UVaLive2572 poj1418 UVa1308 Viva Confetti

一次放下n个圆

问最终可见的圆的数量

应该是比较经典的问题吧

考虑一个圆与其他每个圆的交点O(n)个

将其割成了O(n)条弧

那么看每条弧的中点 分别向内向外调动eps这个点 则最上面的覆盖这个点的圆可见O(n)

总时间复杂度O(n ** 3)

怕炸精度，代码基本抄的rjl的

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<iostream>
#include<cmath>
#include<vector>

using namespace std;

typedef double data_type;

const data_type eps = 5 * 1e-13;
int dcmp(const data_type& x) {
    if(fabs(x) < 0) return 0; return x < 0 ? -1 : 1;
}

const data_type pi = acos(-1.0), dpi = 2 * acos(-1.0);

double NormalizeAngle(double rad) {
    return rad - dpi * floor(rad / dpi);
}

typedef const struct Point& Point_cr;
typedef struct Point {
    data_type x, y;
    Point() {}
    Point(data_type x, data_type y) : x(x), y(y) {}
    Point operator + (Point_cr rhs) const {
        return Point(x + rhs.x, y + rhs.y);
    }
    Point operator - (Point_cr rhs) const {
        return Point(x - rhs.x, y - rhs.y);
    }
    Point operator * (data_type k) const {
        return Point(x * k, y * k);
    }
    Point operator / (double k) const {
        return Point(x / k, y / k);
    }
    double length() const {
        return hypot(x, y);
    }
    double angle() const {
        return atan2(y, x);
    }
}Vector;

double Dot(const Vector& v1, const Vector& v2) {
    return v1.x * v2.x + v1.y * v2.y;
}

double length(const Vector& v) {
    return sqrt(Dot(v, v));
}

typedef const Vector& Vector_cr;
void CircleCircleIntersection(Point_cr c1, double r1, Point c2, double r2, vector<double> &rad) {
    double d = (c1 - c2).length();
    if(dcmp(d) == 0) return;
    if(dcmp(r1 + r2 - d) < 0) return;
    if(dcmp(fabs(r1 - r2) - d) > 0) return;
    double a = (c2 - c1).angle();
    double da = acos((r1 * r1 + d * d - r2 * r2) / (2 * r1 * d));
    rad.push_back(NormalizeAngle(a + da));
    rad.push_back(NormalizeAngle(a - da));
}

const int N = 100 + 10;
int n;
Point centre[N];
double radius[N];
bool vis[N];

int topmost(Point p) {
    for(int i = n - 1; i >= 0; i--) {
        if((centre[i] - p).length() < radius[i]) return i;
    }
    return -1;
}

int main() {
#ifdef DEBUG
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);
#endif
    
    while(scanf("%d", &n) == 1 && n) {
        for(int i = 0; i < n; i++) {
            double x, y, r;
            scanf("%lf%lf%lf", &x, &y, &r);
            centre[i] = Point(x, y);
            radius[i] = r;
        }
        memset(vis, 0, sizeof vis);
        for(int i = 0; i < n; i++) {
            vector<double> rad;
            rad.push_back(0);
            rad.push_back(dpi);
            
            for(int j = 0; j < n; j++) {
                CircleCircleIntersection(centre[i], radius[i], centre[j], radius[j], rad);
            }
            
            sort(rad.begin(), rad.end());
            
            for(unsigned j = 0; j < rad.size(); j++) {
                double mid = (rad[j] + rad[j+1]) / 2.0;
                for(int side = -1; side <= 1; side += 2) {
                    double r2 = radius[i] - side * eps;
                    int t = topmost(Point(centre[i].x + cos(mid) * r2, centre[i].y + sin(mid) * r2));
                    if(t >= 0) vis[t] = 1;
                }
            }
        }
        int ans = 0;
        for(int i = 0; i < n; i++) if(vis[i]) {
            ans++;
        }
        printf("%d
", ans);
    }
    
    return 0;
}