一元稀疏多项式计算器加减乘除运算.docx
《一元稀疏多项式计算器加减乘除运算.docx》由会员分享，可在线阅读，更多相关《一元稀疏多项式计算器加减乘除运算.docx（28页珍藏版）》请在冰豆网上搜索。
一元稀疏多项式计算器加减乘除运算
山东大学
14级计算机科学与技术学院,王士彬
#include
#include
#include
#include
usingnamespacestd;
classterm{
public:
term（intc=0,inte=0）:
coef（c）,exp（e）{}
intcoef;//系数
intexp;//指数
};
classPolynomial{
private:
intdegree;//阶数
listtermList;//存储多项式
public:
Polynomial（）{degree=0;};//---------------------------------------构造函数，创造一个0阶多项式
intDegree（）;//--------------------------------------------------求多项式的阶数
doubleValue（doublex）;//----------------------------------------返回多项式在x下的值
voidClear（）;//--------------------------------------------------清空多项式
Polynomialshunxu（）;//-----------------------指数递增变递减，递减变递增
Polynomialpaixu（）;//------------------------用来对计算后结果的排序处理（主要去掉系数为0的项）
/*
函数方法
*/
voidInput（）;//----------------------------------------------------------------多项式输入
voidOutPut（）;//---------------------------------------------------------------多项式输出
PolynomialAdd（Polynomial&b）;//-----------------------------------------------多项式相加
PolynomialSubtract（Polynomial&b）;//------------------------------------------多项式相减
PolynomialMultiply（Polynomial&b）;//------------------------------------------多项式相乘
PolynomialDivide（Polynomial&b）;//-------------------------------------------多项式相除
/*
操作符重载
*/
friendistream&operator>>（istream&is,Polynomial&obj）;//----------------输入符号重载
friendostream&operator<<（ostream&os,Polynomial&obj）;//----------------输出符号重载
Polynomialoperator+（Polynomial&b）;//------------------------------------加号重载
Polynomialoperator-（Polynomial&b）;//------------------------------------减号重载
Polynomialoperator*（Polynomial&b）;//------------------------------------乘号重载
Polynomialoperator/（Polynomial&b）;//------------------------------------除号重载
};
intPolynomial:
:
Degree（）{
list:
:
iteratoriter=termList.begin（）;
termtemp=（term）*iter;
intdegree=temp.exp;
returndegree;
}
doublePolynomial:
:
Value（doublex）{
doublesum=0;
inti;
list:
:
iteratoriter=termList.begin（）;
for（;iter!
=termList.end（）;iter++）{
termtemp=（term）*iter;
intt=1;
for（i=temp.exp;i!
=0;i--）{
t=t*x;
}
sum+=temp.coef*t;
}
returnsum;
}
voidPolynomial:
:
Clear（）{
termList.clear（）;
}
PolynomialPolynomial:
:
shunxu（）{
Polynomialp1;
list:
:
iteratoriter=termList.begin（）;
for（;iter!
=termList.end（）;iter++）{
termtemp;
termt_a=（term）*iter;
temp.coef=t_a.coef;
temp.exp=t_a.exp;
p1.termList.push_front（temp）;
}
returnp1;
}
//用来对计算后结果的排序处理（在输入时已经对系数为0的情况处理过了，但得出的结果系数可能有等于0的，此方法就是对系数为0的情况处理）
PolynomialPolynomial:
:
paixu（）{
Polynomialaaa;
list:
:
iteratorit=termList.begin（）;
for（;it!
=termList.end（）;）{
termt11=*it;
if（t11.coef==0）{
it++;
}else{
aaa.termList.push_back（t11）;
it++;
}
}
returnaaa;
}
voidPolynomial:
:
Input（）{
intn;
cout<<",请输入多项式的项数：
";
cin>>n;
cout<<"按升幂输入多项式的系数和指数"<for（inti=1;i<=n;i++）{
termt_temp;
cout<<"请输入第"<";
cin>>t_temp.coef;
cin>>t_temp.exp;
if（t_temp.coef!
