n元多项式乘法功能：完成两个n元多项式作乘法,给出明确的等式形式.分步实施：1． 初步完成总体设计,搭好框架,确定人机对话的界面,确定函数个数；2． 完成最低要求：建立一个文件,实现

n元多项式乘法功能：完成两个n元多项式作乘法,给出明确的等式形式.分步实施：1． 初步完成总体设计,搭好框架,确定人机对话的界面,确定函数个数；2． 完成最低要求：建立一个文件,实现
n元多项式乘法
功能：完成两个n元多项式作乘法,给出明确的等式形式.
分步实施：
1． 初步完成总体设计,搭好框架,确定人机对话的界面,确定函数个数；
2． 完成最低要求：建立一个文件,实现两个一元二次多项式作乘法.
3． 进一步要求：实现三元二次多项式的乘法.有兴趣的同学可以自己扩充系统功能.
要求：1）界面友好,函数功能要划分好
2）总体设计应画一流程图
3）程序要加必要的注释
4）要提供程序测试方案
5）程序一定要经得起测试,宁可功能少一些,也要能运行起来,不能运行的程序是没有价值的.

n元多项式乘法功能：完成两个n元多项式作乘法,给出明确的等式形式.分步实施：1． 初步完成总体设计,搭好框架,确定人机对话的界面,确定函数个数；2． 完成最低要求：建立一个文件,实现
是用c语言实现的
/*
* 文件名: 1_3.c(选做题)
* 实验环境: Turbo C 2.0
* 完成时间: 2003年2月22日
*--------------------------------------------------------------------
* 改进说明: 可以实现多个多项式的加法、减法、乘法,并且比书中算法更加
* 合理. 例如: 连加a+b+c+d,连减a-b-c-d,连乘a*b*c*d.
*/
#include
#include
#include
#include
#define TRUE 1
#define FALSE 0
#define POSITIVE 1
#define NEGATIVE -1
typedef int status;
typedef struct NodeType
{
float fCoeff;
int iExpon;
struct NodeType *next;
} NodeType, *LinkType;
typedef LinkType polynomial;
typedef polynomial *PolyPointer;
status MakePolyBuff(PolyPointer *, const int);
status MakeNode(polynomial *, const float, const int);
void AppNodeToList(polynomial *, polynomial); /* 在链表尾追加结点 */
status CreatePolyn(PolyPointer, int);
status ProcStrError(const char[]); /* 检查输入的数据 */
void SortPolyn(PolyPointer, int); /* 根据iExpon域对链表进行升序排序 */
void DestroyBuff(PolyPointer, const int);
void DestroyPolyn(polynomial);
int PolynLength(const polynomial); /* 求链表的长度 */
void AddProcess(PolyPointer, const int, PolyPointer, const int);
void SubstractProcess(PolyPointer, const int, PolyPointer);
void MultiplyProcess(PolyPointer, const int, PolyPointer);
void PrintPolyn(const polynomial);
void MergePolynCoeff(PolyPointer, int); /* 在有序链表中,合并同类项 */
int main(void)
{
int iCounter,
iPolyNum; /* 多项式链表缓冲区中链表的个数 */
PolyPointer PolyBuff = NULL; /* 用户输入的多项式链表缓冲区 */
polynomial PolyAddRes = NULL, /* 存放连加结果链表 */
PolySubRes = NULL, /* 存放连减结果链表 */
PolyMulRes = NULL; /* 存放连乘结果链表 */
char strNum[10];
do
{
printf("请输入需要构造多项式的个数,至少2个: ");
gets(strNum);
iPolyNum = atoi(strNum);
} while (iPolyNum < 2);
MakePolyBuff(&PolyBuff, iPolyNum);
CreatePolyn(PolyBuff, iPolyNum);
SortPolyn(PolyBuff, iPolyNum);
MergePolynCoeff(PolyBuff, iPolyNum);
printf("\n打印用户输入并整合后的多项式:\n");
for (iCounter = 0; iCounter < iPolyNum; iCounter++)
{
printf("第%d个项式:\n", iCounter + 1);
PrintPolyn(*(PolyBuff + iCounter));
}
AddProcess(PolyBuff, iPolyNum, &PolyAddRes, POSITIVE);
printf("\n----------------连加结果-----------------\n");
PrintPolyn(PolyAddRes);
SubstractProcess(PolyBuff, iPolyNum, &PolySubRes);
printf("\n----------------连减结果-----------------\n");
