一元多项式的计算实验报告.doc

计算机学院工程实践一元多项式的计算 总 报 告小组序号：编 撰 人：年 级 班 级：指导教师：提交日期：1. 项目组成员分工表 1 项目组成员分工2. 程序功能(程序实现的功能，功能结构图)实现功能：一元多项式的加、减、乘运算功能结构图：3. 程序设计简介(包括：类及其属性和方法、类之间关系、关键代码等的说明)1.class Nodepublic:Node();Node(float c, int e, Node* next);Node();float coef; /系数int exp; /指数Node* Next; /指向下一项的指针friend class Polynominal;节点类，储存一元多项式每一项的信息。该内含有两个构造函数，一个析构函数及存储系数、指数和Next指针等成员变量。与Polynominal是友元关系，允许Polynominal的访问。具体成员函数如下：1)Node:Node() 默认构造函数。2)Node:Node(float c, int e, Node* next)coef = c;exp = e;Next = next;重载的自定义构造函数，用于给成员变量coef、exp和Next存入数据，Next指向传参来的next指针指向的地址，用于构造链表。2.class Polynominalpublic:Polynominal();Polynominal(Polynominal &a); /拷贝构造函数void GetMSG(CString TempPloy); /获取由对话框输入的字符串并处理CString Output_Node(); /输出最后结果void PolyAdd(Polynominal &a, Polynominal &b); /加法void PolySubtract(Polynominal &a, Polynominal &b); /减法void PolyMultiply(Polynominal &a, Polynominal &b); /乘法void PolySort(); /排序函数，用于乘法之后的按指数排序void OutFile(); /文本输出函数void OutFile(Polynominal &a, Polynominal &b, string ch); /重载文本输出函数void OpposeCoef(Polynominal &a, Node *temp); /系数取反，用于减法运算Node theList; /头节点 ofstream FOut; /输出流;此类用于构造一元多项式。包括加、减、乘各各功能函数，还有两个帮助运算的辅助函数，以及界面输入输出和文本输出函数。成员变量有头节点和输出流。具体成员函数如下：1)Polynominal:Polynominal()默认构造函数2)Polynominal:Polynominal(Polynominal &a)Node* temp = a.theList.Next;Node* tempNode = &theList;for (; temp != NULL;)tempNode-Next = new Node(temp-coef, temp-exp, NULL);temp = temp-Next;tempNode = tempNode-Next;拷贝构造函数，用于计算时对象间的赋值，防止误改数据。3)void Polynominal:GetMSG(CString TempPoly)TempPoly.Remove(_T();Node* TempNode = &theList;int i = 0;for (i;iTempPoly.GetLength(); )CString temp1 ;CString temp2 ;int j = 1;if (TempPoly.GetAt(i) =_T(-)temp1 = temp1 + TempPoly.GetAt(i);i+;if (TempPoly.GetAt(i) = _T(+)i+;if (TempPoly.GetAt(i) = _T(x) )temp1 = temp1 +_T(1);while(j=1)if (TempPoly.GetAt(i) != _T(x)temp1 = temp1 + TempPoly.GetAt(i);i+;else j=0;i+;if (i (TempPoly.GetLength()-1) & TempPoly.GetAt(i) = _T(-)temp2 = temp2 + TempPoly.GetAt(i);i+;if (i = (TempPoly.GetLength()-1) & TempPoly.GetAt(i) = _T(x)temp2 = temp2 + _T(1);elseif (i = TempPoly.GetLength() & TempPoly.GetAt(i-1) = _T(x)temp2 = temp2 + _T(1);elsewhile (i Next = new Node(_ttof(temp1), _ttoi(temp2), NULL); /链表构建TempNode = TempNode-Next;此函数用于把从对话框获取的字符串进行处理，截取出多项式各项系数和指数，并转换为float型和int型，构造一元多项式链表。4)CString Polynominal:Output_Node()int first = 0;CString temp;CString temp_coef;CString temp_exp;Node* TempNode = theList.Next;for (; TempNode != NULL; TempNode = TempNode-Next)if (first = 1 & TempNode-coef 0) temp = temp + _T(+) ;temp_coef.Format(_T(%g), TempNode-coef);temp_exp.Format(_T(%d),TempNode-exp);switch (TempNode-exp)case 0:temp = temp + temp_coef; break; /指数为0则推出case 1:if (TempNode-coef=1)/指数为1则直接输出Xtemp = temp + _T(x); else temp = temp + temp_coef + _T(x); break; default:if (TempNode-coef = 1) /其余指数输出“X”形式 temp = temp + _T(x)+temp_exp;else temp = temp + temp_coef + _T(x)+temp_exp; break; first = 1;return temp;输出函数，将计算所得结果输出到对话框。