一元多项式的计算实验报告

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:开始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.classNode(public:Node();Node(floatc,inte,Node*next);~Node(){};floatcoef;〃系数intexp;〃指数Node*Next;〃指向下一项的指针friendclassPolynominal;};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(floatc,inte,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.classPolynominal(2.classPolynominal(public:Polynominal();Polynominal(Polynominal&a);voidGetMSG(CStringTempPloy);CStringOutput_Node();voidvoidvoidvoidvoidPolyAdd(Polynominal&a,Polynominal&b);PolySubtract(Polynominal&a,PolynominalPolyMultiply(Polynominal&a,PolynominalPolySort();〃排序函数，OutFile();//拷贝构造函数//获取由对话框输入的字符串并处理//输出最后结果〃加法&b);〃减法&b);〃乘法用于乘法之后的按指数排序//文本输出函数voidOutFile(Polynominal&a,Polynominal&b,stringch);〃重载文本输出函数voidOpposeCoef(Polynominal&a,Node*temp);//系数取反，用于减法运算NodetheList;〃头节点ofstreamFOut;//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=newNode(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)voidPolynominal::GetMSG(CStringTempPoly)(TempPoly.Remove(_T("));Node*TempNode=&theList;inti=0;for(i;i<TempPoly.GetLength();)(CStringtempi;CStringtemp2;intj=1;if(TempPoly.GetAt(i)==_T('-'))(tempi=tempi+TempPoly.GetAt(i);i++;}if(TempPoly.GetAt(i)==_T('+')){i++;}if(TempPoly.GetAt(i)==_T('x'))(tempi=tempi+_T('1');if(TempPoly.GetAt(i)!=_T('x')){tempi=tempi+TempPoly.GetAt(i);i++；}elsej=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');else(if(i==TempPoly.GetLength()&&TempPoly.GetAt(i-i)==_T('x'))temp2=temp2+_T('1');else(while(i<TempPoly.GetLength()&&TempPoly.GetAt(i)!=_T('+')&&TempPoly.GetAt(i)!=_T('-')){temp2=temp2+TempPoly.GetAt(i);i++;}}}TempNode->Next=newNode(_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)CStringPolynominal::Output_Node()(intfirst=0;CStringtemp;CStringtemp_coef;CStringtemp_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){case0:temp=temp+temp_coef;break;//指数为0则推出case1:if(TempNode->coef==1)〃指数为1则直接输出Xtemp=temp+_T(〃x〃)；elsetemp=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;elsetemp=temp+temp_coef+_T(〃x”〃)+temp_exp;break;}first=1;}returntemp;}输出函数，将计算所得结果输出到对话框。5)voidPolynominal::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=newNode(p->coef,p->exp,NULL);temp=temp->Next;p=p->Next;}elseif((p->exp)==(q->exp))(temp->Next=newNode(p->coef+q->coef,p->exp,NULL);temp=temp->Next;p=p->Next;q=q->Next;}elseif((p->exp)<(q->exp))(temp->Next=newNode(q->coef,q->exp,NULL);temp=temp->Next;q=q->Next;}}if(q!=NULL)(while(q!=NULL)(temp->Next=newNode(q->coef,q->exp,NULL);temp=temp->Next;q=q->Next;}}if(p!=NULL)(while(p!=NULL)(temp->Next=newNode(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)voidPolynominal::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)voidPolynominal::PolySubtract(Polynominal&a,Polynominal&b)(Node*temp=NULL;Polynominalaa=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)voidPolynominal::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=newNode((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)voidPolynominal::PolySort(){Polynominaltemp;inti=1;floattemp_coef=0;inttemp_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;}else(tempNode=tempNode->Next;tempNode2=tempNode2->Next;}}tempNode3->Next=newNode(temp_coef,temp_exp,NULL);tempNode3=tempNode3->Next;temp_coef=0;temp_exp=0;}else(i=0；}}Node*temp2=&theList;Node*temp3=temp.theList.Next;for(;temp3!=NULL;)(temp2->Next=newNode(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)voidPolynominal::OutFile()(FOut.open(〃PolynominalList.txt〃，ofstream::app);intfirst=1;Node*temp=theList.Next;FOut<<"(";for(;temp!=NULL;temp=temp->Next){if(!first&&temp->coef>0)FOut<<〃+〃;FOut<<temp->coef;switch(temp->exp){case0:break;//指数为0则推出case1:FOut<<〃x〃；break;〃指数为1则直接输出Xdefault:FOut<<〃x”〃<<temp->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)voidPolynominal::OutFile(Polynominal&a,Polynominal&b,stringch)(FOut.open(〃PolynominalList.txt〃，ofstream::app);intfirst=1;Node*temp=theList.Next;OutFile();FOut<<ch;OutFile();FOut<<"=(";for(;temp!