116 lines
2.7 KiB
C++
116 lines
2.7 KiB
C++
#include <stdio.h>
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#include <string.h>
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#include <iostream>
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#include <algorithm>
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#include <vector>
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#include <queue>
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#include <set>
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#include <map>
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#include <string>
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#include <math.h>
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#include <stdlib.h>
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#include <time.h>
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using namespace std;
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vector<double>x;
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void add(int a1,int b1,int c1)
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{
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if(a1 == 0 && b1 == 0)
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{
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return;
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}
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if(a1 == 0)
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{
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double t = -c1*1.0/b1;
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if(t >= 0 && t <= 100)
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x.push_back(t);
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return;
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}
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long long deta = b1*b1 - 4LL*a1*c1;
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if(deta < 0)return;
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if(deta == 0)
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{
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double t = (-1.0 * b1)/(2.0 * a1);
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if(t >= 0 && t <= 100)
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x.push_back(t);
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}
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else
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{
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double t1 = (-1.0 * b1 + sqrt(1.0*deta))/(2.0*a1);
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double t2 = (-1.0 * b1 - sqrt(1.0*deta))/(2.0*a1);
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if(t1 >= 0 && t1 <= 100)
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x.push_back(t1);
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if(t2 >= 0 && t2 <= 100)
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x.push_back(t2);
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}
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}
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int A[100],B[100],C[100];
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int best;
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double F(double x1)
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{
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return sqrt(1.0 + (x1*2*A[best] + 1.0 * B[best])*(x1*2*A[best] + 1.0 * B[best]));
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}
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double simpson(double a,double b)
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{
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double c = a + (b-a)/2;
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return (F(a) + 4*F(c) + F(b))*(b-a)/6;
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}
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double asr(double a,double b,double eps,double A)
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{
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double c = a + (b-a)/2;
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double L = simpson(a,c);
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double R = simpson(c,b);
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if(fabs(L+R-A) <= 15*eps)return L+R+(L+R-A)/15;
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return asr(a,c,eps/2,L) + asr(c,b,eps/2,R);
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}
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double asr(double a,double b,double eps)
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{
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return asr(a,b,eps,simpson(a,b));
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}
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int main()
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{
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int T;
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int k,a,b;
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scanf("%d",&T);
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while(T--)
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{
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int n;
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scanf("%d",&n);
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A[0] = 0;
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B[0] = 0;
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C[0] = 100;
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for(int i = 1;i <= n;i++)
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{
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scanf("%d%d%d",&k,&a,&b);
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A[i] = k;
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B[i] = -2*a*k;
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C[i] = k*a*a + b;
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}
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x.clear();
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for(int i = 0;i <= n;i++)
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for(int j = i+1;j <= n;j++)
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add(A[i]-A[j],B[i] - B[j],C[i] - C[j]);
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double ans = 0;
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x.push_back(0);
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x.push_back(100);
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sort(x.begin(),x.end());
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int sz = x.size();
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for(int i = 0;i < sz-1;i++)
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{
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double x1 = x[i];
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double x2 = x[i+1];
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if(fabs(x2-x1) < 1e-8)continue;
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double mid = (x1 + x2)/2;
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best = 0;
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for(int j = 1;j <= n;j++)
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{
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double tmp1 = mid*mid*A[best] + mid*B[best] + C[best];
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double tmp2 = mid*mid*A[j] + mid*B[j] + C[j];
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if(tmp2 < tmp1)best = j;
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}
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ans += asr(x1,x2,1e-8);
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}
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printf("%.2lf\n",ans);
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}
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return 0;
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}
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