[二分&&高精度]Solve It uva10341

Problem F

Solve It

Input: standard input

Output: standard output

Time Limit: 1 second

Memory Limit: 32 MB

Solve the equation:
        p*e^-x + q*sin(x) + r*cos(x) + s*tan(x) + t*x² + u = 0
        where 0 <= x <= 1.

Input

Input consists of multiple test cases and terminated by an EOF. Each test case consists of 6 integers in a single line: p, q, r, s, t and u (where0 <= p,r <= 20 and -20 <= q,s,t <= 0). There will be maximum 2100 lines in the input file.

Output

For each set of input, there should be a line containing the value of x, correct upto 4 decimal places, or the string "No solution", whichever is applicable.

Sample Input

0 0 0 0 -2 1

1 0 0 0 -1 2

1 -1 1 -1 -1 1

Sample Output

0.7071

No solution

0.7554

Mustaq Ahmed

题意：求一个数x(0<=x<=1)使得函数 p*e^-x + q*sin(x) + r*cos(x) + s*tan(x) + t*x² + u = 0

由于函数时单调的，所以可以使用二分查找。

#include<iostream>
#include<cmath>
#include<iomanip>

using namespace std;

int p,q,r,s,t,u;

double solve(double x)
{
    return (p*exp(-x)+q*sin(x)+r*cos(x)+s*tan(x)+t*x*x+u);
}

int main()
{
    while(cin>>p>>q>>r>>s>>t>>u)
    {
        if(solve(0)<0||solve(1)>0) cout<<"No solution"<<endl;
        else
        {
            double left=0,right=1,mid=(left+right)/2;
            while(abs(solve(mid))>1e-10)
            {
                if(solve(mid)>0) left=mid;
                else if(solve(mid)<0) right=mid;
                mid=(left+right)/2;
            }
            cout<<fixed<<setprecision(4)<<mid<<endl;
        }
    }
    return 0;
}