• HDU 4498 Function Curve (自适应simpson)


    Function Curve

    Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65535/65535 K (Java/Others)
    Total Submission(s): 203    Accepted Submission(s): 67


    Problem Description
    Given sequences of k1, k2, … kn, a1, a2, …, an and b1, b2, …, bn. Consider following function: 

    Then we draw F(x) on a xy-plane, the value of x is in the range of [0,100]. Of course, we can get a curve from that plane. 
    Can you calculate the length of this curve?
     
    Input
    The first line of the input contains one integer T (1<=T<=15), representing the number of test cases. 
    Then T blocks follow, which describe different test cases. 
    The first line of a block contains an integer n ( 1 <= n <= 50 ). 
    Then followed by n lines, each line contains three integers ki, ai, bi ( 0<=ai, bi<100, 0<ki<100 ) .
     
    Output
    For each test case, output a real number L which is rounded to 2 digits after the decimal point, means the length of the curve.
     
    Sample Input
    2 3 1 2 3 4 5 6 7 8 9 1 4 5 6
     
    Sample Output
    215.56 278.91
    Hint
    All test cases are generated randomly.
     
    Source
     
    Recommend
    liuyiding
     

    数值方法计算积分

      1 /* ***********************************************
      2 Author        :kuangbin
      3 Created Time  :2013-10-9 12:04:07
      4 File Name     :E:2013ACM专题学习数学积分HDU4498.cpp
      5 ************************************************ */
      6 
      7 #include <stdio.h>
      8 #include <string.h>
      9 #include <iostream>
     10 #include <algorithm>
     11 #include <vector>
     12 #include <queue>
     13 #include <set>
     14 #include <map>
     15 #include <string>
     16 #include <math.h>
     17 #include <stdlib.h>
     18 #include <time.h>
     19 using namespace std;
     20 
     21 vector<double>x;
     22 
     23 void add(int a1,int b1,int c1)//计算a1*x^2 + b1*x + c = 0的解
     24 {
     25     if(a1 == 0 && b1 == 0)
     26     {
     27         return;
     28     }
     29     if(a1 == 0)
     30     {
     31         double t = -c1*1.0/b1;
     32         if(t >= 0 && t <= 100)
     33             x.push_back(t);
     34         return;
     35     }
     36     long long deta = b1*b1 - 4LL*a1*c1;
     37     if(deta < 0)return;
     38     if(deta == 0)
     39     {
     40         double t = (-1.0 * b1)/(2.0 * a1);
     41         if(t >= 0 && t <= 100)
     42             x.push_back(t);
     43     }
     44     else
     45     {
     46         double t1 = (-1.0 * b1 + sqrt(1.0*deta))/(2.0*a1);
     47         double t2 = (-1.0 * b1 - sqrt(1.0*deta))/(2.0*a1);
     48         if(t1 >= 0 && t1 <= 100)
     49             x.push_back(t1);
     50         if(t2 >= 0 && t2 <= 100)
     51             x.push_back(t2);
     52     }
     53 }
     54 int A[100],B[100],C[100];
     55 int best;
     56 double F(double x1)
     57 {
     58     return sqrt(1.0 + (x1*2*A[best] + 1.0 * B[best])*(x1*2*A[best] + 1.0 * B[best]));
     59 }
     60 double simpson(double a,double b)
     61 {
     62     double c = a + (b-a)/2;
     63     return (F(a) + 4*F(c) + F(b))*(b-a)/6;
     64 }
     65 double asr(double a,double b,double eps,double A)
     66 {
     67     double c = a + (b-a)/2;
     68     double L = simpson(a,c);
     69     double R = simpson(c,b);
     70     if(fabs(L+R-A) <= 15*eps)return L+R+(L+R-A)/15;
     71     return asr(a,c,eps/2,L) + asr(c,b,eps/2,R);
     72 }
     73 double asr(double a,double b,double eps)
     74 {
     75     return asr(a,b,eps,simpson(a,b));
     76 }
     77 
     78 int main()
     79 {
     80     //freopen("in.txt","r",stdin);
     81     //freopen("out.txt","w",stdout);
     82     int T;
     83     int k,a,b;
     84     scanf("%d",&T);
     85     while(T--)
     86     {
     87         int n;
     88         scanf("%d",&n);
     89         A[0] = 0;
     90         B[0] = 0;
     91         C[0] = 100;
     92         for(int i = 1;i <= n;i++)
     93         {
     94             scanf("%d%d%d",&k,&a,&b);
     95             A[i] = k;
     96             B[i] = -2*a*k;
     97             C[i] = k*a*a + b;
     98         }
     99         x.clear();
    100         for(int i = 0;i <= n;i++)
    101             for(int j = i+1;j <= n;j++)
    102                 add(A[i]-A[j],B[i] - B[j],C[i] - C[j]);
    103         double ans = 0;
    104         x.push_back(0);
    105         x.push_back(100);
    106         sort(x.begin(),x.end());
    107         int sz = x.size();
    108         for(int i = 0;i < sz-1;i++)
    109         {
    110             double x1 = x[i];
    111             double x2 = x[i+1];
    112             if(fabs(x2-x1) < 1e-8)continue;
    113             double mid = (x1 + x2)/2;
    114             best = 0;
    115             for(int j = 1;j <= n;j++)
    116             {
    117                 double tmp1 = mid*mid*A[best] + mid*B[best] + C[best];
    118                 double tmp2 = mid*mid*A[j] + mid*B[j] + C[j];
    119                 if(tmp2 < tmp1)best = j;
    120             }
    121             ans += asr(x1,x2,1e-8);
    122         }
    123         printf("%.2lf
    ",ans);
    124     }
    125     return 0;
    126 }
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  • 原文地址:https://www.cnblogs.com/kuangbin/p/3358984.html
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