一元多項式的計算實驗報告

1、計算機學院工程實踐一元多項式的計算 總 報 告小組序號：編 撰 人：年 級 班 級：指導教師：提交日期：1. 項目組成員分工表 1 項目組成員分工2. 程序功能(程序?qū)崿F(xiàn)的功能，功能結(jié)構(gòu)圖)實現(xiàn)功能：一元多項式的加、減、乘運算功能結(jié)構(gòu)圖：3. 程序設(shè)計簡介(包括：類及其屬性和方法、類之間關(guān)系、關(guān)鍵代碼等的說明)1.class Nodepublic:Node();Node(float c, int e, Node* next);Node();float coef; /系數(shù)int exp; /指數(shù)Node* Next; /指向下一項的指針friend class Polynominal;節(jié)點類，儲

2、存一元多項式每一項的信息。該內(nèi)含有兩個構(gòu)造函數(shù)，一個析構(gòu)函數(shù)及存儲系數(shù)、指數(shù)和Next指針等成員變量。與Polynominal是友元關(guān)系，允許Polynominal的訪問。具體成員函數(shù)如下：1)Node:Node() 默認構(gòu)造函數(shù)。2)Node:Node(float c, int e, Node* next)coef = c;exp = e;Next = next;重載的自定義構(gòu)造函數(shù)，用于給成員變量coef、exp和Next存入數(shù)據(jù)，Next指向傳參來的next指針指向的地址，用于構(gòu)造鏈表。2.class Polynominalpublic:Polynominal();Polynominal

3、(Polynominal &a); /拷貝構(gòu)造函數(shù)void GetMSG(CString TempPloy); /獲取由對話框輸入的字符串并處理CString Output_Node(); /輸出最后結(jié)果void PolyAdd(Polynominal &a, Polynominal &b); /加法void PolySubtract(Polynominal &a, Polynominal &b); /減法void PolyMultiply(Polynominal &a, Polynominal &b); /乘法void PolySort

4、(); /排序函數(shù)，用于乘法之后的按指數(shù)排序void OutFile(); /文本輸出函數(shù)void OutFile(Polynominal &a, Polynominal &b, string ch); /重載文本輸出函數(shù)void OpposeCoef(Polynominal &a, Node *temp); /系數(shù)取反，用于減法運算Node theList; /頭節(jié)點 ofstream FOut; /輸出流;此類用于構(gòu)造一元多項式。包括加、減、乘各各功能函數(shù)，還有兩個幫助運算的輔助函數(shù)，以及界面輸入輸出和文本輸出函數(shù)。成員變量有頭節(jié)點和輸出流。具體成員函數(shù)如下：1)P

5、olynominal:Polynominal()默認構(gòu)造函數(shù)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;拷貝構(gòu)造函數(shù)，用于計算時對象間的賦值，防止誤改數(shù)據(jù)。3)void

6、 Polynominal:GetMSG(CString TempPoly)TempPoly.Remove(_T('');Node* TempNode = &theList;int i = 0;for (i;i<TempPoly.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+;

7、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 = (Te

8、mpPoly.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 < TempPoly.GetLength() && TempPoly.GetAt(i) != _T('+')

9、&& TempPoly.GetAt(i) != _T('-')temp2 = temp2 + TempPoly.GetAt(i);i+;TempNode->Next = new Node(_ttof(temp1), _ttoi(temp2), NULL); /鏈表構(gòu)建TempNode = TempNode->Next;此函數(shù)用于把從對話框獲取的字符串進行處理，截取出多項式各項系數(shù)和指數(shù)，并轉(zhuǎn)換為float型和int型，構(gòu)造一元多項式鏈表。4)CString Polynominal:Output_Node()int first = 0;CString

10、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"),T

11、empNode->exp);switch (TempNode->exp)case 0:temp = temp + temp_coef; break; /指數(shù)為0則推出case 1:if (TempNode->coef=1)/指數(shù)為1則直接輸出Xtemp = temp + _T("x"); else temp = temp + temp_coef + _T("x"); break; default:if (TempNode->coef = 1) /其余指數(shù)輸出“X”形式 temp = temp + _T("x")

12、+temp_exp;else temp = temp + temp_coef + _T("x")+temp_exp; break; first = 1;return temp;輸出函數(shù)，將計算所得結(jié)果輸出到對話框。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

13、 (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) < (q-&g

14、t;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

15、);temp = temp->Next;p = p->Next;加法函數(shù)，實現(xiàn)多項式的相加。在其中需要判斷各項指數(shù)的關(guān)系，已實現(xiàn)按指數(shù)大小關(guān)系構(gòu)建鏈表。6)void Polynominal:OpposeCoef(Polynominal &a, Node *temp)temp = a.theList.Next;while (temp != NULL)temp->coef = -(temp->coef);temp = temp->Next;在執(zhí)行減法操作時，用此函數(shù)將被減多項式各位系數(shù)取反，之后可直接調(diào)用加法函數(shù)進行運算；7)void Polynominal:

16、PolySubtract(Polynominal &a, Polynominal &b)Node* temp = NULL;Polynominal aa = b;OpposeCoef(aa, temp);PolyAdd(a, aa);減法函數(shù)。先調(diào)用系數(shù)取反函數(shù)，再調(diào)用加法函數(shù)，可直接實現(xiàn)減法功能。其中為了不改變被減多項式的各項值，在此調(diào)用拷貝構(gòu)造函數(shù)創(chuàng)建臨時對象用于計算。8)void Polynominal:PolyMultiply(Polynominal &a, Polynominal &b)Node *p, *q, *temp;temp = &th

