链式线性表表示和求解一元多项式问题

#include<iostream>
using namespace std;
struct LNode{   //节点类
double p;//系数项
int  e;//指数项
LNode * next;
};

class LsList{//一元多项式链式线性表
private:
LNode head;//头结点
size_t size;//节点个数
double mx;//一元多项式的变量值
public:
LNode & GetHead(){return head;}
size_t & GetSize(){return size;}
size_t GetSize() const {return size;}
LsList()
{//初始化一个空的线性表
size = 0;
head.next = 0;
mx = 0;
}

//初始化一元多项式线性表中的系数项、指数项
LsList(double ps[],int es[],int n)//ps代表系数项数组，es代表指数项数组,n代表该一元多项式的个数
{
size = 0;
head.next = 0;
mx = 0;
int i =0;
LNode * p = &head;
for(;i<n;i++)
{
LNode * p1 = (LNode*)malloc(sizeof(LNode));
p1->e = es[i];
p1->p = ps[i];
p->next = p1;
p = p->next;
size++;
}
p->next = 0;
}
//复制构造函数
LsList(LsList &list2)
{
size = 0;
head.next = 0;
mx = 0;
LNode * p = &head;
LNode *p1  = list2.GetHead().next;
while(p1!=0)
{
LNode * p2 = (LNode*)malloc(sizeof(LNode));
p2->e = p1->e;
p2->p = p1->p;
p->next = p2;
p1 = p1->next;
p = p->next;
size++;
}
p->next = 0;
}
//赋值操作符重载
LsList & operator=(LsList &list2)
{

clear();
LNode * p = &head;
LNode *p1  = list2.GetHead().next;
while(p1!=0)
{
LNode * p2 = (LNode*)malloc(sizeof(LNode));
p2->e = p1->e;
p2->p = p1->p;
p->next = p2;
p1 = p1->next;
p = p->next;
size++;
}
p->next = 0;
return *this;
}

//设置该一元多项式的变量值X
void SetX(double d)
{
mx = d;
}

//清空一个线性表
void clear()
{

LNode * p = head.next;
while(p!=0)
{
LNode * p2 = p->next;
free(p);
p = p2;
}
size = 0;
head.next = 0;
mx = 0;
}

//打印该一元线性表
void PrintLsList()
{
if(mx==0)
{
cout<<"请先设置变量x值"<<endl;
return ;
}
LNode * p = head.next;
while(p!=0)
{
cout<<p->p<<"*"<<mx<<"^"<<p->e;
p = p->next;
if(p!=0&&p->p>0)
cout<<"+";
}
}

//计算该一元多项式结果
double GetResult()
{
double sum =0;
if(mx==0)
{
cout<<"请先设置变量x值"<<endl;
return -1;
}
LNode * p = head.next;
while(p!=0)
{
sum+=(p->p)*pow(mx,p->e);
p = p->next;
}
return sum;
}

//删除多项式中的某一项数据
bool DeleElem(int e)
{
LNode * p1 = &head;
LNode * p = p1->next;
while(p!=0)
{
if(p->e==e)
{
p1->next = p->next;
free(p);
size--;
return true;
}
p1 = p1->next;
p =  p1->next;
}
return false;
}

//给多项式添加一项数据
void AddElem(double pi,int ei)
{

LNode * p = head.next;

if(p==0)
{
LNode * p2 = (LNode*)malloc(sizeof(LNode));
p2->e =ei;
p2->p = pi;
head.next = p2;
size++;
p2->next = 0;
return;
}
if(p->e>ei)
{
LNode * p2 = (LNode*)malloc(sizeof(LNode));
p2->e =ei;
p2->p = pi;
head.next = p2;
p2->next = p;
size++;
return;
}

while(p!=0)
{
if(p->e == ei)
{
if(( p->p + pi)==0)
{
DeleElem(ei);//删除
return;
}
else
{
p->p += pi;
return;
}
}
if((p->e<ei && p->next!=0 && p->next->e>ei)||(p->e<ei&&p->next==0))
{
LNode * p2 = (LNode*)malloc(sizeof(LNode));
p2->e =ei;
p2->p = pi;
p2->next = p->next;
p->next = p2;
size++;
return ;
}
p = p->next;
}

}

//完成多项式的相加运算，并销毁多项式list2
void AddList(LsList &list2)
{
int s1 = size;
int n=0;
size =0;
LNode * p1 = head.next;
LNode * p = &head;
LNode * p2 = list2.GetHead().next;

while(p1!=0&&p2!=0)
{
if(p1->e < p2->e)
{
p->next = p1;
p1 = p1->next;
p = p->next;
size++;
}
else
{
if(p1->e > p2->e)
{
p->next = p2;
p2 = p2->next;
p = p->next;
size++;
}
else{
double db = (p1->p)+(p2->p);
if(db!=0)
{
p1->p  = db;
p->next = p1;
p = p->next;
size++;
p1 = p1->next;
LNode * p3 = p2->next;
free(p2);
p2=p3;
size++;

}
if(db==0)
{
LNode * pa = p1->next;
LNode * pb = p2->next;
free(p1);
free(p2);
p1 = pa;
p2 = pb;
n++;
}
}
}