=0）{
termList.push_back（t_temp）;
}
}
}
voidPolynomial:
:
OutPut（）{
if（termList.empty（））{
cout<<"0";
}else{
list:
:
iteratorit=termList.begin（）;
for（;it!
=termList.end（）;）{
termt11=*it;
if（t11.exp!
=0）{
if（t11.coef==1）{
if（t11.exp==1）{
cout<<"x";
if（++it!
=termList.end（））{
termt112=*it;
if（t112.coef>0）{
cout<<"+";
}else{
cout<<"";
}
}
}else{
cout<<"x^"<if（++it!
=termList.end（））{
termt112=*it;
if（t112.coef>0）{
cout<<"+";
}else{
cout<<"";
}
}
}
}elseif（t11.coef==（-1））{
if（t11.exp==1）{
cout<<"-x";
if（++it!
=termList.end（））{
termt112=*it;
if（t112.coef>0）{
cout<<"+";
}else{
cout<<"";
}
}
}else{
cout<<"-x^"<if（++it!
=termList.end（））{
termt112=*it;
if（t112.coef>0）{
cout<<"+";
}else{
cout<<"";
}
}
}
}else{
if（t11.exp==1）{
cout<if（++it!
=termList.end（））{
termt112=*it;
if（t112.coef>0）{
cout<<"+";
}else{
cout<<"";
}
}
}else{
cout<if（++it!
=termList.end（））{
termt112=*it;
if（t112.coef>0）{
cout<<"+";
}else{
cout<<"";
}
}
}
}
}else{
cout<if（++it!
=termList.end（））{
termt112=*it;
if（t112.coef>0）{
cout<<"+";
}else{
cout<<"";
}
}
}
}
}
}
PolynomialPolynomial:
:
Add（Polynomial&b）{
Polynomialc;
list:
:
iteratoriter_a=termList.begin（）;
list:
:
iteratoriter_b=b.termList.begin（）;
while（iter_a!
=termList.end（）&&iter_b!
=b.termList.end（））{
termt_temp;
termt_a=（term）*iter_a;
termt_b=（term）*iter_b;
if（t_a.expc.termList.push_back（t_b）;
iter_b++;
}elseif（t_a.exp>t_b.exp）{
c.termList.push_back（t_a）;
iter_a++;
}else{
t_temp.coef=t_a.coef+t_b.coef;
t_temp.exp=t_a.exp;
c.termList.push_back（t_temp）;
iter_a++;
iter_b++;
}
}
for（;iter_a!
=termList.end（）;iter_a++）{
c.termList.push_back（*iter_a）;
}
for（;iter_b!
=b.termList.end（）;iter_b++）{
c.termList.push_back（*iter_b）;
}
Polynomialc1=c.paixu（）;
returnc1;
}
PolynomialPolynomial:
:
Subtract（Polynomial&b）{
Polynomialc;
list:
:
iteratoriter_a=termList.begin（）;
list:
:
iteratoriter_b=b.termList.begin（）;
while（iter_a!
=termList.end（）&&iter_b!
=b.termList.end（））{
termtemp;
termt_a=（term）*iter_a;
termt_b=（term）*iter_b;
if（t_a.exp>t_b.exp）{
c.termList.push_back（t_a）;
iter_a++;
}elseif（t_a.exptemp.coef=-t_b.coef;
temp.exp=t_b.exp;
c.termList.push_back（temp）;
iter_b++;
}else{
temp.coef=t_a.coef-t_b.coef;
temp.exp=t_a.exp;
c.termList.push_back（temp）;
iter_a++;
iter_b++;
}
}
for（;iter_a!
=termList.end（）;iter_a++）{
c.termList.push_back（*iter_a）;
}
for（;iter_b!
=b.termList.end（）;iter_b++）{
termtemp2;
termt_b=（term）*iter_b;
temp2.coef=-t_b.coef;
temp2.exp=t_b.exp;
c.termList.push_back（temp2）;
}
Polynomialc1=c.paixu（）;
returnc1;
}
PolynomialPolynomial:
:
Multiply（Polynomial&b）{
Polynomialc;
list:
:
iteratoriter_a=termList.begin（）;
for（;iter_a!
