hdu 2199
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
2
100
-4
Sample Output
1.6152
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
2
100
-4
Sample Output
1.6152
No solution!
迭代法代码:
#include <iostream> #include <stdio.h> #include <string> #include <cstring> #include <iomanip> #include <cmath> #include <algorithm> using namespace std; double cmp(double low,double high,double y); double mcp(double x); int main() { int T; double n,m; while(cin>>T){ while(T--){ cin>>n; if(n<mcp(0)||n>mcp(100)) cout<<"No solution!"<<endl; else { m=cmp(0,100,n); cout<<setiosflags(ios::fixed)<<setprecision(4)<<m<<endl;} } } return 0; } double cmp(double low,double high,double y) { double mid; while(high-low>1e-10){ mid=(low+high)/2.0; if(mcp(mid)>y) high=mid; else low=mid; } return mid; } double mcp(double x){ return 8.0*x*x*x*x+7.0*x*x*x+2.0*x*x+3.0*x+6.0; }
递归法代码:
如果递归的判断终止条件为low<high,时间超限;因为这个类型是double型,有些数会递归很多次以至n次才会的到结果,以至超时;由于提上要求是4位小数,所以只需要让low<high-0.0000001即可;
#include <iostream> #include <stdio.h> #include <string> #include <cstring> #include <iomanip> #include <cmath> #include <algorithm> using namespace std; double cmp(double low,double high,double y); double mcp(double x); int main() { int T; double n,m; while(cin>>T){ while(T--){ cin>>n; if(n<mcp(0)||n>mcp(100)) cout<<"No solution!"<<endl; else { m=cmp(0,100,n); cout<<setiosflags(ios::fixed)<<setprecision(4)<<m<<endl;} } } return 0; } double cmp(double low,double high,double y) { double mid=(low+high)/2; if(high-low>1e-10){ if(mcp(mid)>y) return cmp(low,mid,y); else if(mcp(mid)<y) return cmp(mid,high,y); else return mid; } return mid; } double mcp(double x){ return 8.0*x*x*x*x+7.0*x*x*x+2.0*x*x+3.0*x+6.0; }
思路:先要判断这个函数的单调性,之后在就容易多了,给你一个数y;求解出对应的x,如果x是在0-100之间输出x浮点数为4;否则输出“No solution!”;
说白了就是把y移到等式左边是f(x)= 8*x^4 + 7*x^3 + 2*x^2 + 3*x + 6 -Y;求是零点的值;如果x是在0-100之间输出x,浮点数为4;否则输出“No solution!”;
世上无难事,只怕有心人!