一元高次方程C语言实现(最高五次).doc

一元高次方程c语言实现(windows VC6.0版本)注意：如果在linux vine或者UNIX以及非windows的系统下运行的话将代码pow以及sqrt全部替换为powf和sqrtf以下为代码#include#include#include#include#define MAX 1000/*最大递归次数为1000次*/#define ERROR math errorn/*显示错误信息*/char Fun310,fx510=;/*美化输出结果*/float a1,b1,c1,d1,e1,f1;/*宏定义高次方程各项系数最大五次*/int NUMjdg;/*判断函数最高次数*/float FC(float a,float b);/*解一元一次方程*/float FC3(float a,float b,float c,float d);/*解一元三次方程*/float FC2(float a,float b,float c,int num);/*解一元二次方程*/float FC4(float a,float b,float c,float d,float e);/*解一元四次方程*/float FC5();/*解一元五次方程*/float fun(float x);/*五次函数代值求解*/float dfun(float x);/*五次导函数代值求解*/float iterate(float x);/*牛顿迭代法猜值求解*/int main() float x5;/*五次方程最后一个解*/ FILE *fp;/*解的内容以文件的形式保存*/ char save; char buf256;/*从文件内读取内容保存至buf*/ buf0=0;/*防止乱码，开头定义为NULL*/ fp=fopen(fun.dat,w); strcpy(Fun3,); fclose(fp); printf(Do you want to save the result? y or n);/*是否想保存结果数据？*/ printf(n-); scanf(%c,&save); redo: printf(please input degree numbern-);/*请输入最高次数*/ scanf(%d,&NUMjdg); if(NUMjdg5) goto redo; printf(the number of a?-);/*输入最高次项系数*/ scanf(%f,&a1); if(a1=0) printf(ERROR);return 1; printf(the number of b?-);/*输入第二高次项系数*/ scanf(%f,&b1); if(NUMjdg=1) printf(the result is %gn,FC(a1,b1); goto end1; printf(the number of c?-);/*输入第三高次项系数*/ scanf(%f,&c1); if(NUMjdg=2) FC2(a1,b1,c1,1); goto end2; printf(the number of d?-);/*输入第四高次项系数*/ scanf(%f,&d1); if(NUMjdg=3) FC3(a1,b1,c1,d1); goto end3; printf(the number of e?-);/*输入第五高次项系数*/ scanf(%f,&e1); if(NUMjdg=4) FC4(a1,b1,c1,d1,e1); goto end4; printf(the number of f?-);/*输入常数项系数*/ scanf(%f,&f1); x5=FC5(); end2:end4: if(a1!=0) printf(n*nThere is following result:n); fp=fopen(fun.dat,r); while(fgets(buf,256,fp)!=NULL) printf(%s,buf); fclose(fp); fp=fopen(fun.dat,a); if(NUMjdg=5) fprintf(fp,x%s=%gn,fx5,x5); printf(x%s=%gn,fx5,x5); fclose(fp); end1: end3:if(save=n) unlink(fun.dat); getch(); return 0;/*以下为各项函数的定义*/float fun(float x)return(x*x*x*x*x*a1+x*x*x*x*b1+x*x*x*c1+x*x*d1+x*e1+f1); float dfun(float x)return(5*a1*x*x*x*x+4*b1*x*x*x+3*c1*x*x+2*d1*x+e1);float iterate(float x)float x1; x1=x-fun(x)/dfun(x); return(x1);float FC5() int k=0,i; float x0=-2.0,x1,de; float b,c,d,e,temp5; b1/=a1; c1/=a1; d1/=a1; e1/=a1; f1/=a1; a1=1.0; printf(FC5 a=%g b=%g c=%g d=%g e=%g f=%gn,a1,b1,c1,d1,e1,f1); if(b1=0.0&c1=0.0&d1=0.0&e1=0.0&f1=0.0) return 0.0; temp0=-b1/5; temp1=-c1/(2*b1); temp2=-d1/c1; temp3=2*e1/(-d1); temp4=-5*f1/e1; for(i=0;i=0.00001&kMAX); strcpy(fx5,5); b=b1+x1; c=c1+b*x1; d=d1+c*x1; e=e1+d*x1; FC4(1.0,b,c,d,e); printf(one of the result