Brief description:
圆并扩展，给定 N 个圆，问被这些圆覆盖了 K 次的面积。
( .. .N <= 1000 ... )
Analysis:
…
（好题啊！！！ T T）
/** ` Micro Mezzo Macro Flation -- Overheated Economy ., **/
#include <algorithm>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <cstring>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>
using namespace std;
#define REP(i, n) for (int i=0;i<int(n);++i)
#define FOR(i, a, b) for (int i=int(a);i<int(b);++i)
#define DWN(i, b, a) for (int i=int(b-1);i>=int(a);--i)
#define REP_1(i, n) for (int i=1;i<=int(n);++i)
#define FOR_1(i, a, b) for (int i=int(a);i<=int(b);++i)
#define DWN_1(i, b, a) for (int i=int(b);i>=int(a);--i)
#define REP_C(i, n) for (int n____=int(n),i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=int(b),i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=int(a),i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<int(n);++i)
#define FOR_N(i, a, b) for (i=int(a);i<int(b);++i)
#define DWN_N(i, b, a) for (i=int(b-1);i>=int(a);--i)
#define REP_1_C(i, n) for (int n____=int(n),i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=int(b),i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=int(a),i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=int(n);++i)
#define FOR_1_N(i, a, b) for (i=int(a);i<=int(b);++i)
#define DWN_1_N(i, b, a) for (i=int(b);i>=int(a);--i)
#define REP_C_N(i, n) for (n____=int(n),i=0;i<n____;++i)
#define FOR_C_N(i, a, b) for (b____=int(b),i=a;i<b____;++i)
#define DWN_C_N(i, b, a) for (a____=int(a),i=b-1;i>=a____;--i)
#define REP_1_C_N(i, n) for (n____=int(n),i=1;i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (b____=int(b),i=a;i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (a____=int(a),i=b;i>=a____;--i)
#define DO(n) while(n--)
#define DO_C(n) int n____ = n; while(n____--)
#define TO(i, a, b) int s_=a<b?1:-1,b_=b+s_;for(int i=a;i!=b_;i+=s_)
#define TO_1(i, a, b) int s_=a<b?1:-1,b_=b;for(int i=a;i!=b_;i+=s_)
#define SQZ(i, j, a, b) for (int i=int(a),j=int(b)-1;i<j;++i,--j)
#define SQZ_1(i, j, a, b) for (int i=int(a),j=int(b);i<=j;++i,--j)
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)
#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define BSC(A, X) find(ALL(A), X) // != A.end()
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int(A.size())
#define PB push_back
#define MP(A, B) make_pair(A, B)
#define Rush int T____; RD(T____); DO(T____)
#pragma comment(linker, "/STACK:36777216")
#pragma GCC optimize ("O2")
#define Ruby system("ruby main.rb")
#define Haskell system("runghc main.hs")
#define Pascal system("fpc main.pas")
typedef long long LL;
typedef double DB;
typedef unsigned UINT;
typedef unsigned long long ULL;
typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VD;
typedef set<int> SI;
typedef set<string> SS;
typedef set<LL> SL;
typedef set<DB> SD;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef map<LL, int> MLI;
typedef map<DB, int> MDI;
typedef map<int, bool> MIB;
typedef map<string, bool> MSB;
typedef map<LL, bool> MLB;
typedef map<DB, bool> MDB;
typedef pair<int, int> PII;
typedef pair<int, bool> PIB;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;
typedef set<PII> SII;
typedef map<PII, int> MPIII;
typedef map<PII, bool> MPIIB;
/** I/O Accelerator **/
/* ... :" We are I/O Accelerator ... Use us at your own risk ;) ... " .. */
template<class T> inline void RD(T &);
template<class T> inline void OT(const T &);
inline int RD(){ int x; RD(x); return x;}
template<class T> inline T& _RD(T &x){ RD(x); return x;}
inline void RC(char &c){scanf(" %c", &c);}
inline void RS(char *s){scanf("%s", s);}
template<class T0, class T1> inline void RD(T0 &x0, T1 &x1){RD(x0), RD(x1);}
template<class T0, class T1, class T2> inline void RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2);}
