一元稀疏多项式计算器加减乘除运算

1、山东大学14级计算机科学与技术学院,王士彬#include#include#include #includeusing namespace std;class termpublic:term(int c=0,int e=0):coef(c),exp(e)int coef;/系数 int exp;/指数 ;class Polynomialprivate:int degree;/阶数 list termList;/存储多项式 public:Polynomial()degree=0;/-构造函数，创造一个0阶多项式 int Degree();/-求多项式的阶数 double Value(double

2、 x);/-返回多项式在x下的值 void Clear();/-清空多项式 Polynomial shunxu();/-指数递增变递减，递减变递增 Polynomial paixu();/-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 */ void Input();/-多项式输入 void OutPut();/-多项式输出 Polynomial Add(Polynomial &b);/-多项式相加 Polynomial Subtract(Polynomial &b);/-多项式相减 Polynomial Multiply(Polynomial &b);/-多项式相乘 Po

3、lynomial Divide(Polynomial &b); /-多项式相除 /* 操作符重载 */ friend istream& operator(istream &is,Polynomial &obj);/-输入符号重载 friend ostream& operator(ostream &os,Polynomial &obj);/-输出符号重载 Polynomial operator+(Polynomial &b);/-加号重载 Polynomial operator-(Polynomial &b);/-减号重载 Polynomial operator*(Polynomial &b);

4、/-乘号重载 Polynomial operator/(Polynomial &b);/-除号重载 ; int Polynomial:Degree()list:iterator iter=termList.begin();term temp=(term)*iter; int degree=temp.exp; return degree;double Polynomial:Value(double x)double sum=0;int i;list:iterator iter=termList.begin();for(;iter!=termList.end();iter+)term temp=(

5、term)*iter;int t=1;for(i=temp.exp;i!=0;i-)t=t*x; sum+=temp.coef*t;return sum;void Polynomial:Clear()termList.clear();Polynomial Polynomial:shunxu()Polynomial p1;list:iterator iter=termList.begin();for(;iter!=termList.end();iter+)term temp;term t_a=(term)*iter;temp.coef=t_a.coef;temp.exp=t_a.exp;p1.t

6、ermList.push_front(temp);return p1;/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） Polynomial Polynomial:paixu()Polynomial aaa;list:iterator it =termList.begin();for(;it!=termList.end();)term t11=*it;if(t11.coef=0)it+;elseaaa.termList.push_back(t11);it+;return aaa;void Polynomial

7、:Input()int n;coutn;cout按升幂输入多项式的系数和指数endl;for(int i=1;i=n;i+)term t_temp;cout请输入第it_temp.coef;cint_temp.exp;if(t_temp.coef!=0)termList.push_back(t_temp); void Polynomial:OutPut()if(termList.empty()cout0;elselist:iterator it = termList.begin();for(;it!=termList.end();)term t11=*it;if(t11.exp!=0)if(t

8、11.coef=1)if(t11.exp=1)cout0)cout+;else cout;else coutx0)cout+;else cout;else if(t11.coef=(-1)if(t11.exp=1) cout0)cout+;else cout; else cout-x0)cout+;else cout; elseif(t11.exp=1)coutt11.coef0)cout+;else cout;elsecoutt11.coefx0)cout+;else cout;elsecout0)cout+;else cout; Polynomial Polynomial:Add(Poly

9、nomial &b)Polynomial c;list:iterator iter_a=termList.begin();list:iterator iter_b=b.termList.begin();while(iter_a!=termList.end()&iter_b!=b.termList.end()term t_temp;term t_a=(term)*iter_a;term t_b=(term)*iter_b;if(t_a.expt_b.exp)c.termList.push_back(t_a);iter_a+;elset_temp.coef=t_a.coef+t_b.coef;t_

10、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);Polynomial c1=c.paixu();return c1;Polynomial Polynomial:Subtract(Polynomial &b)Polynomial c;list:iterato

