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#include?

#include

float?f(float?x)?/*定義f函數，以實現f(x)=x*x*x+x*x-3*x-3*/

{

float?y;

y=((x+1)*x-3.0)*x-3.0;

return?y;

}

float?g(float?x)?/*定義g函數，為f函數的導函數*/

{

float?y;

y=(3.0*x+2.0)*x-3.0;

return?y;

}

float?h(float?x)?/*定義h函數，以實現x*x*x=-x*x+3*x+3*/

{

float?y;

y=(3.0-x)*x+3.0;

return?y;

}

rootA()?/*定義rootA函數，以實現用二分法求近似根*/

{

int?i=0;

float?x,y,x1=0,x2=0,y1=0,y2=0;

do

{

printf("Input?x1=");

scanf("%f",&x1);

printf("Input?x2=");

scanf("%f",&x2);

y1=f(x1);

y2=f(x2);

}

while?(y1*y2>=0);?/*定義變量x1,x2為區間的兩端點，同時保證兩個端點的函數值相異*/

do

{

x=(x1+x2)/2;

y=f(x);

if(fabs(y)<1e-6)

break;

if(y*y1>0)

{

x1=x;

y1=y;

}

else

x2=x;

i=i+1;?/*定義變量i以計算迭代次數*/

}

while?(fabs(x2-x1)>=1e-6);?/*設定精確度為1e-6*/

printf("The?running?number?is?%d\n",i);

printf("A?root?of?equation?is?%7f\n",x);

}

rootB()?/*定義rootB函數，以實現用基本迭代法求近似根*/

{

float?x0=0,x1=0,j;

int?k=0,N;

printf("Input?the?divisor:");?/*選定初值*/

scanf("%f",&x0);

printf("Input?the?number:");?/*輸入最大迭代次數*/

scanf("%d",&N);

printf("Input?the?Precision:");?/*輸入精度*/

scanf("%f",&j);

do

{

x1=pow(h(x0),(1.0/3.0));?/*建立迭代格式*/

if(fabs(x1-x0)

{

printf("A?root?of?equation?is?%7f\n",x1);

break;

}

x0=x1;

k=k+1;

}while?(k<=N);

if(k>N)

printf("It?is?Failure!\n");

if(k<=N)

printf("The?running?number?is?%d\n",k);

}

rootC()?/*定義rootC函數，以實現用牛頓切線法求近似根*/

{

float?x0,x1,j;

int?N,k=0;

printf("Input?the?divisor:");

scanf("%f",&x0);

printf("Input?the?number:");

scanf("%d",&N);

printf("Input?the?Precision:");

scanf("%f",&j);

for(k=0;k<=N;k=k+1)

{

if(fabs(g(x0))<=1e-6)

{

printf("It?is?Singular!\n");

break;

}

else

{

x1=x0-(f(x0)/g(x0));?/*迭代函數*/

if(fabs(x1-x0)

{

printf("A?root?of?equation?is?%7f\n",x1);

break;

}

x0=x1;

}

}

if(k>N)

printf("It?is?Failure!\n");

else

printf("The?running?number?is?%d\n",k);

}

void?main()?/*主函數*/

{

int?choose;

char?yes_no;

printf("Which?method?do?you?want?to?choose?(1,2,3)\n");

printf("1---------ErFenFa\n");

printf("2---------JiBenDieDaiFa\n");

printf("3---------NiuDunQieXianFa\n");

do

{

printf("You?choose?is?");

scanf("%d",&choose);

switch(choose)

{

case?1:?rootA();break;

case?2:?rootB();break;

case?3:?rootC();break;

case?0:?break;

default:?printf("It?is?error!\n");

}

if(choose==0)

break;

printf("Are?you?want?to?contain?(Y/N)");

do

{

scanf("%c",&yes_no);

}

while?(yes_no!='Y'&&yes_no!='y'&&yes_no!='N'&&yes_no!='n');

}

while?(yes_no=='Y'||yes_no=='y');

}

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