# UVA-1476 Error Curves three points

Source: Internet
Author: User

Error Curves

Josephina is a clever girl and addicted to machine learning recently. She pays much attention to a

Method called Linear discriminant analysis, which have many interesting properties.
In order to test the algorithm ' s e?ciency, she collects many datasets. What's more, each data is
Divided into and parts:training data and test data. She gets the parameters of the model on training
Data and test the model on test data.
To his surprise, she? NDS each DataSet ' s test error curve is just a parabolic curve. A Parabolic curve
Corresponds to a quadratic function. In mathematics, a quadratic function is a polynomial function of
The form f (x) = ax2 + bx + C. The quadratic would degrade to linear function if a = 0.
It's very easy to calculate the minimal error if there are only one Test error curve. However, there
is several datasets, which means Josephina would obtain many parabolic curves. Josephina wants to
Get the tuned parameters, the best performance in all datasets. So she should take the all error
Curves into account, i.e, she had to deal with many quadric functions and make a new error de?nition
To represent the total error. Now, she focuses on the following new function ' s minimal which related to
The new function F (x) is de?ned as follow:
F (x) = Max (Si (x)), i = 1. . . N. The domain of x is [0,1000]. Si (x) is a quadric function.
Josephina wonders the minimum of F (x). Unfortunately, it ' s too hard for her and solve this problem.
As a super programmer, can you help her?
Input
The input contains multiple test cases. The. RST line is the number of cases T (T < 100). Each case
Begins with a number n (n≤10000). Following n lines, each line contains three integers a (0≤a≤100),
B (|b|≤5000), C (|c|≤5000), which mean the corresponding coe?cients of a quadratic function.
Output
For each test case, the output of the answer in a line. Round to 4 digits after the decimal point.
Sample Input
2
1
2 0 0
2
2 0 0
2-4 2
Sample Output
0.0000
0.5000

Test Instructions :

Given n two times curve S (x), define F (x) =max (Si (x)) to find the minimum value of f (x) on 0~1000.

Exercises

Three-point basic problem, three-point convex.

`#include <iostream>#include<cstdio>#include<cstring>#include<algorithm>using namespacestd; typedefLong Longll;Const intN =10000+Ten;intT,a[n],b[n],c[n],n;DoubleFDoublex) {DoubleAns = a[1] * x * x + b[1] * x + c[1];  for(inti =1; I <= N; i++) {ans= Max (ans, a[i] * x * x + b[i] * x +C[i]); }    returnans;}DoubleThree_search (DoubleLDoubler) { for(inti =0; I < -; i++) {        DoubleMID = L + (r-l)/3; DoubleMid2 = R-(r-l)/3; if(f (Mid) > F (mid2)) L =mid; ElseR =Mid2; }    returnf (l);}intMain () {scanf ("%d",&T);  while(t--) {scanf ("%d",&N);  for(inti =1; I <= N; i++) scanf ("%d%d%d",&a[i],&b[i],&C[i]); DoubleAns = three_search (0, +); printf ("%.4f\n", ans); }    return 0;}`

UVA-1476 Error Curves three points

Related Keywords:

The content source of this page is from Internet, which doesn't represent Alibaba Cloud's opinion; products and services mentioned on that page don't have any relationship with Alibaba Cloud. If the content of the page makes you feel confusing, please write us an email, we will handle the problem within 5 days after receiving your email.

If you find any instances of plagiarism from the community, please send an email to: info-contact@alibabacloud.com and provide relevant evidence. A staff member will contact you within 5 working days.

## A Free Trial That Lets You Build Big!

Start building with 50+ products and up to 12 months usage for Elastic Compute Service

• #### Sales Support

1 on 1 presale consultation

• #### After-Sales Support

24/7 Technical Support 6 Free Tickets per Quarter Faster Response

• Alibaba Cloud offers highly flexible support services tailored to meet your exact needs.