is %gn,x1); return x1; /*解法请参照盛金公式，费拉里公式，牛顿迭代法，一元二次求根公式*/float FC4(float a,float b,float c,float d,float e) float y; float M,N,P; float y04; int i; b/=a; c/=a; d/=a; e/=a; a=1.0; printf(FC4 a:%g b:%g c:%g d:%g e:%gn,a,b,c,d,e); y00=8.0; y01=-4.0*c; y02=-1*(8.0*e-2.0*b*d); y03=-e*(b*b-4.0*c)-d*d; for(i=1;ia=%g b=%g c=%g d=%gn,a,b,c,d); A=b*b-3*a*c; B=b*c-9*a*d; C=c*c-3*b*d; delta=B*B-4*A*C; printf(fc3A:%g B:%g C:%gn,A,B,C); printf(fc3 delta:%gn,delta); if(NUMjdg=3) printf(There is following result:nn); fp=fopen(fun.dat,w); else strcpy(Fun3,fun3:); if(delta=0) if(A=B) if(b=0) printf(%sx1=x2=x3=%dn,Fun3,0); else printf(%sx1=x2=x3=%gn,Fun3,-b/(3*a); if(b=0) fprintf(fp,%sx1=x2=x3=%dn,Fun3,0); else fprintf(fp,%sx1=x2=x3=%gn,Fun3,-b/(3*a); fun0=-b/(3*a); fun1=fun0; fun2=fun1; if(NUMjdg=3) printf(n); fclose(fp); return fun0; else k=B/A; printf(%sx1=%gn,Fun3,fun0=-b/a+k); printf(%sx2=%gn,Fun3,fun1=-k/2); fprintf(fp,%sx1=%gn,Fun3,fun0=-b/a+k); fprintf(fp,%sx2=%gn,Fun3,fun1=-k/2); if(NUMjdg=3) printf(n); fclose(fp); if(fun0fun1) return fun0; else return fun1; else if(delta0) y1=A*b+1.5*a*(-B+pow(delta,0.5); if(y10.0)y_1=-1; y2=A*b+1.5*a*(-B-pow(delta,0.5); if(y20)y_2=-1; if(NUMjdg!=3)printf(y1: %gny2: %gn,y1,y2); x0=(-b-y_1*pow(fabs(y1),1.0/3.0)-y_2*pow(fabs(y2),1.0/3.0)/(3*a); x1=(-2*b+y_1*pow(fabs(y1),1.0/3.0)+y_2*pow(fabs(y2),1.0/3.0)/(6*a); ni=pow(3.0,0.5)*(y_1*pow(fabs(y1),1.0/3.0)-y_2*pow(fabs(y2),1.0/3.0)/(6*a); printf(%sx1=%gn,Fun3,fun0=x0); printf(%sx2=%g+%gin,Fun3,x1,fabs(ni); printf(%sx3=%g-%gin,Fun3,x1,fabs(ni); fprintf(fp,%sx1=%gn,Fun3,fun0=x0); fprintf(fp,%sx2=%g+%gin,Fun3,x1,fabs(ni); fprintf(fp,%sx3=%g-%gin,Fun3,x1,fabs(ni); fun1=fun0; fun2=fun1; if(NUMjdg=3)printf(n); fclose(fp); return fun0; else T=(2*A*b-3*a*B)/(2*pow(A,1.5); theta=acos( T); theta/=3; if(NUMjdg!=3) printf(T:%gn,T); printf(theta: %gn,theta); /cs = theta+2/3*i*acos(-1); x0=(-b-2*pow(A,0.5)*cos(theta)/(3*a); x1=(-b+pow(A,0.5)*(cos(theta)+pow(3,0.5)*sin(theta)/(3*a); x2=(-b+pow(A,0.5)*(cos(theta)-pow(3,0.5)*sin(theta)/(3*a); for(i=0;i3;i+) printf(%sx%d=%gn,Fun3,i+1,funi=xi); if(NUMjdg=3)for(i=0;ifun1)temp=fun0; elsetemp=fun1; if(NUMjdg=3)printf(n); fclose(fp); if(tempfun2)return temp; elsereturn fun2; float FC2(float a,float b,float c,int num) FILE *fp; float d; printf(FC2 a:%g b:%g c:%gn,a,b,c); d=b*b-4*a*c; fp=fopen(fun.dat,a); if(d0) fprintf(fp,x%d=%g+%g in,num,-b/2/a,pow(-d,0.5)/(2*a); fprintf(fp,x%d=%g-%g in,num+1,-b/2/a,pow(-d,0.5)/(2*a); else if(d=0) if(b=0.0)fprintf(fp,x%d=x%d=0n,num,num+1); els