MFC实现一元稀疏多项式运算器

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&&current->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&&current->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);

欢迎大家纠正错误，完整代码见GitHub链接，主要是了解MFC框架即可。