template<class T0, class T1, class T2, class T3> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6);}
template<class T0, class T1> inline void OT(T0 &x0, T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(T0 &x0, T1 &x1, T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}
template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}
template<class T> inline void CLR(T &A){A.clear();}
template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2){FLC(A0), FLC(A1), FLC(A2);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3){FLC(A0), FLC(A1), FLC(A2), FLC(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4), FLC(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4), FLC(A5), FLC(A6);}
template<class T> inline void SRT(T &A){sort(ALL(A));}
template<class T, class C> inline void SRT(T &A, C B){sort(ALL(A), B);}
/** Add - On **/
const int MOD = 1000000007;
const int INF = 0x7fffffff;
const DB EPS = 1e-12;
const DB OO = 1e15;
// <<= ` 0. Daily Use .,
template<class T> inline void checkMin(T &a,const T b){if (b<a) a=b;}
template<class T> inline void checkMax(T &a,const T b){if (b>a) a=b;}
template <class T, class C> inline void checkMin(T& a, const T b, C c){if (c(b,a)) a = b;}
template <class T, class C> inline void checkMax(T& a, const T b, C c){if (c(a,b)) a = b;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
int Ceil(int x, int y){return (x - 1) / y + 1;}
// <<= ` 1. Bitwise Operation .,
inline bool _1(int x, int i){return x & 1<<i;}
inline int _1(int i){return 1<<i;}
inline int _U(int i){return _1(i) - 1;};
inline int count_bits(int x){
x = (x & 0x55555555) + ((x & 0xaaaaaaaa) >> 1);
x = (x & 0x33333333) + ((x & 0xcccccccc) >> 2);
x = (x & 0x0f0f0f0f) + ((x & 0xf0f0f0f0) >> 4);
x = (x & 0x00ff00ff) + ((x & 0xff00ff00) >> 8);
x = (x & 0x0000ffff) + ((x & 0xffff0000) >> 16);
return x;
}
template<class T> inline T low_bit(T x) {
return x & -x;
}
template<class T> inline T high_bit(T x) {
T p = low_bit(x);
while (p != x) x -= p, p = low_bit(x);
return p;
}
// <<= ` 2. Modular Arithmetic Basic .,
inline void INC(int &a, int b){a += b; if (a >= MOD) a -= MOD;}
inline int sum(int a, int b){a += b; if (a >= MOD) a -= MOD; return a;}
inline void DEC(int &a, int b){a -= b; if (a < 0) a += MOD;}
inline int dff(int a, int b){a -= b; if (a < 0) a += MOD; return a;}
inline void MUL(int &a, int b){a = int((LL)a * b % MOD);}
inline int pdt(int a, int b){return int((LL)a * b % MOD);}
// <<= '9. Comutational Geometry .,
struct Po; struct Vt; struct Line; struct Seg;
inline int sgn(DB x, DB y){
x -= y;
return x < -EPS ? -1 : x > EPS;
}
struct Po{
DB x, y;
Po(DB _x = 0, DB _y = 0):x(_x), y(_y){}
friend ostream& operator <<(ostream& out, Po p){
return out << "(" << p.x << ", " << p.y << ")";
}
};
inline DB dist_sqr(Po a, Po b){
return sqr(a.x - b.x) + sqr(a.y - b.y);
}
inline DB dist(Po a, Po b){
return sqrt(dist_sqr(a, b));
}
struct Vt{
DB x, y;
Vt(DB _x = 0, DB _y = 0):x(_x), y(_y){}
DB length(){
if (x == 0 && y == 0) return OO;
return sqrt(sqr(x) + sqr(y));
}
};
bool operator ==(Po a, Po b){
return a.x == b.x && a.y == b.y;
}
Vt operator -(Po a, Po b){
return Vt(a.x - b.x, a.y - b.y);
}
struct Line{
Po a, b;
Line(Po _a = Po(), Po _b = Po()):a(_a), b(_b){}
Line(DB x0, DB y0, DB x1, DB y1):a(Po(x0, y0)), b(Po(x1, y1)){}
Line(Seg l);
friend ostream& operator<<(ostream& out, Line l){
return out << l.a << " - " << l.b;
}
};
struct Seg{
Po a, b;
Seg(Po _a = Po(), Po _b = Po()):a(_a), b(_b){}
Seg(DB x0, DB y0, DB x1, DB y1):a(Po(x0, y0)), b(Po(x1, y1)){}
DB length(){
Vt t = b - a;
return t.length();
}
};
Line::Line(Seg l):a(l.a), b(l.b){}
inline DB det(DB x1, DB y1, DB x2, DB y2){return x1 * y2 - x2 * y1;}