=NULL;temp=temp->Next){if(!first&&temp->coef>0)FOut<<〃+〃;FOut<<temp->coef;switch(temp->exp){case0:break;//指数为0则推出case1:FOut<<〃x〃；break;〃指数为1则直接输出Xdefault:FOut<<〃x”〃<<temp->exp;break;//其余指数输出“X""形式}first=0;}FOut<<")";FOut<<〃\n\n〃；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1Nodefloatcoef;intexp;Node*Next;Node();Node(floatc,inte,Node*next);2PolynominalNodetheList;ofstreamFOut;Polynominal();Polynominal(Polynominal&a);voidGetMSG(CStringTempPloy);CStringOutput_Node();voidPolyAdd(Polynominal&a,Polynominal&b);voidPolySubtract(Polynominal&a,Polynominal&b);voidPolyMultiply(Polynominal&a,Polynominal&b);voidPolySort();voidOutFile();voidOutFile(Polynominal&a,Polynominal&b,stringch);voidOpposeCoef(Polynominal&a,Node*temp);3.2.类关系图友元classNodeclassPolynominal3.3.数据结构设计数据成员:1.ClassNode：floatintNode*友元classNodeclassPolynominal3.3.数据结构设计数据成员:1.ClassNode：floatintNode*coef;exp;Next;〃系数〃指数〃指向下一项的指制2.classPolynominalNodetheList;〃头节点ofstreamFOut;//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#define#ifndef#definePOLYNOMINA_HPOLYNOMINAH#include#include#include#include#include//拷贝构造函数//获取由对话框输入的字符串并处理//输出最后结果"Node.h”<string><afxstr.h><fstream><iostream>#include#include#include#include#include//拷贝构造函数//获取由对话框输入的字符串并处理//输出最后结果Polynominal();Polynominal(Polynominal&a);voidGetMSG(CStringTempPloy);CStringOutput_Node();voidPolyAdd(Polynominal&a,Polynominal&b);//加法voidPolySubtract(Polynominal&a,Polynominal&b);//减法voidPolyMultiply(Polynominal&a,Polynominal&b);//乘法voidPolySort();〃排序函数，用于乘法之后的按指数排序voidOutFile();//文本输出函数voidOutFile(Polynominal&a,Polynominal&b,stringch);//重载文本输出函数voidOpposeCoef(Polynominal&a,Node*temp);//系数取反，用于减法运算NodetheList;//头节点ofstreamFOut;〃输出流};#endif函数实现：#include"stdafx.h”#include"Polynominal.h”#include"conio.h"Polynominal::Polynominal()(}Polynominal::Polynominal(Polynominal&a)(Node*temp=a.theList.Next;Node*tempNode=&theList;for(;temp!=NULL;)(tempNode->Next=newNode(temp->coef,temp->exp,NULL);temp=temp->Next;tempNode=tempNode->Next;}}voidPolynominal::GetMSG(CStringTempPoly)(TempPoly.Remove(_T("));Node*TempNode=&theList;inti=0;for(i;i<TempPoly.GetLength();)(CStringtempi;CStringtemp2;intj=1;if(TempPoly.GetAt(i)==_T('-'))(tempi=tempi+TempPoly.GetAt(i);i++；}if(TempPoly.GetAt(i)==_T('+')){i++；}if(TempPoly.GetAt(i)==_T('x'))(tempi=tempi+_T('1');}while(j==1)(if(TempPoly.GetAt(i)!=_T('x')){tempi=tempi+TempPoly.GetAt(i);i++；}elsej=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');else(if(i==TempPoly.GetLength()&&TempPoly.GetAt(i-i)==_T('x'))temp2=temp2+_T('I');else(while(i<TempPoly.GetLength()&&TempPoly.GetAt(i)!=_T('+')&&TempPoly.GetAt(i)!=_T('-')){temp2=temp2+TempPoly.GetAt(i);i++；}}}TempNode->Next=newNode(_ttof(tempi),_ttoi(temp2),NULL);TempNode=TempNode->Next;}}CStringPolynominal::Output_Node()(intfirst=0;CStringtemp;CStringtemp_coef;CStringtemp_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)(case0:temp=temp+temp_coef;break;//指数为0则推出case1:if(TempNode->coef==1)〃指数为1则直接输出Xtemp=temp+_T(〃x〃)；elsetemp=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;elsetemp=temp+temp_coef+_T(〃x”〃)+temp_exp;break;}first=1;}returntemp;}voidPolynominal::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=newNode(p->coef,p->exp,NULL);temp=temp->Next;p=p->Next;}elseif((p->exp)==(q->exp))(temp->Next=newNode(p->coef+q->coef,p->exp,NULL);temp=temp->Next;p=p->Next;q=q->Next;}elseif((p->exp)<(q->exp))(temp->Next=newNode(q->coef,q->exp,NULL);temp=temp->Next;q=q->Next;}if(q!=NULL)(while(q!=NULL)(temp->Next=newNode(q->coef,q->exp,NULL);temp=temp->Next;q=q->Next;}}if(p!=NULL)(while(p!=NULL)(temp->Next=newNode(p->coef,p->exp,NULL);temp=temp->Next;p=p->Next;}}}voidPolynominal::OpposeCoef(Polynominal&a,Node*temp){temp=a.theList.Next;while(temp!=NULL)(temp->coef=-(temp->coef);temp=temp->Next;}}voidPolynominal::PolySubtract(Polynominal&a,Polynominal&b)(Node*temp=NULL;Polynominalaa=b;OpposeCoef(aa,temp);PolyAdd(a,aa);}voidPolynominal::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=newNode((p->coef*q->coef),(p->exp+q->exp),NULL);q=q->Next;temp=temp->Next;}p=p->Next;q=b.theList.Next;}PolySort();}voidPolynominal::PolySort(){Polynominaltemp;inti=1;floattemp_coef=0;inttemp_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;}else(tempNode=tempNode->Next;tempNode2=tempNode2->Next;}}tempNode3->Next=newNode(temp_coef,temp_exp,NULL);tempNode3=tempNode3->Next;temp_coef=0;