UVA 10341 Solve It

Posted 2020-09-26 十年换你一句好久不见

https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=113&page=show_problem&problem=1282

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 (where 0 ≤ p, r ≤ 20 and ?20 ≤ q,s,t ≤ 0). There will be maximum 2100 lines in the input ?le.
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

解题思路

       函数可判断出来为单调递减函数，因此判断两端点后二分查找

#include <iostream>
#include <cstdio>
#include <cstring>
#include <queue>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <algorithm>
using namespace std;
typedef long long ll;
#define mod (10e-8)
double p,q,r,s,t,u;
double check(double x)
{
    return p*exp((-1)*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=0.0,right=1.0,mid;
        if(check(left)*check(right)>0){
            puts("No solution");
            continue;
        }
        while((right-left)>mod)
        {
            mid=(left+right)/2.0;
            if(check(left)*check(mid)>0) left=mid;
            else right=mid;
        }
        printf("%.4f\n",mid);
    }
    return 0;
}