PrintPolyn(PolySubRes);
MultiplyProcess(PolyBuff, iPolyNum, &PolyMulRes);
printf("\n----------------连乘结果-----------------\n");
PrintPolyn(PolyMulRes);
printf("\n运行完毕!\n");
/* 回收资源 */
DestroyBuff(PolyBuff, iPolyNum);
DestroyPolyn(PolyAddRes);
DestroyPolyn(PolySubRes);
DestroyPolyn(PolyMulRes);
getch();
return 0;
}
status MakePolyBuff(PolyPointer *polyBuffHead, const int iPolyNum)
{
int iCounter;
*polyBuffHead = (PolyPointer)
malloc(sizeof(polynomial) * iPolyNum);
if (!(*polyBuffHead))
{
printf("错误,内存溢出!\n");
return FALSE;
}
for (iCounter = 0; iCounter < iPolyNum; iCounter++)
*(*polyBuffHead + iCounter) = NULL;
return TRUE;
}
status CreatePolyn(PolyPointer PolyBuff, int iPolyNum)
{
int iCounter, iExpon;
float fCoeff;
char strNum[100], strTemp[64], *cpCurr, *cpCurrNum;
polynomial pNewNode = NULL, pInsPos = NULL;
printf("\n请输入构造多项式的系数和指数...\n");
printf("输入一个多项式的方式为: 系数, 指数; ... ; 系数, 指数;\n例如: 3, 4; 5, 6; 7, 8;\n");
for (iCounter = 0; iCounter < iPolyNum; iCounter++)
{
printf("\n请输入第%d个多项式:\n", iCounter + 1);
gets(strNum);
if(!ProcStrError(strNum)) return FALSE;
cpCurr = cpCurrNum = strNum;
while (*cpCurr != '\0')
{
if (*cpCurr == ',')
{
strncpy(strTemp, cpCurrNum, cpCurr - cpCurrNum);
strTemp[cpCurr - cpCurrNum] = '\0';
fCoeff = (float)atof(strTemp);
cpCurrNum = cpCurr + 1;
}
else if (*cpCurr == ';')
{
strncpy(strTemp, cpCurrNum, cpCurr - cpCurrNum);
strTemp[cpCurr - cpCurrNum] = '\0';
iExpon = atoi(strTemp);
MakeNode(&pNewNode, fCoeff, iExpon);
AppNodeToList(PolyBuff + iCounter, pNewNode);
cpCurrNum = cpCurr + 1;
}
cpCurr++;
}
}
return TRUE;
}
status MakeNode(LinkType *pp, const float coeff, const int expon)
{
if (!(*pp = (LinkType)malloc(sizeof(NodeType) * 1)))
{
printf("Error, the memory is overflow!\n");
return FALSE;
}
(*pp)->fCoeff = coeff;
(*pp)->iExpon = expon;
(*pp)->next = NULL;
return TRUE;
}
void AppNodeToList(polynomial *pHead, polynomial pNewNode)
{
static polynomial pCurrNode;
if (!(*pHead))
(*pHead) = pCurrNode = pNewNode;
else
{
pCurrNode->next = pNewNode;
pCurrNode = pCurrNode->next;
}
}
void SortPolyn(PolyPointer PolyBuff, int iPolyNum)
{
int iCounter;
polynomial pTemp, pTempCurrNode, /* 临时链表 */
pPrevMinExp, pCurrMinExp,/* 指向最小iExpon结点的指针 */
pCurrNode, pPrevNode;
for (iCounter = 0; iCounter < iPolyNum; iCounter++)
{
pTemp = NULL;
while (*(PolyBuff + iCounter) != NULL)
{
pPrevNode = pPrevMinExp = pCurrMinExp =
*(PolyBuff + iCounter);
pCurrNode = (*(PolyBuff + iCounter))->next;
while (pCurrNode != NULL)
{
if (pCurrMinExp->iExpon > pCurrNode->iExpon)
{
pPrevMinExp = pPrevNode;
pCurrMinExp = pCurrNode;
}
pPrevNode = pCurrNode;
pCurrNode = pCurrNode->next;
}