inline DB dot(Vt a, Vt b){return a.x * b.x + a.y * b.y;}
inline DB cross(Vt a, Vt b){return a.x * b.y - b.x * a.y;}
inline DB cross(Po p0, Po p1, Po p2){return cross(p1 - p0, p2 - p0);}
inline DB dot(Line l1, Line l2){return dot(l1.b - l1.a, l2.b - l2.a);}
inline DB cross(Line l1, Line l2){return cross(l1.b - l1.a, l2.b - l2.a);}
struct Circle{
Po o; DB r;
void input(){
scanf("%lf%lf%lf", &o.x, &o.y, &r);
}
bool operator < (Circle rhs) const {
return r < rhs.r;
}
};
const int Contain = -2, Inscribe = -1, Cross = 0, Exscribe = 1, Disjoint = 2;
inline int sgn(Circle a, Circle b){
DB d = dist_sqr(a.o, b.o);
if (sgn(sqr(a.r + b.r), d) < 0) return Disjoint;
if (sgn(sqr(a.r + b.r), d) == 0) return Exscribe;
if (sgn(sqr(a.r - b.r), d) == 0) return Inscribe;
if (sgn(sqr(a.r - b.r), d) > 0) return Contain;
return Cross;
}
// <<= ' 0. I/O Accelerator interface .,
template<class T> inline void RD(T &x){
//cin >> x;
//scanf("%d", &x);
char c; for (c = getchar(); c < '0'; c = getchar()); x = c - '0'; for (c = getchar(); c >= '0'; c = getchar()) x = x * 10 + c - '0';
//char c; c = getchar(); x = c - '0'; for (c = getchar(); c >= '0'; c = getchar()) x = x * 10 + c - '0';
}
int ____Case;
template<class T> inline void OT(const T &x){
//cout << x << endl;
printf("%d\n", x);
//printf("%.2lf\n", x);
//printf("Case %d: %d\n", ++____Case, x);
}
#define For_each(it, A) for (SII::iterator it = A.begin(); it != A.end(); ++it)
/* .................................................................................................................................. */
const int N = 1009;
Circle C[N]; DB Area[N];
int n, n_;
int main(){
//freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
REP_C(i, _RD(n)) C[i].input();
REP(i, n){
vector<pair<DB, int> > I;
int cov = 1;
REP(j, n){
if (sgn(C[i], C[j]) <= Inscribe){
if (C[i] < C[j]) ++cov;
continue;
}
if (sgn(C[i], C[j]) >= Exscribe)
continue;
Vt l = C[j].o - C[i].o; DB a = l.length(), b = C[i].r, c = C[j].r;
DB alpha = atan2(l.y, l.x), beta = acos((sqr(a)+sqr(b)-sqr(c))/(2*a*b));
DB a0 = alpha - beta, a1 = alpha + beta;
if (sgn(a0, -M_PI) < 0) a0 += 2.0 * M_PI;
if (sgn(a1, M_PI) > 0) a1 -= 2.0 * M_PI;
if (sgn(a0, a1) > 0) ++cov;
I.PB(MP(a0, 1)), I.PB(MP(a1, -1));
}
I.PB(MP(-M_PI, 1)), I.PB(MP(M_PI, -1));
SRT(I);
#define pre I[j-1].first
#define cur I[j].first
#define alpha (cur - pre)
#define event_type I[j].second
FOR(j, 1, SZ(I)){
Area[cov] += sqr(C[i].r) * (alpha - sin(alpha)) + det(C[i].o.x + C[i].r * cos(pre), C[i].o.y + C[i].r * sin(pre), C[i].o.x + C[i].r * cos(cur), C[i].o.y + C[i].r * sin(cur)) ;
cov += event_type;
}
}
FOR(i, 1, n) Area[i] -= Area[i+1];
REP_1(i, n) printf("[%d] = %.3f\n", i, Area[i] / 2);
}
External Link:
http://www.spoj.pl/problems/CIRUT/
-补—
用 数值积分的方法 过不掉 。。。
下面是我精度开到 1e-29 都过不掉的代码。。
。。。。。
/** ` Micro Mezzo Macro Flation -- Overheated Economy ., **/
#include <algorithm>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <cstring>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>
using namespace std;
#define REP(i, n) for (int i=0;i<int(n);++i)
#define FOR(i, a, b) for (int i=int(a);i<int(b);++i)
#define DWN(i, b, a) for (int i=int(b-1);i>=int(a);--i)
#define REP_1(i, n) for (int i=1;i<=int(n);++i)
#define FOR_1(i, a, b) for (int i=int(a);i<=int(b);++i)
#define DWN_1(i, b, a) for (int i=int(b);i>=int(a);--i)
#define REP_C(i, n) for (int n____=int(n),i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=int(b),i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=int(a),i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<int(n);++i)
#define FOR_N(i, a, b) for (i=int(a);i<int(b);++i)
#define DWN_N(i, b, a) for (i=int(b-1);i>=int(a);--i)
