MFC实现一元稀疏多项式运算器
首先看看效果图，下面一一介绍各个按钮的实现
基本要求
- 输入并建立两个多项式
- 多项式a与b相加，建立和多项式c
- 多项式a与b相减，建立差多项式d
- 输出多项式a, b, c, d。输出格式：比如多项式a为：A(x)=c1xe1+ c2xe2+…+ cmxem，其中，ci和ei分别为第i项的系数和指数，且各项按指数的升幂排列，即0≤e1＜e2＜…＜em
功能已加强，这里我实现了输入可以不需要保持递增，输出依然递增有序，即加入了查找位置的函数。
首先看一下我界面，较为粗糙，实现计算器界面（个人感觉手动输入更为方便，但实习的拓展要求是计算器的仿真界面Orz）
这个可以自己添加一个头文件，用于多项式的类定义（下面的重载>> <<属于多余的，如果单纯C++控制台程序的可以应用，MFC工程可以直接忽略）。
#include<algorithm>
#include<iostream>
using namespace std;
typedef long long ll;
bool flag = 0;
struct Term
{
double coef;//系数
int exp;//指数
Term* link;
Term(double c, int e, Term* next = NULL)
{
coef = c; exp = e; link = next;
}
Term*InsertAfter(double c, int e);
friend ostream& operator <<(ostream&, const Term&);
};
class Polynomial//多项式类定义
{
public:
Term * first;
friend ostream&operator<<(ostream&, const Polynomial&);
friend istream&operator>>(istream&, Polynomial&);
friend Polynomial operator+(Polynomial&, Polynomial&);
friend Polynomial operator-(Polynomial&, Polynomial&);
Polynomial() { first = new Term(0, -10000000); }//构造函数，建立空链表
Polynomial(Polynomial&R);//复制构造函数
int maxOrder();//计算最大阶数
Term* find_place(int e);
bool inser_order(double c, int e);
Term*getHead()const { return first; };//取得单链表的头指针
//~Polynomial();
};
Polynomial x, y;
Term* Term::InsertAfter(double c, int e)
{
link = new Term(c, e, link);
return link;
}
ostream& operator<<(ostream& out, const Term&x)
{
if (x.coef == 0.0)return out;
out << x.coef;
switch (x.exp)
{
case 0:break;
case 1:out << "X"; break;
default:out << "X" << x.exp;
break;
}
return out;
}
Polynomial::Polynomial(Polynomial&R)
{
//复制构造函数
first = new Term(0, -1);
Term *destptrr = first, *srcptr = R.getHead()->link;
while (srcptr != NULL)
{
destptrr->InsertAfter(srcptr->coef, srcptr->exp);
srcptr = srcptr->link;
destptrr = destptrr->link;
}
}
int Polynomial::maxOrder()
{
//升序排序计算最大阶数，即为最后一项
Term*current = first;
while (current->link != NULL)
{
current = current->link;
}
return current->exp;
}
//寻找需要插入的位置，由inser_order(double c, int e)调用
Term* Polynomial::find_place(int e)
{
Term* current = first;
while (current->link!=NULL&¤t->link->exp<e)
{
current = current->link;
}
return current;
}
//插入，保持递增单链表
bool Polynomial::inser_order(double c, int e)
{
Term*current = find_place(e);
Term*temp=NULL;
//if (current == NULL) { AfxMessageBox(_T("插入出错！")); return false; }
Term* newnode= new Term(c, e, temp);
if (newnode == NULL) { AfxMessageBox(_T("插入出错！")); return false; }
newnode->link = current->link;
current->link = newnode;
return true;
}
istream& operator>>(istream&in, Polynomial& x)
{
//输入，尾插法建立多项式
Term* rear = x.getHead(); double c; int e;
while (true)
{
cout << "input a term(c,exp)" << endl;
in >> c >> e;
if (e < 0)break;
rear = rear->InsertAfter(c, e);
}
return in;
}
ostream& operator<<(ostream &out, Polynomial&x) {
Term*current = x.getHead()->link;//头指针为空，不输出
cout << "多项式:" << endl;
bool h = true;
while (current != NULL)
{
if (h == false && current->coef > 0)out << "+";
h = false;
out << *current;
current = current->link;
}
out << endl;
return out;
}
Polynomial operator+(Polynomial&A, Polynomial&B)
{
Term*pa, *pb, *pc, *p; double temp;
Polynomial C; pc = C.first;
pa = A.getHead()->link; pb = B.getHead()->link;
while (pa != NULL && pb != NULL)
{
if (pa->exp == pb->exp)
{
temp = pa->coef + pb->coef;
if (fabs(temp) > 0.0001)
pc = pc->InsertAfter(temp, pa->exp);
pa = pa->link; pb = pb->link;
}
else if (pa->exp < pb->exp) {
pc = pc->InsertAfter(pa->coef, pa->exp);
pa = pa->link;
}
else {
pc = pc->InsertAfter(pb->coef, pb->exp);
pb = pb->link;
}
}
if (pa != NULL)p = pa;
else p = pb;
while (p != NULL)
{
pc = pc->InsertAfter(p->coef, p->exp);
p = p->link;
