HDU2199：Can you solve this equation?（数学 + 二分）

Can you solve this equation?

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 19065    Accepted Submission(s): 8406

Problem Description

Now,given the equation 8*x^4 + 7*x^3 + 2*x^2 + 3*x + 6 == Y,can you find its solution between 0 and 100;
Now please try your lucky.

 

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 a real number Y (fabs(Y) <= 1e10);

 

Output

For each test case, you should just output one real number(accurate up to 4 decimal places),which is the solution of the equation,or “No solution!”,if there is no solution for the equation between 0 and 100.

 

Sample Input

2
100
-4

 

Sample Output

1.6152
No solution!

 

Author

Redow

思路：二分解方程。

# include <stdio.h>
# include <math.h>
double fun(double x)
{
    return 8*x*x*x*x + 7*x*x*x + 2*x*x + 3*x + 6;
}
int main()
{
    int t;
    double y, l, r;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%lf",&y);
        if(y<fun(0) || y>fun(100))
        {
            puts("No solution!");
            continue;
        }
        l = 0;
        r = 100;
        double mid = (l+r)/2;
        while(fabs(fun(mid)-y)>1e-6)
        {
            if(fun(mid)<y)
                l = mid;
            else
                r = mid;
            mid = (l+r)/2;
        }
        printf("%.4f\n",mid);
    }
    return 0;
}