=termList.end（）;iter_a++）{
Polynomialc1;//这个c1的位置只能放在这里，局部变量
list:
:
iteratoriter_b=b.termList.begin（）;
for（;iter_b!
=b.termList.end（）;iter_b++）{
termtemp;
termt_a=（term）*iter_a;
termt_b=（term）*iter_b;
temp.coef=t_a.coef*t_b.coef;
temp.exp=t_a.exp+t_b.exp;
c1.termList.push_back（temp）;
}
c=c.Add（c1）;
c1.Clear（）;
}
returnc;
}
PolynomialPolynomial:
:
Divide（Polynomial&b）{
Polynomiala;//被除数
list:
:
iteratoriter_a=termList.begin（）;
for（;iter_a!
=termList.end（）;iter_a++）{
termtemp;
termt_a=（term）*iter_a;
temp.coef=t_a.coef;
temp.exp=t_a.exp;
a.termList.push_back（temp）;
}
//---------------------------------------------------------
Polynomialquotient,remainder,temp1,temp2;
list:
:
iteratorqa_a=a.termList.begin（）;
list:
:
iteratorqb_b=b.termList.begin（）;
termqa=（term）*qa_a;
termqb=（term）*qb_b;
temp1=a;
//cout<<"要到达while循环了"<while（qa.exp>=qb.exp）{
termtemp2_term;
temp2_term.coef=qa.coef/qb.coef;
temp2_term.exp=qa.exp-qb.exp;
quotient.termList.push_back（temp2_term）;
Polynomialcenter_quotient;
center_quotient.termList.push_back（temp2_term）;
Polynomialtt=b*center_quotient;
a=a-tt;
a=a.paixu（）;
list:
:
iteratorqa_1=a.termList.begin（）;
qa=（term）*qa_1;
}
Polynomialji=quotient*b;//Polynomial
remainder=temp1-ji;
returnremainder;
}
istream&operator>>（istream&is,Polynomial&obj）{
intn;
cout<<"请输入多项式的项数：
";
cin>>n;
cout<<"按升幂输入多项式的系数和指数"<for（inti=1;i<=n;i++）{
termt_temp;
cout<<"请输入第"<";
cin>>t_temp.coef;
cin>>t_temp.exp;
if（t_temp.coef!
=0）{
obj.termList.push_back（t_temp）;
}
}
returnis;
}
ostream&operator<<（ostream&os,Polynomial&obj）{
if（obj.termList.empty（））{
cout<<"0";
}else{
list:
:
iteratorit=obj.termList.begin（）;
for（;it!
=obj.termList.end（）;）{
termt11=*it;
if（t11.exp!
=0）{
if（t11.coef==1）{
if（t11.exp==1）{
cout<<"x";
if（++it!
=obj.termList.end（））{
termt112=*it;
if（t112.coef>0）{
cout<<"+";
}else{
cout<<"";
}
}
}else{
cout<<"x^"<if（++it!
=obj.termList.end（））{
termt112=*it;
if（t112.coef>0）{
cout<<"+";
}else{
cout<<"";
}
}
}
}elseif（t11.coef==（-1））{
if（t11.exp==1）{
cout<<"-x";
if（++it!
=obj.termList.end（））{
termt112=*it;
if（t112.coef>0）{
cout<<"+";
}else{
cout<<"";
}
}
}else{
cout<<"-x^"<if（++it!
=obj.termList.end（））{
termt112=*it;
if（t112.coef>0）{
cout<<"+";
}else{
cout<<"";
}
}
}
}else{
if（t11.exp==1）{
cout<if（++it!
=obj.termList.end（））{
termt112=*it;
if（t112.coef>0）{
cout<<"+";
}else{
cout<<"";
}
}
}else{
cout<if（++it!
=obj.termList.end（））{
termt112=*it;
if（t112.coef>0）{
cout<<"+";
}else{
cout<<"";
}
}
}
}
}else{
cout<
升级会员 