#include <iostream.h>
#include <stdio.h>
#include <math.h>

//////////////////函数--用卡丹公式解一元三次方程/////////////////
void fun(double a,double b,double c,double d,
   double *real_y1,double *real_y2,double *real_y3,
   double *imag_y1,double *imag_y2,double *imag_y3)
{
 double p,q,r,u,v,g,h,fai;
 p=(3.0*a*c-b*b)/(3*a*a);
 q=(2.0*pow(b,3.0)-9*a*b*c+27.0*a*a*d)/(27.0*pow(a,3.0));
 r=b/(3.0*a);
 h=pow(q/2.0,2.0)+pow(p/3.0,3.0);
 g=sqrt(h);
 if(h>=0)
 {
  if(-q/2.0+g<0)
  u=-pow(fabs(-q/2.0+g),1.0/3.0);
  else
  u=pow((-q/2.0+g),1.0/3.0);
  if(-q/2.0-g<0)
  v=-pow(fabs(-q/2.0-g),1.0/3.0);
  else
  v=-pow((-q/2.0-g),1.0/3.0);
  if(h==0)
  {
   *real_y1=u+v-r;            *imag_y1=0;
      *real_y2=-(u+v)/2-r;       *imag_y2=0;
   *real_y3=-(u+v)/2-r;       *imag_y3=0;
  }
  else
  {
   *real_y1=u+v-r;       *imag_y1=0;
   *real_y2=-(u+v)/2;    *imag_y2=sqrt(3.0)*(u-v)/2;
   *real_y3=-(u+v)/2;    *imag_y3=-sqrt(3.0)*(u-v)/2;
  }
 }
 else
 {
  fai=acos((-q/2)/(sqrt(pow(fabs(p),3)/27)));
  *real_y1=2*sqrt(fabs(p)/3.0)*cos(fai/3.0)-r;
  *real_y2=-2*sqrt(fabs(p)/3.0)*cos((fai+3.1415926)/3.0)-r;
        *real_y3=-2*sqrt(fabs(p)/3.0)*cos((fai-3.1415926)/3.0)-r;
  *imag_y1=0;   *imag_y2=0;    *imag_y3=0;
 }
}
//////////////////////////////////主函数////////////////////////////////
 void main()
 {
  double a,b,c,d;
  double real_x1,real_x2,real_x3;
  double *preal_x1=&real_x1;
  double *preal_x2=&real_x2;
  double *preal_x3=&real_x3;
  double imag_x1,imag_x2,imag_x3;
  double *pimag_x1=&imag_x1;
  double *pimag_x2=&imag_x2;
  double *pimag_x3=&imag_x3;
  cout<<"请输入方程的系数a,b,c,d:"<<"\n"<<endl;
  cout<<"系数a=";
  cin>>a;
  cout<<endl;
  cout<<"系数b=";
  cin>>b;
  cout<<endl;
  cout<<"系数c=";
  cin>>c;
  cout<<endl;
  cout<<"系数d=";
  cin>>d;
  cout<<endl;
  fun(a,b,c,d,preal_x1,preal_x2,preal_x3,pimag_x1,pimag_x2,pimag_x3);
  cout<<"  "<<"   "<<"根的实部"<<"      "<<"根的虚部"<<"\n"<<endl;
  printf("x1   %.5f      %.5f\n\n",real_x1,imag_x1);
  printf("x2   %.5f      %.5f\n\n",real_x2,imag_x2);
  printf("x3   %.5f      %.5f\n\n",real_x3,imag_x3);
 }

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