hdu 2899 Strange fuction
2014-08-07 15:51
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[align=left]Problem Description[/align]
Now, 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.
[align=left]Input[/align]
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 only one real numbers Y.(0 < Y <1e10)
[align=left]Output[/align]
Just the minimum value (accurate up to 4 decimal places),when x is between 0 and 100.
[align=left]Sample Input[/align]
[align=left]Sample Output[/align]
Now, 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.
[align=left]Input[/align]
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 only one real numbers Y.(0 < Y <1e10)
[align=left]Output[/align]
Just the minimum value (accurate up to 4 decimal places),when x is between 0 and 100.
[align=left]Sample Input[/align]
2 100 200
[align=left]Sample Output[/align]
-74.4291 -178.8534----------------------------------#include<stdio.h> #include<math.h> double res(double x,double y) { return 6*pow(x,7)+8*pow(x,6)+7*pow(x,3)+5*pow(x,2)-y*x; } double dao(double x) { return 42*pow(x,6)+48*pow(x,5)+21*pow(x,2)+10*x; } int main() { int t; double le,ri,mid,y; scanf("%d",&t); while(t--) { scanf("%lf",&y); le = 0; ri = 100; if(dao(le)-y>=1e-6) // 左边界(dao返回的结果最小)代入后如果导数大于零,说明函数单调递增// 我觉得当函数是开口向下的抛物线时,能 //不能取到最小值,取决于 y 的值 { printf("%.4f\n",res(le,y)); continue; } else if(dao(ri)-y<=1e-6) //右边界(dao返回的结果最大)代入,小于0,说明函数单调递减 { printf("%.4f\n",res(ri,y)); continue; } while(ri-le>1e-6)// 当函数是凹的或者凸的时候,二分搜索直到导数接近于0的时候 { mid = (le+ri) / 2; if(dao(mid)-y>=1e-6)// mid处递增,说明最小值在左边 ri = mid; else //否则,最小值在右边 le = mid; } printf("%.4f\n",(res(le,y)+res(ri,y))/2); } return 0; }
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