Hdoj 2199.Can you solve this equation? 题解

Problem Description

Now,given the equation 8x^4 + 7x^3 + 2x^2 + 3x + 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

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思路

这个问题可以用二分法解决，因为给定的函数是单调的，所以可以根据要求的精度不断二分找答案

详见代码

代码

#include<bits/stdc++.h>
using namespace std;

double f(double x)
{
	return 8*x*x*x*x + 7*x*x*x + 2*x*x + 3*x + 6 ;
}
	
int main() 
{
	int n;
	cin >> n;
	while(n--)
	{
		double t;
		cin >> t;
		double l = 0, r = 100.0;
		if(t<f(0) || t>f(100.0))
		{
			cout << "No solution!
";
			continue;
		}//因为函数单调，所以可以这么判断
		double mid;	
		while(r-l>1e-8)
		{
			mid = (l+r)/2;
			double ans = f(mid);
			if(ans>t)
				r = mid;
			if(ans<t)
				l = mid;
		}
		printf("%.4lf
",l);
	}
	return 0;
}