Hdu 2899 - Strange fuction 二分/三分求函數極值點

 

Strange fuction

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 4527 Accepted Submission(s): 3251


Problem Description Now, here is a fuction:
F(x) = 6 * x^7+8*x^6+7*x^3+5*x^2-y*x (0 <= x <=100)
Can you find the minimum value when x is between 0 and 100.
Input The first line of the input contains an integer T(1<=T<=100) which means the number of test cases. Then T lines follow, each line has only one real numbers Y.(0 < Y <1e10)
Output Just the minimum value (accurate up to 4 decimal places),when x is between 0 and 100.
Sample Input

2
100
200

Sample Output

-74.4291
-178.8534

 

這是一個開口向上的函數，我們只要求這個函數的極（最）小值即可，可以三分直接求，當然也可以先把函數求導，然後二分求解，水題...附上兩種解法

 

//三分求極值
#include 
#include 
#include 
#include 
#include 
#include 
const double INF = 0x7fffffff;
const double eps = 1e-10;
int T;
double Y,X;
double Calc(double x) { return 6*pow(x,7)+8*pow(x,6)+7*pow(x,3)+5*pow(x,2)-Y*x; }
void Search() {
    double l,r,mid,Rmid,MVal,RMVal;
    l = 0;r = 100;
    while(r-l>=eps)
    {
        mid = (l+r)/2.0;Rmid = (mid+r)/2.0;
        MVal = Calc(mid);RMVal = Calc(Rmid);
        if(MVal < RMVal)
        {
            r = Rmid;
        }
        else if(MVal > RMVal)
        {
            l = mid;
        }
        else
        {
            r = mid;
            l = Rmid;
        }
    }
    printf(%.4lf
,Calc(mid));
}
int main() {
    //freopen(input.in,r,stdin);
    for(scanf(%d,&T);T--;)
    {
        scanf(%lf,&Y);
        Search();
    }
    return 0;
}


//二分求極值
#include 
#include 
#include 
#include 
#include 
#include 
const double INF = 0x7fffffff;
const double eps = 1e-10;
int T;
double Y,X;
double Calc(double x) { return 42*pow(x,6)+48*pow(x,5)+21*pow(x,2)+10*pow(x,1)-Y; }
double F(double x) { return 6*pow(x,7)+8*pow(x,6)+7*pow(x,3)+5*pow(x,2)-Y*x; }
void Search(){
    double l,r,mid,MVal;
    l = 0;r = 100;
    while(r-l>=eps)
    {
        mid = (l+r)/2.0;
        MVal = Calc(mid);
        if(MVal > 0)
        {
            r = mid;
        }
        else if(MVal < 0)
        {
            l = mid;
        }
        else break;
    }
    printf(%.4lf
,F(mid));
}
int main() {
   // freopen(input.in,r,stdin);
    for(scanf(%d,&T);T--;)
    {
        scanf(%lf,&Y);
        Search();
    }
    return 0;
}