UVa

Solve the equation:

　　　　　　　　p ∗ e −x + q ∗ sin(x) + r ∗ cos(x) + s ∗ tan(x) + t ∗ x 2 + 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 (where 0 ≤ 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 up to 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

题意：给出一个方程，求解X;

思路：因为方程是单调递减的，所以二分求解；

#include<iostream>
#include<cstdio>
#include<cmath>
#define EPS (10e-8)
using namespace std;
double p,q,r,s,t,u;
inline double fomula(double x){
    return p*exp(-x)+q*sin(x)+r*cos(x)+s*tan(x)+t*x*x+u;
}
int main(){
    while(scanf("%lf%lf%lf%lf%lf%lf",&p,&q,&r,&s,&t,&u)!=EOF){
        double left=0, right=1, mid;
        bool flag=false;
        if(fomula(left)*fomula(right) > 0){
            printf("No solution
");
            continue;
        }
        while(right-left > EPS){
            mid = (left+right)/2;
            if(fomula(mid)*fomula(left) > 0) left=mid;
            else right=mid;
        }

        printf("%.4f
", mid);
    }
    return 0;
}