/* 将系数最小的结点从原链表中取出 */
if (pCurrMinExp == *(PolyBuff + iCounter))
*(PolyBuff + iCounter) = pPrevMinExp->next;
else
pPrevMinExp->next = pCurrMinExp->next;
/* 将系数最小的结点插入升序链表 */
pCurrMinExp->next = NULL;
if (!pTemp)
pTemp = pTempCurrNode = pCurrMinExp;
else
{
pTempCurrNode->next = pCurrMinExp;
pTempCurrNode = pTempCurrNode->next;
}
}
*(PolyBuff + iCounter) = pTemp;
}
}
void MergePolynCoeff(PolyPointer PolyBuff, int iPolyNum)
{
int iCounter;
float MergeCoeffRes = 0;
polynomial TempList, ResList = NULL, pCurrNode, pPreNode,
pNewNode = NULL;
for (iCounter = 0; iCounter < iPolyNum; iCounter++)
{
pPreNode = TempList= *(PolyBuff + iCounter);
MergeCoeffRes = pPreNode->fCoeff;
pCurrNode = (*(PolyBuff + iCounter))->next;
while (pCurrNode != NULL)
{
while ((pCurrNode != NULL) &&
(pCurrNode->iExpon == pPreNode->iExpon))
{
MergeCoeffRes += pCurrNode->fCoeff;
pPreNode = pCurrNode;
pCurrNode = pCurrNode->next;
}
/* 在ResList中加入新结点 */
if (MergeCoeffRes != 0)
{
MakeNode(&pNewNode, MergeCoeffRes, pPreNode->iExpon);
AppNodeToList(&ResList, pNewNode);
MergeCoeffRes = 0;
}
pPreNode = pCurrNode;
}
DestroyPolyn(TempList);
*(PolyBuff + iCounter) = ResList;
ResList = NULL;
}
}
void AddProcess(PolyPointer polyBuff, const int iPolyNum,
PolyPointer pResult, const int iSign)
{
int iCounter;
float fCoeffRes;
polynomial pNewNode, pCurrNode_1, pCurrNode_2,
pDelList = NULL, /* 下次要删除的中间结果链表 */
pResList = NULL; /* 中间结果链表 */
pCurrNode_1 = *(polyBuff);
for (iCounter = 1; iCounter < iPolyNum; iCounter++)
{
pCurrNode_2 = *(polyBuff + iCounter);
while (pCurrNode_1 != NULL && pCurrNode_2 != NULL)
{
if (pCurrNode_1->iExpon == pCurrNode_2->iExpon)
{
fCoeffRes = 0;
fCoeffRes = pCurrNode_1->fCoeff +
iSign * pCurrNode_2->fCoeff;
if (fCoeffRes != 0)
{
MakeNode(&pNewNode, fCoeffRes,
pCurrNode_1->iExpon);
AppNodeToList(&pResList, pNewNode);
}
pCurrNode_1 = pCurrNode_1->next;
pCurrNode_2 = pCurrNode_2->next;
}
else if (pCurrNode_1->iExpon < pCurrNode_2->iExpon)
{
MakeNode(&pNewNode, pCurrNode_1->fCoeff,
pCurrNode_1->iExpon);
AppNodeToList(&pResList, pNewNode);
pCurrNode_1 = pCurrNode_1->next;
}
else /* 当pCurrNode_1->iExpon > pCurrNode_2->iExpon时候 */
{
MakeNode(&pNewNode, iSign * pCurrNode_2->fCoeff,
pCurrNode_2->iExpon);
AppNodeToList(&pResList, pNewNode);
pCurrNode_2 = pCurrNode_2->next;
}
}
/* 加入余下的多项式 */
while (pCurrNode_1 != NULL)
{
MakeNode(&pNewNode, pCurrNode_1->fCoeff,
pCurrNode_1->iExpon);
AppNodeToList(&pResList, pNewNode);
pCurrNode_1 = pCurrNode_1->next;
}
while (pCurrNode_2 != NULL)
{
MakeNode(&pNewNode, iSign * pCurrNode_2->fCoeff,
pCurrNode_2->iExpon);
AppNodeToList(&pResList, pNewNode);
pCurrNode_2 = pCurrNode_2->next;