11、r iter_a=termList.begin();list:iterator iter_b=b.termList.begin();while(iter_a!=termList.end()&iter_b!=b.termList.end()term temp;term t_a=(term)*iter_a;term t_b=(term)*iter_b;if(t_a.expt_b.exp)c.termList.push_back(t_a);iter_a+;else if(t_a.expt_b.exp)temp.coef=-t_b.coef;temp.exp=t_b.exp;c.termList.pu

12、sh_back(temp);iter_b+;elsetemp.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+)term temp2;term t_b=(term)*iter_b;temp2.coef=-t_b.coef;temp2.exp=t_b.exp;c.termLis

13、t.push_back(temp2);Polynomial c1=c.paixu();return c1;Polynomial Polynomial:Multiply(Polynomial &b)Polynomial c;list:iterator iter_a=termList.begin();for(;iter_a!=termList.end();iter_a+)Polynomial c1;/这个 c1的位置只能放在这里，局部变量 list:iterator iter_b=b.termList.begin();for(;iter_b!=b.termList.end();iter_b+)te

14、rm temp;term t_a=(term)*iter_a;term t_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();return c; Polynomial Polynomial:Divide(Polynomial &b)Polynomial a;/被除数 list:iterator iter_a=termList.begin();for(;iter_a!=termList.end();iter_

15、a+)term temp;term t_a=(term)*iter_a;temp.coef=t_a.coef;temp.exp=t_a.exp; a.termList.push_back(temp); /-Polynomial quotient,remainder,temp1,temp2;list:iterator qa_a=a.termList.begin();list:iterator qb_b=b.termList.begin(); term qa=(term)*qa_a;term qb=(term)*qb_b;temp1=a;/cout要到达while循环了=qb.exp)term t

16、emp2_term;temp2_term.coef=qa.coef/qb.coef;temp2_term.exp=qa.exp-qb.exp;quotient.termList.push_back(temp2_term);Polynomial center_quotient;center_quotient.termList.push_back(temp2_term);Polynomial tt=b*center_quotient;a=a-tt;a=a.paixu();list:iterator qa_1=a.termList.begin(); qa=(term)*qa_1; Polynomia

17、l ji=quotient*b; / Polynomial remainder =temp1-ji; return remainder; istream &operator(istream &is,Polynomial &obj)int n;coutn;cout按升幂输入多项式的系数和指数endl;for(int i=1;i=n;i+)term t_temp;cout请输入第it_temp.coef;cint_temp.exp;if(t_temp.coef!=0)obj.termList.push_back(t_temp); return is;ostream& operator(ostrea

18、m &os,Polynomial &obj)if(obj.termList.empty()cout0;elselist:iterator it = obj.termList.begin();for(;it!=obj.termList.end();)term t11=*it;if(t11.exp!=0)if(t11.coef=1)if(t11.exp=1)cout0)cout+;else cout;else coutx0)cout+;else cout;else if(t11.coef=(-1)if(t11.exp=1) cout0)cout+;else cout; else cout-x0)c

19、out+;else cout; elseif(t11.exp=1)coutt11.coef0)cout+;else cout;elsecoutt11.coefx0)cout+;else cout;elsecout0)cout+;else cout; return os;Polynomial Polynomial:operator+(Polynomial &b)Polynomial c;list:iterator iter_a=termList.begin();list:iterator iter_b=b.termList.begin();while(iter_a!=termList.end()

20、&iter_b!=b.termList.end()term t_temp;term t_a=(term)*iter_a;term t_b=(term)*iter_b;if(t_a.expt_b.exp)c.termList.push_back(t_a);iter_a+;elset_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);f

21、or(;iter_b!=b.termList.end();iter_b+)c.termList.push_back(*iter_b);Polynomial c1=c.paixu();return c1;Polynomial Polynomial:operator-(Polynomial &b)Polynomial c;list:iterator iter_a=termList.begin();list:iterator iter_b=b.termList.begin();while(iter_a!=termList.end()&iter_b!=b.termList.end()term temp