#define REP_1_C(i, n) for (int n____=int(n),i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=int(b),i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=int(a),i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=int(n);++i)
#define FOR_1_N(i, a, b) for (i=int(a);i<=int(b);++i)
#define DWN_1_N(i, b, a) for (i=int(b);i>=int(a);--i)
#define REP_C_N(i, n) for (n____=int(n),i=0;i<n____;++i)
#define FOR_C_N(i, a, b) for (b____=int(b),i=a;i<b____;++i)
#define DWN_C_N(i, b, a) for (a____=int(a),i=b-1;i>=a____;--i)
#define REP_1_C_N(i, n) for (n____=int(n),i=1;i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (b____=int(b),i=a;i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (a____=int(a),i=b;i>=a____;--i)
#define DO(n) while(n--)
#define DO_C(n) int n____ = n; while(n____--)
#define TO(i, a, b) int s_=a<b?1:-1,b_=b+s_;for(int i=a;i!=b_;i+=s_)
#define TO_1(i, a, b) int s_=a<b?1:-1,b_=b;for(int i=a;i!=b_;i+=s_)
#define SQZ(i, j, a, b) for (int i=int(a),j=int(b)-1;i<j;++i,--j)
#define SQZ_1(i, j, a, b) for (int i=int(a),j=int(b);i<=j;++i,--j)
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)
#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define BSC(A, X) find(ALL(A), X) // != A.end()
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int(A.size())
#define PB push_back
#define MP(A, B) make_pair(A, B)
#define Rush int T____; RD(T____); DO(T____)
#pragma comment(linker, "/STACK:36777216")
#pragma GCC optimize ("O2")
#define Ruby system("ruby main.rb")
#define Haskell system("runghc main.hs")
#define Pascal system("fpc main.pas")
typedef long long LL;
typedef double DB;
typedef unsigned UINT;
typedef unsigned long long ULL;
typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VD;
typedef set<int> SI;
typedef set<string> SS;
typedef set<LL> SL;
typedef set<DB> SD;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef map<LL, int> MLI;
typedef map<DB, int> MDI;
typedef map<int, bool> MIB;
typedef map<string, bool> MSB;
typedef map<LL, bool> MLB;
typedef map<DB, bool> MDB;
typedef pair<int, int> PII;
typedef pair<int, bool> PIB;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;
typedef set<PII> SII;
typedef map<PII, int> MPIII;
typedef map<PII, bool> MPIIB;
/** I/O Accelerator **/
/* ... :" We are I/O Accelerator ... Use us at your own risk ;) ... " .. */
template<class T> inline void RD(T &);
template<class T> inline void OT(const T &);
inline int RD(){ int x; RD(x); return x;}
template<class T> inline T& _RD(T &x){ RD(x); return x;}
inline void RC(char &c){scanf(" %c", &c);}
inline void RS(char *s){scanf("%s", s);}
template<class T0, class T1> inline void RD(T0 &x0, T1 &x1){RD(x0), RD(x1);}
template<class T0, class T1, class T2> inline void RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2);}
template<class T0, class T1, class T2, class T3> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6);}
template<class T0, class T1> inline void OT(T0 &x0, T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(T0 &x0, T1 &x1, T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}
template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}
template<class T> inline void CLR(T &A){A.clear();}
template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2){FLC(A0), FLC(A1), FLC(A2);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3){FLC(A0), FLC(A1), FLC(A2), FLC(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4), FLC(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4), FLC(A5), FLC(A6);}
template<class T> inline void SRT(T &A){sort(ALL(A));}
template<class T, class C> inline void SRT(T &A, C B){sort(ALL(A), B);}
/** Add - On **/
const int MOD = 1000000007;
const int INF = 0x7fffffff;
const DB PI = acos(-1.0);
const DB EPS = 1e-29;
const DB OO = 1e15;
// <<= ` 0. Daily Use .,