}
return C;
}
Polynomial operator-(Polynomial&A, Polynomial&B)
{
Term*pa, *pb, *pc, *p; double temp;
Polynomial C; pc = C.first;
pa = A.getHead()->link; pb = B.getHead()->link;
while (pa != NULL && pb != NULL)
{
if (pa->exp == pb->exp)
{
temp = pa->coef-pb->coef;
if (fabs(temp) > 0.0001)
pc = pc->InsertAfter(temp, pa->exp);
pa = pa->link; pb = pb->link;
}
else if (pa->exp < pb->exp) {
pc = pc->InsertAfter(pa->coef, pa->exp);
pa = pa->link;
}
else {
pc = pc->InsertAfter(pb->coef*(-1), pb->exp);
pb = pb->link;
}
}
bool flag = true;
if (pa != NULL)p = pa;
else {
p = pb; flag = false;
}
while (p != NULL)
{
if(flag)
pc = pc->InsertAfter(p->coef, p->exp);
else pc = pc->InsertAfter(p->coef*(-1), p->exp);
p = p->link;
}
return C;
}
接下来实现计算器按钮的实现,下面是按钮1的相关代码，其他按钮类似
void CPolynomialDlg::OnBnClickedButton1()
{
UpdateData(true);//写入
CString str;
mEdit.GetWindowTextW(str);//得到编辑框的文字
str = str + _T("1");//CString后面加1
mEdit.SetWindowTextW(str);//编辑框显示更新内容
UpdateData(false);
// TODO: 在此添加控件通知处理程序代码
}
接下来是切换多项式的代码，并且读入一个多项式。处理思路是一次读入系数和指数，采取后插法实现单链表的建立。这里用到CString到double和int的转化，需要注意的是，转double会出现一些后导0，影响美观，需要去掉。我处理的麻烦了点，在大佬那知道了这个函数CString.Delete(CString.Getlength()-1,1)，就懒得改了。
void CPolynomialDlg::OnBnClickedButtonnext()
{
CString str;
CString temp, temp1, temp2, temp3;
mEdit.GetWindowTextW(str);
double c = 0; int e = 0;
int j; int i;
//Term* rear;
//if (flag) rear = y.getHead();
// else rear = x.getHead();
for (j = 0; j < str.GetLength(); j++)
{
temp = temp1 = temp2 = temp3 = "";
if (str[j] == ' ')continue;
c = 0; e = 0;
while (str[j] != ' '&&j < str.GetLength()) { temp += str[j]; j++; }
for (i = 0; i < temp.GetLength(); i++)
{
if (temp[i] != '.')temp1 += temp[i];
else break;
}
c += _ttof(temp1);//CString转double
i++;
for (i; i < temp.GetLength(); i++)
temp2 += temp[i];
if(c<0)
c -= _ttof(temp2) / pow(10, temp2.GetLength());
else c += _ttof(temp2) / pow(10, temp2.GetLength());
while(str[j]==' ')j++;
while (str[j] != ' '&&j < str.GetLength()) { temp3 += str[j]; j++; }
e = _ttoi(temp3);
//输入，尾插法建立多项式
// if (flag)
//rear = rear->InsertAfter(c, e);
if (!flag)x.inser_order(c, e);
else y.inser_order(c, e);
// rear->InsertAfter(c, e, y.first);
// else rear = rear->InsertAfter(c, e,x.first);
// else rear->InsertAfter(c, e, x.first);
}
if(!flag)
AfxMessageBox(_T("第一个表达式建立完毕！"));
else AfxMessageBox(_T("第二个表达式建立完毕！"));
mEdit.SetWindowTextW(_T(""));
flag = !flag;
// TODO: 在此添加控件通知处理程序代码
}
关键就是计算函数了，也就是确定按钮,这里用到了下拉框选择操作，用index判断即可。最后作为CString输出也有点格式优化，大家可以看一下。
void CPolynomialDlg::OnBnClickedOk()
{
// TODO: 在此添加控件通知处理程序代码
//CDialogEx::OnOK();
CString temp;
int index = combox.GetCurSel();
//combox.GetLBText(index, temp);
CString str;
Polynomial C;
if (index == 0)
C = x + y;
else
C = x-y;
Term*current = C.getHead()->link;//头指针为空，不输出
// cout << "多项式:" << endl;
bool h = true;
while (current != NULL)
{
if (h == false && current->coef > 0)str+='+';
h = false;
//str+= *current;
if (current->coef == 0.0)
continue;
CString strr, str0;
if (current->coef == 1.0&¤t->exp!=0);
else
{
strr.Format(_T("%3f"), current->coef);
int len = strr.GetLength();
int i;
for (i = len - 1; i >= 0; i--)
{
//小数点的处理
if (strr[i] == '0' || strr[i] == '.');
else break;
}
for (int j = 0; j <= i; j++)
str += strr[j];
}
switch (current->exp)//系数输出，0,1单独处理
{
case 0:break;
case 1:str+="X"; break;
default: {str += "X"; strr.Format(_T("%d"), current->exp); str += strr; }
break;
}
current = current->link;
}
n_Edit.SetWindowTextW(str);
}
最后的就是释放空间的按钮，以便实现多次运算，这里偷了个懒，一个小程序，就没有delete了,最好还是顺着单链表delete。
// CDialogEx::OnCancel();
n_Edit.SetWindowTextW(_T(""));//编辑框的清空
x.first = new Term(0, -1);
y.first = new Term(0, -1);