17、eList;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();乘法函數(shù)。按項相乘，運算完之后，再調(diào)用排序函數(shù)，實現(xiàn)同指數(shù)項系數(shù)相加，并按照指數(shù)大小輸出。9)void Polynomin

18、al: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

19、_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;te

20、mpNode2 = 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);te

21、mp2 = temp2->Next;temp3 = temp3->Next;實現(xiàn)相乘之后的排序，是最后的鏈表按照指數(shù)大小排列，并且每個指數(shù)只有一項。10)void Polynominal:OutFile()FOut.open("PolynominalList.txt", ofstream:app);int first = 1;Node* temp = theList.Next;FOut << " ( "for (; temp != NULL; temp = temp->Next)if (!first&&tem

22、p->coef > 0)FOut << "+"FOut << temp->coef;switch (temp->exp)case 0:break; /指數(shù)為0則推出case 1:FOut << "x" break; /指數(shù)為1則直接輸出Xdefault:FOut << "x" << temp->exp; break; /其余指數(shù)輸出“X”形式first = 0;FOut << " ) "FOut.close();文

23、本輸出函數(shù)，用于兩個多項式的文本輸出。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 << " = ( "for (; temp != NULL; temp = temp-&

24、gt;Next)if (!first&&temp->coef > 0)FOut << "+"FOut << temp->coef;switch (temp->exp)case 0:break; /指數(shù)為0則推出case 1:FOut << "x" break; /指數(shù)為1則直接輸出Xdefault:FOut << "x" << temp->exp; break; /其余指數(shù)輸出“X”形式first = 0;FOut <<

25、; " ) "FOut << "nn"FOut.close();重載文本輸出函數(shù)，用于最后結(jié)果的一次性文本輸出。3.1. 類設(shè)計表 2 類表序號類名屬性方法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);

26、 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 O

27、pposeCoef(Polynominal &a, Node *temp); 3.2. 類關(guān)系圖3.3. 數(shù)據(jù)結(jié)構(gòu)設(shè)計數(shù)據(jù)成員：1.Class Node：float coef; /系數(shù)int exp; /指數(shù)Node* Next; /指向下一項的指針2.class PolynominalNode theList; /頭節(jié)點 ofstream FOut; /輸出流此類中theList是頭節(jié)點，其成員變量Next指向新建節(jié)點，構(gòu)造成鏈表。3.4. 關(guān)鍵代碼與運行界面關(guān)鍵代碼：#ifndef POLYNOMINA_H#define POLYNOMINA_H#include "Nod

28、e.h"#include <string>#include <afxstr.h>#include <fstream>#include <iostream>using namespace std;class Polynominalpublic:Polynominal();Polynominal(Polynominal &a); /拷貝構(gòu)造函數(shù)void GetMSG(CString TempPloy); /獲取由對話框輸入的字符串并處理CString Output_Node(); /輸出最后結(jié)果void PolyAdd(Polyno

29、minal &a, Polynominal &b); /加法void PolySubtract(Polynominal &a, Polynominal &b); /減法void PolyMultiply(Polynominal &a, Polynominal &b); /乘法void PolySort(); /排序函數(shù)，用于乘法之后的按指數(shù)排序void OutFile(); /文本輸出函數(shù)void OutFile(Polynominal &a, Polynominal &b, string ch); /重載文本輸出函數(shù)void O

30、pposeCoef(Polynominal &a, Node *temp); /系數(shù)取反，用于減法運算Node theList; /頭節(jié)點 ofstream FOut; /輸出流;#endif函數(shù)實現(xiàn)：#include "stdafx.h"#include "Polynominal.h"#include "conio.h"Polynominal:Polynominal()Polynominal:Polynominal(Polynominal &a)Node* temp = a.theList.Next;Node* te

31、mpNode = &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;i<TempPoly.GetLength(

32、); )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 + T

33、empPoly.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() &&

34、amp; TempPoly.GetAt(i-1) = _T('x')temp2 = temp2 + _T('1');elsewhile (i < TempPoly.GetLength() && TempPoly.GetAt(i) != _T('+') && TempPoly.GetAt(i) != _T('-')temp2 = temp2 + TempPoly.GetAt(i);i+;TempNode->Next = new Node(_ttof(temp1), _ttoi(temp2)

35、, 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("+") ;

36、temp_coef.Format(_T("%g"), TempNode->coef);temp_exp.Format(_T("%d"),TempNode->exp);switch (TempNode->exp)case 0:temp = temp + temp_coef; break; /指數(shù)為0則推出case 1:if (TempNode->coef=1)/指數(shù)為1則直接輸出Xtemp = temp + _T("x"); else temp = temp + temp_coef + _T("x&qu

37、ot;); break; default:if (TempNode->coef = 1) /其余指數(shù)輸出“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.t

38、heList.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 = tem

39、p->Next;p = p->Next;q = q->Next;else if (p->exp) < (q->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 != NUL

40、L)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(Polyno

41、minal &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

42、= 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;N

43、ode* 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->

44、;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(t