C++实现多项式操作及其加减乘除

/* * Polynomial.h * *  Created on: Oct 6, 2015 *      Author: chris */#ifndef POLYNOMIAL_H_#define POLYNOMIAL_H_#include<iostream>struct Term{double coef;int exp;Term * next;Term():coef(0), exp(0), next(NULL) {}Term(double _coef, int _exp = 0):coef(_coef), exp(_exp), next(NULL) {}};class Polynomial{Term poly;public:Polynomial() {}Polynomial(const Polynomial & rhs);Polynomial & operator = (const Polynomial & rhs);~Polynomial();void PolyClear();int  PolyLength() const;bool PolyEmpty() const;bool AddTerm(double coef, int exp);void Simplify();//arithmetic.Polynomial & AddPoly(const Polynomial & rhs);Polynomial & SubPoly(const Polynomial & rhs);Polynomial & MultPoly(const Polynomial & rhs);Polynomial & DivPoly(const Polynomial & rhs, Polynomial & rem);Polynomial & DivPoly(const Polynomial & rhs);void display() const;void Swap(Polynomial & rhs);private:void _Copy(const Polynomial & rhs);};#endif /* POLYNOMIAL_H_ */

/* * Polynomial.cpp * *  Created on: Oct 6, 2015 *      Author: chris */#include "Polynomial.h"#include <iostream>#include <cmath>#include <iomanip>using namespace std;Polynomial::Polynomial(const Polynomial & rhs){_Copy(rhs);}Polynomial & Polynomial::operator = (const Polynomial & rhs){if(this == &rhs) return *this;this->~Polynomial();_Copy(rhs);return *this;}Polynomial::~Polynomial(){PolyClear();}void Polynomial::PolyClear(){Term *pH = poly.next, *pT = NULL;while(pH) {pT = pH;pH = pH->next;delete pT;}poly.next = NULL;}int Polynomial::PolyLength() const{Term * pT = poly.next;int cnt = 0;while(pT) {++cnt;pT = pT->next;}return cnt;}bool Polynomial::PolyEmpty() const{return poly.next == NULL;}bool Polynomial::AddTerm(double coef, int exp){Term *pnew = new Term(coef, exp);if(!pnew) return false;Term *prior = &poly, *pcur = poly.next;while(pcur && exp < pcur->exp) {prior = pcur;pcur = pcur->next;}if(!pcur || exp > pcur->exp) {    pnew->next = prior->next;    prior->next = pnew;}else {pcur->coef += coef;delete pnew;}return true;}void Polynomial::Simplify(){//combine homogeneous terms.Term * prior = poly.next;while(prior && prior->next) {Term * pT = prior->next;if(prior->exp == pT->exp) {prior->next = pT->next;prior->coef += pT->coef;delete pT;}else {prior = pT;}}//delete zeros terms.prior = &poly;while(prior->next) {Term * pT = prior->next;if(fabs(pT->coef - 0) < 1e-6 ) {prior->next = pT->next;delete pT;}elseprior = pT;}}Polynomial & Polynomial::AddPoly(const Polynomial & rhs){for(Term * pT = rhs.poly.next; pT; pT = pT->next) {AddTerm(pT->coef, pT->exp);}Simplify();return *this;}Polynomial & Polynomial::SubPoly(const Polynomial & rhs){for(Term *pT = rhs.poly.next; pT; pT = pT->next) {AddTerm(-pT->coef, pT->exp);}Simplify();return *this;}Polynomial & Polynomial::MultPoly(const Polynomial & rhs){Polynomial prod;for(Term* pT1 = poly.next; pT1; pT1 = pT1->next) {for(Term* pT2 = rhs.poly.next; pT2; pT2 = pT2->next) {prod.AddTerm(pT1->coef * pT2->coef, pT1->exp + pT2->exp);}}Swap(prod);Simplify();return *this;}Polynomial & Polynomial::DivPoly(const Polynomial & rhs, Polynomial & rem){rem.PolyClear();Swap(rem);Term *remHead = rem.poly.next, *divHead = rhs.poly.next;while(remHead && remHead->exp >= divHead->exp) {Term quot(remHead->coef/divHead->coef,remHead->exp-divHead->exp);AddTerm(quot.coef, quot.exp);for(Term * pT = divHead; pT; pT = pT->next) {rem.AddTerm(-quot.coef*pT->coef, quot.exp+pT->exp);}rem.Simplify();remHead = rem.poly.next;}return *this;}Polynomial & Polynomial::DivPoly(const Polynomial & rhs){Polynomial rem;return DivPoly(rhs,rem);}void Polynomial::display() const{Term * pT = poly.next;if(pT == NULL) {cout << "0" << endl;return;}bool first = true;while(pT) {//sign.if(pT->coef >= 0) {if(!first) {    cout << "+";}}elsecout << "-";//coefif(fabs(fabs(pT->coef) - 1) > 1e-3)cout << fabs(pT->coef);//xif(pT->exp != 0) {cout << "x";//expif(pT->exp != 1)cout << "^";if(pT->exp > 0)cout << pT->exp;elsecout << "(" << pT->exp << ")";}pT = pT->next;first = false;}}void Polynomial::Swap(Polynomial & rhs){Term * pT = rhs.poly.next;rhs.poly.next = poly.next;poly.next = pT;}//privatevoid Polynomial::_Copy(const Polynomial & rhs){    Term* pT = rhs.poly.next;    while(pT) {    AddTerm(pT->coef, pT->exp);    pT = pT->next;    }}

/* * Main.cpp * *  Created on: Oct 6, 2015 *      Author: chris */#include<iostream>#include"Polynomial.h"using namespace std;int main(void){Polynomial poly1, poly2;poly1.AddTerm(5, 2);poly1.AddTerm(3, 1);poly1.AddTerm(7, 0);poly1.display();cout << endl;poly2.AddTerm(4, 2);poly2.AddTerm(2, 0);poly2.display();cout << endl;poly1.AddPoly(poly2);poly1.display();cout << endl;poly1.SubPoly(poly2);poly1.display();cout << endl;poly1.MultPoly(poly2);poly1.display();cout << endl;Polynomial rem;poly1.DivPoly(poly2, rem);poly1.display();cout << endl;rem.display();cout << endl;return 0;}