}
if (pDelList != NULL) DestroyPolyn(pDelList);
pCurrNode_1 = pResList;
pDelList = pResList;
pResList = NULL;
}
*pResult = pCurrNode_1;
}
void SubstractProcess(PolyPointer polyBuff, const int iPolyNum,
PolyPointer pResult)
{
AddProcess(polyBuff, iPolyNum, pResult , NEGATIVE);
}
void MultiplyProcess(PolyPointer polyBuff, const int iPolyNum,
PolyPointer pResult)
{
int iCounter = 1, jCounter = 0, iLength; /* 缓冲区的长度 */
PolyPointer pTemPBuff = NULL; /* 存放中间结果的缓冲区 */
polynomial pCurrNode_1, pCurrNode_2, pNewNode = NULL;
/* 初始化 */
pCurrNode_1 = polyBuff[0];
iLength = PolynLength(polyBuff[0]);
MakePolyBuff(&pTempBuff, iLength);
while (TRUE)
{
while (pCurrNode_1 != NULL)
{
pCurrNode_2 = polyBuff[iCounter];
while (pCurrNode_2 != NULL)
{
MakeNode(&pNewNode,
pCurrNode_1->fCoeff * pCurrNode_2->fCoeff,
pCurrNode_1->iExpon + pCurrNode_2->iExpon);
AppNodeToList(&pTempBuff[jCounter], pNewNode);
pCurrNode_2 = pCurrNode_2->next;
}
jCounter++;
pCurrNode_1 = pCurrNode_1->next;
}
/* 回收旧的中间结果 */
if (pResult != NULL) DestroyPolyn(*pResult);
/* 获得新的中间结果 */
AddProcess(pTempBuff, iLength, pResult , POSITIVE);
DestroyBuff(pTempBuff, iLength); /* 回收存中间结果的缓冲区 */
jCounter = 0;
if (++iCounter >= iPolyNum)
break;
else
{
iLength = PolynLength(*pResult);
MakePolyBuff(&pTempBuff, iLength);
pCurrNode_1 = *pResult;
}
}
}
void PrintPolyn(const polynomial polyList)
{
polynomial pCurrNode = polyList;
printf("多项式的长度为: %d\n", PolynLength(polyList));
while (pCurrNode != NULL)
{
printf("%.2fX^%d", pCurrNode->fCoeff, pCurrNode->iExpon);
if (pCurrNode->next != NULL)
if (pCurrNode->next->fCoeff > 0 )
printf("+");
pCurrNode = pCurrNode->next;
}
printf("\n");
}
int PolynLength(const polynomial polyList)
{
int iLength = 0;
polynomial pCurrNode = polyList;
while (pCurrNode != NULL)
{
pCurrNode = pCurrNode->next;
iLength++;
}
return iLength;
}
void DestroyBuff(PolyPointer polyBuff, const int iPolyNum)
{
int iCounter;
for (iCounter = 0; iCounter < iPolyNum; iCounter++)
DestroyPolyn(polyBuff[iCounter]);
free(polyBuff);
}
void DestroyPolyn(polynomial polyList)
{
polynomial pCurrNode;
while (polyList != NULL)
{
pCurrNode = polyList;
polyList = polyList->next;
free(pCurrNode);
}
}
status ProcStrError(const char str[])
{
const char *cpCurr = str;
if (!strlen(str))
{
printf("你没有输入数据!\n");
return FALSE;
}
while (*cpCurr != '\0')
{
if (!(*cpCurr == ' ' || *cpCurr == ',' || *cpCurr == ';'
|| *cpCurr == '-')
&& ('0' > *cpCurr || *cpCurr > '9')
|| (*(cpCurr + 1) == '\0' && *cpCurr != ';'))
{
printf("输入数据出错,请注意正确的输入方式!\n");
return FALSE;
}
cpCurr++;
}
return TRUE;
}
参考资料：http://www.21tx.com/dev/2005/05/11/13108.html