你的支持是我最大的动力，你的意见是我前进的导航。
| 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 2100-4 |
| Sample Output 1.6152No solution! |
| Author Redow |
| Recommend lcy |
题目大意就是x∈[0, 100], Y∈[-10^10, 10^10]，求8*x^4 + 7*x^3 + 2*x^2 + 3*x + 6 = Y 的解。
题目很简单，首先先需要些前期工作，通过一导，二导就会发现，其实对于 f(x) = 8*x^4 + 7*x^3 + 2*x^2 + 3*x + 6, x∈[0, 100]时，这个函数是递增的。所以用二分法即可解题。
代码如下
1 #include2 #include 3 double f (double x) //for convenience 4 { 5 return 8 * pow(x, 4) + 7 * pow(x, 3) + 2 * pow(x, 2) + 3 * x + 6; 6 } 7 int main() 8 { 9 int T;10 double x1, x2, x3, y, y1, y2, y3;11 scanf("%d", &T);12 while(T--)13 {14 x1 = 0;15 x2 = 100; 16 scanf("%lf", &y); //heed17 y1 = f(x1) - y;18 y2 = f(x2) - y;19 if (y1 > 0 || y2 < 0)20 printf("No solution!\n");21 else22 {23 while (fabs(y1 - y2) >= 0.0001)24 {25 x3 = (x1 + x2) / 2;26 y3 = f(x3) - y;27 if (y3 >= 0)28 x2 = x3;29 else30 x1 = x3;31 y1 = f(x1) - y;32 y2 = f(x2) - y;33 }34 printf("%0.4f\n", x3);35 }36 }37 return 0;38 }
1 #include2 #include 3 double f (double x) //for convenience 4 { 5 return 8 * pow(x, 4) + 7 * pow(x, 3) + 2 * pow(x, 2) + 3 * x + 6; 6 } 7 int main() 8 { 9 int T;10 double x1, x2, x3, y, y1, y2, y3;11 scanf("%d", &T);12 while(T--)13 {14 x1 = 0;15 x2 = 100; 16 scanf("%lf", &y); //heed17 y1 = f(x1) - y;18 y2 = f(x2) - y;19 if (y1 > 0 || y2 < 0)20 printf("No solution!\n");21 else22 {23 while (fabs(x1 - x2) >= 0.000001)24 {25 x3 = (x1 + x2) / 2;26 y3 = f(x3) - y;27 if (y3 >= 0)28 x2 = x3;29 else30 x1 = x3;31 }32 printf("%0.4f\n", x3);33 }34 }35 return 0;36 }
注意点：
1、应该花大部分时间在思路上，编码应该快速完成
2、尽量用double，用double时，要注意用"%lf"输入。float 有38位，double有308位
3、这个题目要求x精确到4位，刚开始时，我以为我以x取到4位小数为结束条件，一直错！后来来发现应该以y1，y2很接近为结束结束条件。原因很简单以为x取到4位时，有可能这个y还很不精确。当然，也可以让x1和x2很接近，如上面的second program也是对的。
4、C中有fabs，pow，在math.h头文件中。