Hdu2899 -- Strange fuction

Strange fuction Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission (s): 3344 Accepted Submission (s): 2446


Problem DescriptionNow, here is a fuction:
F (x) = 6 * x ^ 7 + 8 * x ^ 6 + 7 * x ^ 3 + 5 * x ^ 2-y * x (0 <= x <= 100)
Can you find the minimum value when x is between 0 and 100.
InputThe 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 only one real numbers Y. (0 <Y <1e10)
OutputJust the minimum value (accurate up to 4 decimal places), when x is between 0 and 100.
Sample Input

2100200

 
Sample Output

-74.4291-178.8534

 
AuthorRedow
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You can find that for this function, if y <= 0, the function increases monotonically within [0,100], so the minimum value is 0.
If y> 0, observe its function and find that the function increases monotonically. So we only need to find the zero point of the function (that is, the minimum point of the original function), then we can use the binary solution.
After finding the extreme point, if it is in [0,100], it will be substituted into the function. Otherwise, it indicates that the function is monotonically decreasing within [0,100]. Just replace 100 into the function.

# Include <map> # include <set> # include <list> # include <stack> # include <queue> # include <vector> # include <cmath> # include <cstdio> # include <cstring> # include <iostream> # include <algorithm> using namespace std; int main () {int t; scanf ("% d \ n", & t); while (t --) {double y; scanf ("% lf ", & y); if (y <= 0) {printf ("0.0000 \ n"); continue;} double l = 0, r = 100, mid; while (r-l> 1e-6) {mid = (l + r)/2; double dx = 42.0 * pow (mid, 6) + 48.0 * pow (mid, 5) + 21.0 * pow (mid, 2) + 10.0 * mid; if (abs (dx-y) <1e-6) {break;} else if (dx-y> 1e-6) {r = mid;} else {l = mid;} if (mid-100.0> 1e-6) {mid = 100.0;} double ans = 6 * pow (mid, 7) + 8 * pow (mid, 6) + 7 * pow (mid, 3) + 5 * pow (mid, 2)-y * mid; printf ("%. 4f \ n ", ans);} return 0 ;}

Hdu2899 -- Strange fuction