SPOJ CIRU - The area of the union of circles (圆的面积并)
CIRU - The area of the union of circles
You are given N circles and expected to calculate the area of the union of the circles !
Input
The first line is one integer n indicates the number of the circles. (1 <= n <= 1000)
Then follows n lines every line has three integers
Xi Yi Ri
indicates the coordinate of the center of the circle, and the radius. (|Xi|. |Yi| <= 1000, Ri <= 1000)
Note that in this problem Ri may be 0 and it just means one point !
Output
The total area that these N circles with 3 digits after decimal point
Example
Input:
3
0 0 1
0 0 1
100 100 1 Output:
6.283
代码详解见 : http://www.cnblogs.com/oyking/p/3424999.html
#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <string>
#include <map>
#include <stack>
#include <queue>
#include <vector>
#define inf 0x3f3f3f3f
#define met(a,b) memset(a,b,sizeof a)
#define pb push_back
typedef long long ll;
using namespace std;
const int N = 1e5+;
const int M = ;
const double PI = acos(-1.0);
const double EPS = 1e-; inline int sgn(double x) {
return (x > EPS) - (x < -EPS);
} struct Point {
double x, y;
Point() {}
Point(double x, double y): x(x), y(y) {}
void read() {
scanf("%lf%lf", &x, &y);
}
double angle() {
return atan2(y, x);
}
Point operator + (const Point &rhs) const {
return Point(x + rhs.x, y + rhs.y);
}
Point operator - (const Point &rhs) const {
return Point(x - rhs.x, y - rhs.y);
}
Point operator * (double t) const {
return Point(x * t, y * t);
}
Point operator / (double t) const {
return Point(x / t, y / t);
}
double length() const {
return sqrt(x * x + y * y);
}
Point unit() const {
double l = length();
return Point(x / l, y / l);
}
}; double cross(const Point &a, const Point &b) {
return a.x * b.y - a.y * b.x;
} double dist(const Point &p1, const Point &p2) {
return (p1 - p2).length();
} Point rotate(const Point &p, double angle, const Point &o = Point(, )) {
Point t = p - o;
double x = t.x * cos(angle) - t.y * sin(angle);
double y = t.y * cos(angle) + t.x * sin(angle);
return Point(x, y) + o;
} struct Region {
double st, ed;
Region() {}
Region(double st, double ed): st(st), ed(ed) {}
bool operator < (const Region &rhs) const {
if(sgn(st - rhs.st)) return st < rhs.st;
return ed < rhs.ed;
}
}; struct Circle {
Point c;
double r;
vector<Region> reg;
Circle() {}
Circle(Point c, double r): c(c), r(r) {}
void read() {
c.read();
scanf("%lf", &r);
}
void add(const Region &r) {
reg.push_back(r);
}
bool contain(const Circle &cir) const {
return sgn(dist(cir.c, c) + cir.r - r) <= ;
}
bool intersect(const Circle &cir) const {
return sgn(dist(cir.c, c) - cir.r - r) < ;
}
}; double sqr(double x) {
return x * x;
} void intersection(const Circle &cir1, const Circle &cir2, Point &p1, Point &p2) {
double l = dist(cir1.c, cir2.c);
double d = (sqr(l) - sqr(cir2.r) + sqr(cir1.r)) / ( * l);
double d2 = sqrt(sqr(cir1.r) - sqr(d));
Point mid = cir1.c + (cir2.c - cir1.c).unit() * d;
Point v = rotate(cir2.c - cir1.c, PI / ).unit() * d2;
p1 = mid + v, p2 = mid - v;
} Point calc(const Circle &cir, double angle) {
Point p = Point(cir.c.x + cir.r, cir.c.y);
return rotate(p, angle, cir.c);
} const int MAXN = ; Circle cir[MAXN];
bool del[MAXN];
int n; double solve() {
double ans = ;
for(int i = ; i < n; ++i) {
for(int j = ; j < n; ++j) if(!del[j]) {
if(i == j) continue;
if(cir[j].contain(cir[i])) {
del[i] = true;
break;
}
}
}
for(int i = ; i < n; ++i) if(!del[i]) {
Circle &mc = cir[i];
Point p1, p2;
bool flag = false;
for(int j = ; j < n; ++j) if(!del[j]) {
if(i == j) continue;
if(!mc.intersect(cir[j])) continue;
flag = true;
intersection(mc, cir[j], p1, p2);
double rs = (p2 - mc.c).angle(), rt = (p1 - mc.c).angle();
if(sgn(rs) < ) rs += * PI;
if(sgn(rt) < ) rt += * PI;
if(sgn(rs - rt) > ) mc.add(Region(rs, PI * )), mc.add(Region(, rt));
else mc.add(Region(rs, rt));
}
if(!flag) {
ans += PI * sqr(mc.r);
continue;
}
sort(mc.reg.begin(), mc.reg.end());
int cnt = ;
for(int j = ; j < int(mc.reg.size()); ++j) {
if(sgn(mc.reg[cnt - ].ed - mc.reg[j].st) >= ) {
mc.reg[cnt - ].ed = max(mc.reg[cnt - ].ed, mc.reg[j].ed);
} else mc.reg[cnt++] = mc.reg[j];
}
mc.add(Region());
mc.reg[cnt] = mc.reg[];
for(int j = ; j < cnt; ++j) {
p1 = calc(mc, mc.reg[j].ed);
p2 = calc(mc, mc.reg[j + ].st);
ans += cross(p1, p2) / ;
double angle = mc.reg[j + ].st - mc.reg[j].ed;
if(sgn(angle) < ) angle += * PI;
ans += 0.5 * sqr(mc.r) * (angle - sin(angle));
}
}
return ans;
} int main() {
scanf("%d", &n);
for(int i = ; i < n; ++i) cir[i].read();
printf("%.3f\n", solve() + EPS);
}
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