template<class T> inline void checkMin(T &a,const T b){if (b<a) a=b;}
template<class T> inline void checkMax(T &a,const T b){if (b>a) a=b;}
template <class T, class C> inline void checkMin(T& a, const T b, C c){if (c(b,a)) a = b;}
template <class T, class C> inline void checkMax(T& a, const T b, C c){if (c(a,b)) a = b;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
int Ceil(int x, int y){return (x - 1) / y + 1;}
// <<= ` 1. Bitwise Operation .,
inline bool _1(int x, int i){return x & 1<<i;}
inline int _1(int i){return 1<<i;}
inline int _U(int i){return _1(i) - 1;};
inline int count_bits(int x){
x = (x & 0x55555555) + ((x & 0xaaaaaaaa) >> 1);
x = (x & 0x33333333) + ((x & 0xcccccccc) >> 2);
x = (x & 0x0f0f0f0f) + ((x & 0xf0f0f0f0) >> 4);
x = (x & 0x00ff00ff) + ((x & 0xff00ff00) >> 8);
x = (x & 0x0000ffff) + ((x & 0xffff0000) >> 16);
return x;
}
template<class T> inline T low_bit(T x) {
return x & -x;
}
template<class T> inline T high_bit(T x) {
T p = low_bit(x);
while (p != x) x -= p, p = low_bit(x);
return p;
}
// <<= ` 2. Modular Arithmetic Basic .,
inline void INC(int &a, int b){a += b; if (a >= MOD) a -= MOD;}
inline int sum(int a, int b){a += b; if (a >= MOD) a -= MOD; return a;}
inline void DEC(int &a, int b){a -= b; if (a < 0) a += MOD;}
inline int dff(int a, int b){a -= b; if (a < 0) a += MOD; return a;}
inline void MUL(int &a, int b){a = (LL)a * b % MOD;}
inline int pdt(int a, int b){return (LL)a * b % MOD;}
// <<= ' 0. I/O Accelerator interface .,
template<class T> inline void RD(T &x){
//cin >> x;
scanf("%d", &x);
//char c; for (c = getchar(); c < '0'; c = getchar()); x = c - '0'; for (c = getchar(); c >= '0'; c = getchar()) x = x * 10 + c - '0';
//char c; c = getchar(); x = c - '0'; for (c = getchar(); c >= '0'; c = getchar()) x = x * 10 + c - '0';
}
int k;
template<class T> inline void OT(const T &x){
//..
}
inline int sgn(DB x){
return x < -EPS ? -1 : x > EPS;
}
/* .................................................................................................................................. */
const int N = 1009;
DB Area[N];
int x[N], y[N], r[N], o[N]; // Circle
#define m ((l + r) / 2)
#define l(a) x[a] - r[a]
#define r(a) x[a] + r[a]
inline bool c1(int a, int b){return r[a] < r[b];} //Sort by Radius
inline bool c2(int a, int b){return l(a) < l(b);} //Sort by left point.
inline bool Cover(int a, int b){return sqr(r[a] - r[b]) >= sqr(x[a] - x[b]) + sqr(y[a] - y[b]);}
int n;
//vector<pair<DB, DB> > I; // Interval
vector<pair<DB, int> > I;
#define time I[i].first - I[i-1].first
#define type I[i].second
inline DB f(DB xx){
DB res = 0;
CLR(I); REP(i, n){
DB d = fabs(xx - x[i]);
if (d < r[i]) d = sqrt(sqr(r[i]) - sqr(d)), I.PB(MP(y[i] - d, -1)), I.PB(MP(y[i] + d, +1));
}
SRT(I); int cov = 0; REP(i, SZ(I)){
if (cov >= k) res += time;
cov -= type;
}
return res;
}
inline DB s(DB l, DB r, DB fl, DB fm, DB fr){
return (fl + 4 * fm + fr) * (r - l);
}
inline DB _S(DB l, DB r, DB fl, DB fm, DB fr){
DB flm = f((l + m) / 2), frm = f((m + r) / 2);
DB sl = s(l, m, fl, flm, fm), ss = s(l, r, fl, fm, fr), sr = s(m, r, fm, frm, fr);
if (fabs(ss - sl - sr) < EPS / 15) return sl + sr;
else return _S(l, m, fl, flm, fm) + _S(m, r, fm, frm, fr);
}
inline DB S(DB l, DB r){
return _S(l, r, f(l), f(m), f(r));
}
int main(){
//freopen("in.txt", "r", stdin);
REP_C(i, _RD(n)) RD(x[i], y[i], r[i]);
REP(i, n) o[i] = i; sort(o, o + n, c2);
int _x[N], _y[N], _r[N];
REP(i, n) _x[i] = x[o[i]], _y[i] = y[o[i]], _r[i] = r[o[i]];
CPY(x, _x), CPY(y, _y), CPY(r, _r);
x[n+1] = +OO; REP_1_N(k, n+1){
DB ll = -OO, rr = -OO; REP_C(i, n+1){
if(rr < l(i)) Area[k] += S(ll, rr), ll = l(i), rr = r(i);
else checkMax(rr, DB(r(i)));
}
}
REP_1(i, n) printf("[%d] = %.3lf\n", i, (Area[i] -= Area[i+1]) /= 6);
}
