线性表的应用——求解两个多项式相加问题描述（链表求解）

问题描述：假设一个多项式形式为：p(x)=c1*x^(e1)+c2*x^(e2)+...+cm*x^(em)；其中ei（1≤i≤m）为整数类型的指数，并且没有相同指数的多项式项；ci（1≤i≤m）为实数类型的序数。

编写求两个多项式相加的程序。

示例代码：

#include <iostream>
using namespace std;
const int MAX = 10;
struct PolyNode //多项式单链表结点类型
{
double coef; //系数
int exp; //指数
PolyNode *next; //指向下一个结点的指针
};
class PolyClass2 //多项式单链表类
{
PolyNode *head; //多项式单链表的头结点指针
public:
PolyClass2(); //构造函数
~PolyClass2(); //析构函数,释放head单链表的所有结点
void DispPoly(); //输出多项式单链表
void CreateListR(double a[], int b[], int n); //由含有n个元素的系数数组a和指数数组b采用尾插法建立多项式单链表
void Sort(); //对一个多项式单链表按exp域递减排序
friend void PolyAdd(PolyClass2 &, PolyClass2 &, PolyClass2 &); //友元函数,用于求两个多项式相加运算
};

PolyClass2::PolyClass2() //构造函数
{
head = new PolyNode();
head->next = NULL;
}
PolyClass2::~PolyClass2() //析构函数,释放head单链表的所有结点
{
PolyNode *pre = head, *p = pre->next;
while (p != NULL)
{
delete pre;
pre = p;
p = p->next;
}
delete pre;
}
void PolyClass2::DispPoly() //输出多项式单链表
{
bool first = true;
PolyNode *p = head->next;
while (p != NULL)
{
if (first)
first = false;
else if (p->coef>0)
cout << "+";
if (p->exp == 0)
cout << p->coef;
else if (p->exp == 1)
cout << p->coef << "x";
else
cout << p->coef << "x^" << p->exp;
p = p->next;
}
cout << endl;
}
void PolyClass2::CreateListR(double a[], int b[], int n) //由含有n个元素的系数数组a和指数数组b采用尾插法建立多项式单链表
{
PolyNode *s, *r;
int i;
r = head;
for (i = 0; i<n; i++)
{
s = new PolyNode();
s->coef = a[i];
s->exp = b[i];
r->next = s;
r = s;
}
r->next = NULL;
}
void PolyClass2::Sort() //对一个多项式单链表按exp域递减排序
{
PolyNode *p, *pre, *q;
q = head->next; //q指向开始结点
if (q == NULL) return;
p = head->next->next;
if (p == NULL) return;
q->next = NULL;
while (p != NULL)
{
q = p->next;
pre = head;
while (pre->next != NULL && pre->next->exp>p->exp)
pre = pre->next;
p->next = pre->next;
pre->next = p;
p = q;
}
}
void PolyAdd(PolyClass2 &poly1, PolyClass2 &poly2, PolyClass2 &poly3)//由两个多项式poly1、poly2相加运算得到ploy3
{
PolyNode *pa = poly1.head->next; //pa指向poly1的开始结点
PolyNode *pb = poly2.head->next; //pb指向poly2的开始结点
PolyNode *s, *r;
double c;
r = poly3.head;
while (pa != NULL && pb != NULL)
{
if (pa->exp>pb->exp)
{
s = new PolyNode();
s->exp = pa->exp;
s->coef = pa->coef;
r->next = s; r = s;
pa = pa->next;
}
else if (pa->exp<pb->exp)
{
s = new PolyNode();
s->exp = pb->exp;
s->coef = pb->coef;
r->next = s; r = s;
pb = pb->next;
}
else
{
c = pa->coef + pb->coef;
if (c != 0)
{
s = new PolyNode();
s->exp = pa->exp;
s->coef = c;
r->next = s; r = s;
}
pa = pa->next;
pb = pb->next;
}
}
if (pb != NULL) pa = pb;
while (pa != NULL)
{
s = new PolyNode();
s->exp = pa->exp;
s->coef = pa->coef;
r->next = s; r = s;
pa = pa->next;
}
r->next = NULL;
}
void main()
{
PolyClass2 Poly1, Poly2, Poly3; //建立3个多项式单链表对象
double a[MAX];
int b[MAX], n;
//===创建第1个多项单链表
a[0] = 2.0; b[0] = 3;
a[1] = 3.2; b[1] = 5;
a[2] = -6.0; b[2] = 1;
a[3] = 10.0; b[3] = 0;
n = 4;
Poly1.CreateListR(a, b, n);
cout << "第1个多项式: "; Poly1.DispPoly();
Poly1.Sort();
cout << "排序后结果: "; Poly1.DispPoly();
//===创建第2个多项单链表
a[0] = 6.0; b[0] = 1;
a[1] = 1.8; b[1] = 5;
a[2] = -2.0; b[2] = 3;
a[3] = 1.0; b[3] = 2;
a[4] = -2.5; b[4] = 4;
a[5] = -5.0; b[5] = 0;
n = 6;
Poly2.CreateListR(a, b, n);
cout << "第2个多项式: "; Poly2.DispPoly();
Poly2.Sort();
cout << "排序后结果: "; Poly2.DispPoly();
//===
PolyAdd(Poly1, Poly2, Poly3);
cout << "相加后多项式:"; Poly3.DispPoly();
cout << "销毁3个多项式单链表\n";
}