22、;term t_a=(term)*iter_a;term t_b=(term)*iter_b;if(t_a.expt_b.exp)c.termList.push_back(t_a);iter_a+;else if(t_a.expt_b.exp)temp.coef=-t_b.coef;temp.exp=t_b.exp;c.termList.push_back(temp);iter_b+;elsetemp.coef=t_a.coef-t_b.coef;temp.exp=t_a.exp;c.termList.push_back(temp);iter_a+;iter_b+;for(;iter_a!=t

23、ermList.end();iter_a+)c.termList.push_back(*iter_a);for(;iter_b!=b.termList.end();iter_b+)term temp2;term t_b=(term)*iter_b;temp2.coef=-t_b.coef;temp2.exp=t_b.exp;c.termList.push_back(temp2);Polynomial c1=c.paixu();return c1;Polynomial Polynomial:operator*(Polynomial &b)Polynomial c;list:iterator it

24、er_a=termList.begin();for(;iter_a!=termList.end();iter_a+)Polynomial c1;/这个 c1的位置只能放在这里，局部变量 list:iterator iter_b=b.termList.begin();for(;iter_b!=b.termList.end();iter_b+)term temp;term t_a=(term)*iter_a;term t_b=(term)*iter_b;temp.coef=t_a.coef*t_b.coef;temp.exp=t_a.exp+t_b.exp;c1.termList.push_bac

25、k(temp);c=c+c1;return c;Polynomial Polynomial:operator/(Polynomial &b)Polynomial a;/被除数 list:iterator iter_a=termList.begin();for(;iter_a!=termList.end();iter_a+)term temp;term t_a=(term)*iter_a;temp.coef=t_a.coef;temp.exp=t_a.exp; a.termList.push_back(temp); /-Polynomial quotient,remainder,temp1,te

26、mp2;list:iterator qa_a=a.termList.begin();list:iterator qb_b=b.termList.begin(); term qa=(term)*qa_a;term qb=(term)*qb_b;temp1=a;/cout要到达while循环了=qb.exp)term temp2_term;temp2_term.coef=qa.coef/qb.coef;temp2_term.exp=qa.exp-qb.exp;quotient.termList.push_back(temp2_term);Polynomial center_quotient;cen

27、ter_quotient.termList.push_back(temp2_term);Polynomial tt=b*center_quotient;a=a-tt;a=a.paixu();list:iterator qa_1=a.termList.begin(); qa=(term)*qa_1; /cout一直在while循环里endl; / cout出while循环了endl; Polynomial ji=quotient*b; remainder =temp1-ji; return quotient;int main() time_t t; time(&t); coutendl; cou

28、t 欢迎使用一元稀疏多项式计算器 endl;/ cout 功能：多项式的加，减，乘，除及按x求值 王 士 彬 endl; cout 输入：多项式的项数，系数，指数 2014级计算机学院endl; cout 各种运算后的结果 endl; cout-运行时间：ctime(&t)endl; cout 【功能选择项】endl; cout endl; cout 1,输入多项式A和B 2,计算多项式A+B endl; cout 3,计算多项式A-B 4,计算多项式A*B endl; cout 5,计算多项式A/B 6,计算A在x处的值 endl; cout 7,计算多项式A的阶数 8,退出 endl; c

29、out endl;int i;Polynomial p1,p2,p3,p4,p5,p6,p7;Polynomial p1_1;Polynomial p2_2; couti;while(i!=1)cout请先建立多项式A和Bendl; couti; doswitch(i)case 1:p1.Clear();p2.Clear();p1_1.Clear();p2_2.Clear(); coutp1; coutp2; p1_1=p1.shunxu();/降幂 p2_2=p2.shunxu();/降幂 cout多项式A为：p1_1endl;cout多项式B为：p2_2endl; cout-1输入AB 2加 3减 4乘 5除 6求值 7求阶数 8退出endl;couti; if(i