, a.y * p);}
Point operator / (Point a, double p) { return Point(a.x / p, a.y / p);}

inline double cross(Point a, Point b) { return a.x * b.y - a.y * b.x;}
inline double dot(Point a, Point b) { return a.x * b.x + a.y * b.y;}
inline double veclen(Point a) { return sqrt(dot(a, a));}
inline Point rotate(Point a) {
    double cosx = cos(0.001), sinx = sin(0.001);
    return Point(a.x * cosx - a.y * sinx, a.x * sinx + a.y * cosx);
}

struct Line {
    Point s, t;
    Line() {}
    Line(Point s, Point t) : s(s), t(t) {}
    Point vec() { return t - s;}
    Point point(double p) { return s + vec() * p;}
} ;
inline Point llint(Line a, Line b) { return a.point(cross(b.vec(), a.s - b.s) / cross(a.vec(), b.vec()));}
void scan(Point &a) { cin >> a.x >> a.y;}
const int N = 55;
Point tri[N][4];

bool check(int n) {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < 3; j++) {
            if (sgn(tri[i][j].x - tri[i][j + 1].x) == 0) return 1;
        }
    }
    return 0;
}
void adjust(int n) { for (int i = 0; i < n; i++) for (int j = 0; j < 4; j++) tri[i][j] = rotate(tri[i][j]);}
inline bool between(Point p, Point a, Point b) { return sgn(dot(a - p, b - p)) <= 0;}
bool cmpy(Point a, Point b) { return a.y < b.y;}

bool triline(Line l, int id, Point *ip) {
    Point tmp[3];
    int tt = 0;
    for (int i = 0; i < 3; i++) {
        tmp[tt] = llint(l, Line(tri[id][i], tri[id][i + 1]));
        if (between(tmp[tt], tri[id][i], tri[id][i + 1])) tt++;
    }
    sort(tmp, tmp + tt, cmpy);
    ip[0] = tmp[0], ip[1] = tmp[tt - 1];
    return tt > 1;
}

typedef pair<double, int> Break;
bool cmp(Break a, Break b) { return sgn(a.x - b.x) < 0 || sgn(a.x - b.x) == 0 && a.y < b.y;}
Break ips_l[N << 2], ips_r[N << 2];
double area[N], len_l[N], len_r[N], event[N * N << 4];
void scanline(int n) {
    memset(area, 0, sizeof(area));
    int tt = 0;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < 3; j++) {
            Point a = tri[i][j], b = tri[i][j + 1];
            event[tt++] = a.x;
            for (int k = 0; k < n; k++) {
                for (int l = 0; l < 3; l++) {
                    Point c = tri[k][l], d = tri[k][l + 1];
                    if (sgn(cross(b - a, d - c)) == 0) continue;
                    Point ip = llint(Line(a, b), Line(c, d));
                    //cout << ip.x << ' ' << ip.y << endl;
                    if (between(ip, a, b) && between(ip, c, d)) {
                        event[tt++] = ip.x;
                    }
                }
            }
        }
    }
    sort(event, event + tt);
    tt = (int) (unique(event, event + tt) - event);
    Line cur;
    Point tmp[2];
    for (int i = 1, c, cnt; i < tt; i++) {
        if (sgn(event[i - 1] - event[i]) == 0) continue;
        c = 0;
        cur = Line(Point(event[i - 1] + EPS, 0.0), Point(event[i - 1] + EPS, 1.0));
        for (int j = 0; j < n; j++) {
            if (triline(cur, j, tmp)) {
                ips_l[c++] = Break(tmp[0].y, 1), ips_l[c++] = Break(tmp[1].y, -1);
            }
        }
        sort(ips_l, ips_l + c, cmp);
        cnt = 0;
        memset(len_l, 0, sizeof(len_l));
        for (int j = 0; j < c; j++) {
            if (cnt > 0) len_l[cnt] += ips_l[j].x - ips_l[j - 1].x;
            cnt += ips_l[j].y;
        }
        c = 0;
        cur = Line(Point(event[i] - EPS, 0.0), Point(event[i] - EPS, 1.0));
        for (int j = 0; j < n; j++) {
            if (triline(cur, j, tmp)) {
                ips_r[c++] = Break(tmp[0].y, 1), ips_r[c++] = Break(tmp[1].y, -1);
            }
        }
        sort(ips_r, ips_r + c, cmp);
        cnt = 0;
        memset(len_r, 0, sizeof(len_r));
        for (int j = 0; j < c; j++) {
            if (cnt > 0) len_r[cnt] += ips_r[j].x - ips_r[j - 1].x;
            cnt += ips_r[j].y;
        }
        for (int j = 1; j <= n; j++) area[j] += (len_l[j] + len_r[j]) * (event[i] - event[i - 1]) / 2;
    }
}

int main() {
    ios::sync_with_stdio(0);
    cout << setiosflags(ios::fixed) << setprecision(8);
    int T, n;
    cin >> T;
    while (T-- && cin >> n) {
        int tt = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < 3; j++) scan(tri[tt][j]);
            tri[tt][3] = tri[tt][0];
            if (sgn(cross(tri[tt][1] - tri[tt][0], tri[tt][2] - tri[tt][0]))) tt++;
        }
        while (check(tt)) adjust(tt);
        scanline(tt);
        for (int i = 1; i <= n; i++) area[i] = fabs(area[i]);
        for (int i = 1; i <= n; i++) cout << area[i] << endl;
    }
    return 0;
}

——written by Lyon