5)void Polynominal:PolyAdd(Polynominal &a, Polynominal &b)Node *p, *q, *temp;temp = &theList;p = a.theList.Next;q = b.theList.Next;while (p != NULL & q != NULL)if (p-exp) (q-exp)temp-Next = new Node(p-coef, p-exp, NULL);temp = temp-Next;p = p-Next;else if (p-exp) = (q-exp)temp-Next = new Node(p-coef + q-coef, p-exp, NULL);temp = temp-Next;p = p-Next;q = q-Next;else if (p-exp) exp)temp-Next = new Node(q-coef, q-exp, NULL);temp = temp-Next;q = q-Next;if (q != NULL)while (q != NULL)temp-Next = new Node(q-coef, q-exp, NULL);temp = temp-Next;q = q-Next;if (p != NULL)while (p != NULL)temp-Next = new Node(p-coef, p-exp, NULL);temp = temp-Next;p = p-Next;加法函数，实现多项式的相加。在其中需要判断各项指数的关系，已实现按指数大小关系构建链表。6)void Polynominal:OpposeCoef(Polynominal &a, Node *temp)temp = a.theList.Next;while (temp != NULL)temp-coef = -(temp-coef);temp = temp-Next;在执行减法操作时，用此函数将被减多项式各位系数取反，之后可直接调用加法函数进行运算；7)void Polynominal:PolySubtract(Polynominal &a, Polynominal &b)Node* temp = NULL;Polynominal aa = b;OpposeCoef(aa, temp);PolyAdd(a, aa);减法函数。先调用系数取反函数，再调用加法函数，可直接实现减法功能。其中为了不改变被减多项式的各项值，在此调用拷贝构造函数创建临时对象用于计算。8)void Polynominal:PolyMultiply(Polynominal &a, Polynominal &b)Node *p, *q, *temp;temp = &theList;p = a.theList.Next;q = b.theList.Next;while (p != NULL)while (q != NULL)temp-Next = new Node(p-coef*q-coef), (p-exp + q-exp), NULL);q = q-Next;temp = temp-Next;p = p-Next;q = b.theList.Next;PolySort();乘法函数。按项相乘，运算完之后，再调用排序函数，实现同指数项系数相加，并按照指数大小输出。9)void Polynominal:PolySort()Polynominal temp;int i = 1;float temp_coef = 0;int temp_exp = 0;Node* tempNode = theList.Next;Node* tempNode2 = &theList;Node* tempNode3 = &temp.theList;while (i = 1)tempNode = theList.Next;tempNode2 = &theList;for (; tempNode != NULL;)if (tempNode-exp temp_exp)temp_exp = tempNode-exp;tempNode = tempNode-Next;tempNode = theList.Next;if (tempNode != NULL)for (; tempNode != NULL;)if (tempNode-exp = temp_exp)temp_coef = temp_coef + tempNode-coef;tempNode2-Next = tempNode-Next;tempNode = tempNode-Next;elsetempNode = tempNode-Next;tempNode2 = tempNode2-Next;tempNode3-Next = new Node(temp_coef, temp_exp, NULL);tempNode3 = tempNode3-Next;temp_coef = 0;temp_exp = 0;elsei = 0;Node* temp2 = &theList;Node* temp3 = temp.theList.Next;for (; temp3 != NULL;)temp2-Next = new Node(temp3-coef, temp3-exp, NULL);temp2 = temp2-Next;temp3 = temp3-Next;实现相乘之后的排序，是最后的链表按照指数大小排列，并且每个指数只有一项。10)void Polynominal:OutFile()FOut.open(PolynominalList.txt, ofstream:app);int first = 1;Node* temp = theList.Next;FOut Next)if (!first&temp-coef 0)FOut +;FOut coef;switch (temp-exp)case 0:break; /指数为0则推出case 1:FOut x; break; /指数为1则直接输出Xdefault:FOut x exp; break; /其余指数输出“X”形式first = 0;FOut ) ;FOut.close();文本输出函数，用于两个多项式的文本输出。