数据结构实验1(一元多项式的相加和相乘)

实验要求：

1.设计带表头的结点的单链表表示多项式类。

2.在该类上增加成员函数void PolyMul(Polynominal &r)，并重载*运算符。

3.实现菜单驱动的main函数，测试多项式的各个运算：输入多项式，显示多项式，以及多项式加法和乘法运算。

4.采用带表头的非循环链表存储多项式。

大致结构以及加法的运算书上的代码已经给出。乘法运算：将乘数多项式的每一项与被乘数多项式的所有项分别相乘(系数相乘，指数

相加)，得到中间多项式。调用PolyAdd函数将这些中间多项式依次加到结果多项式中。

实现代码：

#include "iostream"#include "cstdio"#include "cstring"#include "algorithm"using namespace std;class Term{public:Term(int c, int e);Term(int c, int e, Term *nxt);Term* InsertAfter(int c, int e); // 在this指针指示的结点后插入新节点private:int coef, exp; // coef * x^expTerm* link;friend ostream & operator << (ostream &, const Term &);friend class Polynominal;/* data */};Term::Term(int c, int e) : coef(c), exp(e){link = 0;}Term::Term(int c, int e, Term *nxt) : coef(c), exp(e){link = nxt;}Term *Term::InsertAfter(int c, int e) // 为新项申请结点的存储单元，并用Term函数将c, e, this -> link 的值填入新节点的相应域{link = new Term(c, e, link);return link;}ostream & operator << (ostream& out, const Term& val){if(val.coef == 0) return out;if(val.coef != 1) out << val.coef;switch(val.exp) {case 0: break;case 1: out << "x"; break;default: out << "x^" << val.exp; break;}return out;}class Polynominal{public:Polynominal();~Polynominal();void AddTerms(istream& in);void Output(ostream& out) const;void PolyAdd(Polynominal& r);void PolyMul(Polynominal& r);private:Term* theList;friend ostream & operator << (ostream &, const Polynominal &);friend istream & operator >> (istream &, Polynominal &);friend Polynominal & operator + (Polynominal &, Polynominal &);friend Polynominal & operator * (Polynominal &, Polynominal &);/* data */};Polynominal::Polynominal(){theList = new Term(0, -1); // 表头结点theList -> link = NULL; // 尾结点为空}Polynominal::~Polynominal(){Term *p = theList -> link;while(p != NULL) {theList -> link = p -> link;delete p;p = theList -> link;}delete theList;}void Polynominal::AddTerms(istream& in) // 按降幂输入各项，构造单循环链表{Term* q = theList;int c, e;while(true) {cout << "Input a term(coef, exp):" << endl << endl;cin >> c >> e;q = q -> InsertAfter(c, e); // 将c，e插入表尾结点q之后if(e < 0) break; // 当输入指数小于0时，构造结束}}void Polynominal::Output(ostream& out) const{int first = 1;Term *p = theList -> link;for( ; p != NULL && p -> exp >= 0; p = p -> link) {if(!first && (p -> coef > 0)) out << "+"; // 在非第一项的正系数前输出+号first = 0;out << *p; // 调用Term类上重载的"<<"操作}cout << endl;}void Polynominal::PolyAdd(Polynominal& r){Term *q, *q1 = theList, *p; // q1指向表头结点p = r.theList -> link; // p指向第一个要处理的结点q = q1 -> link; // q1是q的前驱，p和q就指向两个当前进行比较的项while(p != NULL && p -> exp >= 0) { // 对r的单链表遍历，直到全部结点都处理完while(p -> exp < q -> exp) { // 跳过q -> exp大的项q1 = q;q = q -> link;}if(p -> exp == q -> exp) { // 指数相等时，系数相加q -> coef = q -> coef + p -> coef;if(q -> coef == 0) { // 若相加后系数为0，则删除qq1 -> link = q -> link;delete (q);q = q1 -> link; // 重置q指针}else { // 若相加后系数不为0，则移动q1和qq1 = q;q = q -> link;}}else q1 = q1 -> InsertAfter(p -> coef, p -> exp); // 若p -> exp > q -> exp则以p的系数和指数生成新结点，插入q1后p = p -> link;}}void Polynominal::PolyMul(Polynominal& r){Polynominal result; // 存储结果Term *n = result.theList; // n指向result的头结点n = n -> InsertAfter(0, 0); // 将0, 0插入result的头结点之后Term *p = r.theList -> link; // p指向第一个要处理的结点while(p -> exp >= 0) { // 对r的单链表遍历，直到全部结点都处理完Polynominal tmp; // tmp存储当前结果Term *m = tmp.theList; // m指向tmp头结点Term *q = theList -> link; // q指向表头结点的后继结点while(q -> exp >= 0) { // 遍历当前单链表m = m -> InsertAfter((p -> coef) * (q -> coef), (p -> exp) + (q -> exp)); // 生成新结点插入m后q = q -> link;}result.PolyAdd(tmp); // 当前结果加到result上p = p -> link;}Term *q = theList -> link;while(q != NULL) { // 清空原数据theList -> link = q -> link;delete q;q = theList -> link;}q = theList;q = q -> InsertAfter(0, 0);PolyAdd(result); // result加到当前对象上}ostream & operator << (ostream &out, Polynominal &x){x.Output(out);return out;}istream & operator >> (istream &in, Polynominal &x){x.AddTerms(in);return in;}Polynominal & operator + (Polynominal &a, Polynominal &b){a.PolyAdd(b);return a;}Polynominal & operator * (Polynominal &a, Polynominal &b){a.PolyMul(b);return a;}int main(int argc, char const *argv[]){cout << "*********************" << endl;cout << "  按1进行多项式加法" << endl;cout << "  按2进行多项式乘法" << endl;cout << "     按0退出程序" << endl;cout << "*********************" << endl;int num;while(cin >> num && num) {cout << "请输入多项式p：" << endl;Polynominal p, q;cin >> p;cout << p << endl;cout << "请输入多项式q：" << endl;cin >> q;cout << q << endl;if(num == 1) {Polynominal ans = p + q;cout << "p + q = " << ans << endl;}else {Polynominal ans = p * q;cout << "p * q = " << ans << endl;}cout << "*********************" << endl;cout << "  按1进行多项式加法" << endl;cout << "  按2进行多项式乘法" << endl;cout << "     按0退出程序" << endl;cout << "*********************" << endl << endl;}cout << endl << "感谢检查" << endl;return 0;}