}

if(p1==0)
{
p->next = p2;
size += list2.GetSize() - size - n;
}
else
{
p->next = p1;
size += s1 - size - n;
}

list2.GetHead().next = 0;
}

//完成多项式的相减运算，并销毁多项式list2
void Sub(LsList &list2)
{
LNode *p  = list2.GetHead().next;
while(p!=0)
{
p->p = -(p->p);
p = p->next;
}
AddList(list2);
}

//完成多项式的相乘运算，并销毁多项式list2
void Mul(LsList &list2)
{
LNode *p  = list2.GetHead().next;
LsList ili = *this;
while(p!=0)
{
LsList li = ili;
for(LNode * p1 = li.GetHead().next;p1!=0;p1 = p1->next)
{
p1->p = (p1->p)*(p->p);
p1->e = p1->e + p->e;
}
AddList(li);
p = p->next;
}
}

////完成多项式的相除运算，并销毁多项式list2
//void Devi()
//{
//
//
//}
};

int main()
{
/*
*测试一
*/
//创建一个空的线性表
LsList list1;
//给该空的线性表添加项信息
list1.AddElem(1,2);
list1.AddElem(1.5,3);
list1.AddElem(2,4);
//设置该一元多项式的变量x的值
list1.SetX(3);
cout<<endl;
cout<<"创建一个空的线性表后添加每项的数据"<<endl;
cout<<"输出该一元多项式的表达式和求值:"<<endl;
list1.PrintLsList();
//输出该一元多项式的表达式和求值
cout<<" = "<<list1.GetResult()<<endl;

/*
*测试二
*/
//用每项的信息数组初始化线性表
double ps[5] = {1,2.5,3,5.4,6};//每项的系数信息数组
int es[5] = {1,2,4,6,7};//每项的指数信息数组
LsList list2(ps,es,5);
//设置该一元多项式的变量x的值
list2.SetX(2);
cout<<endl;
cout<<"用每项的信息数组初始化线性表"<<endl;
cout<<"输出该一元多项式的表达式和求值:"<<endl;
//输出该一元多项式的表达式和求值
list2.PrintLsList();
cout<<" = "<<list2.GetResult()<<endl;

/*
*测试三
*/
//直接赋值构造一个一元多项式线性表对象
LsList list3 = list2;
//设置该一元多项式的变量x的值
list3.SetX(2);
cout<<endl;
cout<<"直接赋值构造一个一元多项式线性表对象"<<endl;
cout<<"输出该一元多项式的表达式和求值:"<<endl;
//输出该一元多项式的表达式和求值
list3.PrintLsList();
cout<<" = "<<list3.GetResult()<<endl;
//给该线性表再添加一项数据
cout<<endl;
cout<<"给该线性表再添加一项数据:其中系数为4，指数为5"<<endl;
list3.AddElem(4,5);
cout<<"输出该一元多项式的表达式和求值:"<<endl;
//输出该一元多项式的表达式和求值
list3.PrintLsList();
cout<<" = "<<list3.GetResult()<<endl;
//给该线性表再添加一项数据
cout<<endl;
cout<<"给该线性表再添加一项数据:其中系数为-1，指数为2"<<endl;
list3.AddElem(-1,2);
cout<<"输出该一元多项式的表达式和求值:"<<endl;
//输出该一元多项式的表达式和求值
list3.PrintLsList();
cout<<" = "<<list3.GetResult()<<endl;
//删除线性表中的一项数据信息
cout<<endl;
cout<<"删除该一元多项式中指数项为2的项"<<endl;
list3.DeleElem(2);
cout<<"输出该一元多项式的表达式和求值:"<<endl;
//输出该一元多项式的表达式和求值
list3.PrintLsList();
cout<<" = "<<list3.GetResult()<<endl;

/*
*测试四
*/
LsList myList = list2;
LsList myList1 = list3;
myList.SetX(2);
myList1.SetX(2);
cout<<endl;
cout<<"输出该一元多项式list2的表达式:"<<endl;
//输出该一元多项式的表达式
list2.PrintLsList();
cout<<" = "<<list2.GetResult()<<endl;
cout<<endl;

cout<<endl;
cout<<"输出该一元多项式list3的表达式:"<<endl;
//输出该一元多项式的表达式
myList1.PrintLsList();
cout<<" = "<<myList1.GetResult()<<endl;
cout<<endl;
//将list2一元多项式加上list3一元多项式
myList.AddList(myList1);
cout<<endl;
cout<<"输出将list2一元多项式加上list3一元多项式的表达式和求值:"<<endl;
//输出该一元多项式的表达式和求值
myList.PrintLsList();
cout<<" = "<<myList.GetResult()<<endl;

//将list2一元多项式减去list3一元多项式
LsList myList3 = list2;
LsList myList4 = list3;
myList3.SetX(2);
myList4.SetX(2);
myList3.Sub(myList4);
cout<<endl;
cout<<"输出将list2一元多项式减去list3一元多项式的表达式和求值:"<<endl;
//输出该一元多项式的表达式和求值
myList3.PrintLsList();
cout<<" = "<<myList3.GetResult()<<endl;

//将list2一元多项式乘以list3一元多项式

myList3 = list2;
myList4 = list3;
myList3.SetX(2);
myList4.SetX(2);
myList3.Mul(myList4);
cout<<endl;
cout<<"输出将list2一元多项式乘以list3一元多项式的表达式和求值:"<<endl;
//输出该一元多项式的表达式和求值
myList3.PrintLsList();
cout<<" = "<<myList3.GetResult()<<endl;

list2.clear();
list3.clear();
return 0;
}