11)void Polynominal:OutFile(Polynominal &a, Polynominal &b, string ch)FOut.open(PolynominalList.txt, ofstream:app);int first = 1;Node* temp = theList.Next;a.OutFile();FOut ch;b.OutFile();FOut Next)if (!first&temp-coef 0)FOut +;FOut coef;switch (temp-exp)case 0:break; /指数为0则推出case 1:FOut x; break; /指数为1则直接输出Xdefault:FOut x exp; break; /其余指数输出“X”形式first = 0;FOut ) ;FOut nn;FOut.close();重载文本输出函数，用于最后结果的一次性文本输出。3.1. 类设计表 2 类表序号类名属性方法1Nodefloat coef; int exp; Node* Next; Node();Node(float c, int e, Node* next);2PolynominalNode theList; ofstream FOut; Polynominal();Polynominal(Polynominal &a); void GetMSG(CString TempPloy); CString Output_Node(); void PolyAdd(Polynominal &a, Polynominal &b); void PolySubtract(Polynominal &a, Polynominal &b); void PolyMultiply(Polynominal &a, Polynominal &b); void PolySort(); void OutFile(); void OutFile(Polynominal &a, Polynominal &b, string ch); void OpposeCoef(Polynominal &a, Node *temp); 3.2. 类关系图3.3. 数据结构设计数据成员：1.Class Node：float coef; /系数int exp; /指数Node* Next; /指向下一项的指针2.class PolynominalNode theList; /头节点 ofstream FOut; /输出流此类中theList是头节点，其成员变量Next指向新建节点，构造成链表。3.4. 关键代码与运行界面关键代码：#ifndef POLYNOMINA_H#define POLYNOMINA_H#include Node.h#include #include #include #include using namespace std;class Polynominalpublic:Polynominal();Polynominal(Polynominal &a); /拷贝构造函数void GetMSG(CString TempPloy); /获取由对话框输入的字符串并处理CString Output_Node(); /输出最后结果void PolyAdd(Polynominal &a, Polynominal &b); /加法void PolySubtract(Polynominal &a, Polynominal &b); /减法void PolyMultiply(Polynominal &a, Polynominal &b); /乘法void PolySort(); /排序函数，用于乘法之后的按指数排序void OutFile(); /文本输出函数void OutFile(Polynominal &a, Polynominal &b, string ch); /重载文本输出函数void OpposeCoef(Polynominal &a, Node *temp); /系数取反，用于减法运算Node theList; /头节点 ofstream FOut; /输出流;#endif函数实现：#include stdafx.h#include Polynominal.h#include conio.hPolynominal:Polynominal()Polynominal:Polynominal(Polynominal &a)Node* temp = a.theList.Next;Node* tempNode = &theList;for (; temp != NULL;)tempNode-Next = new Node(temp-coef, temp-exp, NULL);temp = temp-Next;tempNode = tempNode-Next;void Polynominal:GetMSG(CString TempPoly)TempPoly.Remove(_T();Node* TempNode = &theList;int i = 0;for (i;iTempPoly.GetLength(); )CString temp1 ;CString temp2 ;int j = 1;if (TempPoly.GetAt(i) =_T(-)temp1 = temp1 + TempPoly.GetAt(i);i+;if (TempPoly.GetAt(i) = _T(+)i+;if (TempPoly.GetAt(i) = _T(x) )temp1 = temp1 +_T(1);while(j=1)if (TempPoly.GetAt(i) != _T(x)temp1 = temp1 + TempPoly.GetAt(i);i+;else j=0;i+;if (i (TempPoly.GetLength()-1) & TempPoly.GetAt(i) = _T(-)temp2 = temp2 + TempPoly.GetAt(i);i+;if (i = (TempPoly.GetLength()-1) & TempPoly.GetAt(i) = _T(x)temp2 = temp2 + _T(1);elseif (i = TempPoly.GetLength() & TempPoly.GetAt(i-1) = _T(x)temp2 = temp2 + _T(1);elsewhile (i Next = new Node(_ttof(temp1), _ttoi(temp2), NULL);TempNode = TempNode-Next;CString Polynominal:Output_Node()int first = 0;CString temp;CString temp_coef;CString temp_exp;Node* TempNode = theList.Next;for (; TempNode != NULL; TempNode = TempNode-Next)if (first = 1 & TempNode-coef 0) temp = temp + _T(+) ;temp_coef.Format(_T(%g), TempNode-coef);temp_exp.Format(_T(%d),TempNode-exp);switch (TempNode-exp)case 0:temp = temp + temp_coef; break; /指数为0则推出case 1:if (TempNode-coef=1)/指数为1则直接输出Xtemp = temp + _T(x); else temp = temp + temp_coef + _T(x); break; default:if (TempNode-coef = 1) /其余指数输出“X”形式 temp = temp + _T(x)+temp_exp;else temp = temp + temp_coef + _T(x)+temp_exp; break; first = 1;return temp;void Polynominal:PolyAdd(Polynominal &a, Polynominal &b)Node *p, *q, *temp;temp = &theList;p = a.theList.Next;q = b.theList.Next;while (p != NULL & q != NULL)if (p-exp) (q-exp)temp-Next = new Node(p-coef, p-exp, NULL);temp = temp-Next;p = p-Next;else if (p-exp) = (q-exp)temp-Next = new Node(p-coef + q-coef, p-exp, NULL);temp = temp-Next;p = p-Next;q = q-Next;else if (p-exp) exp)temp-Next = new Node(q-coef, q-exp, NULL);temp = temp-Next;q = q-Next;if (q != NULL)while (q != NULL)temp-Next = new Node(q-coef, q-exp, NULL);temp = temp-Next;q = q-Next;if (p != NULL)while (p != NULL)temp-Next = new Node(p-coef, p-exp, NULL);temp = temp-Next;p = p-Next;void Polynominal:OpposeCoef(Polynominal &a, Node *temp)temp = a.theList.Next;while (temp != NULL)temp-coef = -(temp-coef);temp = temp-Next;void Polynominal:PolySubtract(Polynominal &a, Polynominal &b)Node* temp = NULL;Polynominal aa = b;OpposeCoef(aa, temp);PolyAdd(a, aa);void Polynominal:PolyMultiply(Polynominal &a, Polynominal &b)Node *p, *q, *temp;temp = &theList;p = a.theList.Next;q = b.theList.Next;while (p != NULL)while (q != NULL)temp-Next = new Node(p-coef*q-coef), (p-exp + q-exp), NULL);q = q-Next;temp = temp-Next;p = p-Next;q = b.theList.Next;PolySort();void Polynominal:PolySort()Polynominal temp;int i = 1;float temp_coef = 0;int temp_exp = 0;Node* tempNode = theList.Next;Node* tempNode2 = &theList;Node* tempNode3 = &temp.theList;while (i = 1)tempNode = theList.Next;tempNode2 = &theList;for (; tempNode != NULL;)if (tempNode-exp temp_exp)temp_exp = tempNode-exp;tempNode = tempNode-Next;tempNode = theList.Next;if (tempNode != NULL)for (; tempNode != NULL;)if (tempNode-exp = temp_exp)temp_coef = temp_coef + tempNode-coef;tempNode2-Next = tempNode-Next;tempNode = tempNode-Next;elsetempNode = tempNode-Next;tempNode2 = tempNode2-Next;tempNode3-Ne