Question

用单链表实现一元多项式加法

void Add(LinkList<elem> &A,LinkList<elem> B)
{
pre=A.first;p=pre->next;
qre=B.first;q=qre->next;//指针初始化
while(p&&q)
{
if(p->exp<q->exp)
{
pre=p;
p=p->next;
}
else if(p->exp>q->exp)
{
v=q->next;
pre->next=q;
q->next=p;
q=v;
}
else
{
p->coef=p->coef+q->coef;
if(p->coef==0)//系数为0，删除节点p和q
{
pre->next=p->next;
delete p;
p=pre->next;
}
}
else//系数不为0，只删除节点q
{
pre=p；
p=p->next;

}
qre->next=q->next//删除节点q
delete q;
q=qre->next;
}
if (q) pre->next=q;//将节点q连接在第一个单链表的后面
delete B.first;
}

这是算法 目前不太熟悉如何将整个程序写出来 包括一个测试程序 对工程的结构也不太熟悉 哪位大牛帮忙解决一下 谢谢啦

Answer 1

#include<stdio.h>
#include<stdlib.h>
#include<ctype.h>

typedef struct _POLYNODE{
int coef;//系数
int exp;//指数
struct _POLYNODE *next;
}polynode,*polyptr;

void createPoly(polynode **P, char ch[]);//建立多项式链表
void polyAdd(polynode *A,polynode *B);//多项式加
void polyMinus(polynode *A,polynode *B);//减
void polyMulti(polynode *A,polynode *B);//乘
void polyDiv(polynode *A,polynode *B);//除
void order(polynode **P);//排序
void display(polynode *P);//展示多项式
void destroy(polynode **P);//销毁多项式
void menu();//命令菜单
int isPut(char ch[]);
//菜单
void menu(){
printf("1.输入多项式.\n"
"2.多项式相加.\n"
"3.多项式相减.\n"
"4.多项式相乘.\n"
"5.多项式相除.\n"
"6.显示多项式.\n"
"7.销毁多项式.\n"
"8.退出.\n");
}
//判断菜单选择
int IsChoice(int choice){
if(0 < choice && 9 > choice)
return 1;
else
return 0;
}

int isPut(char ch[]){
int i,j = 1;
for(i = 0; ch[i] != '\0'; i++){
{if(0 == j && '^' == ch[i])
return 0;
if('^' == ch[i] && 1 == j)
j = 0;
if(('+' ==ch[i] || '-' == ch[i] || '*' == ch[i] || '/' == ch[i]) && 0 == j)
j = 1;

}
if('.' != ch[i] && 'x' != ch[i] && 'X' != ch[i] && '^' != ch[i] && '+' != ch[i] && '-' != ch[i] && '*' != ch[i] && '/' != ch[i] && !isdigit(ch[i]))
return 0;
else{
if('+' ==ch[0] || '*' == ch[0] || '/' == ch[0] || '^' == ch[0] || '.' == ch[0])
return 0;
if('\0' == ch[i+1] && '+' ==ch[0] || '*' == ch[0] || '/' == ch[0] || '^' == ch[0])
return 0;
// 上面是判断字符串首尾是否合格 下面是中间部分
if(0 != i && ch[i+1] != '\0' ){
if(('X' == ch[i] || 'x' == ch[i]) && !isdigit(ch[i-1]) && '+' != ch[i-1] && '-' != ch[i-1] && '*' != ch[i-1] && '/' != ch[i-1] && '.' != ch[i-1])
return 0;
if(('X' == ch[i] || 'x' == ch[i]) && '^' != ch[i+1] && '+' != ch[i+1] && '-' != ch[i+1] && '*' != ch[i+1] && '/' != ch[i+1])
return 0;
if(('+' == ch[i] || '-' == ch[i] || '*' == ch[i] || '/' == ch[i]) && !isdigit(ch[i-1]) && 'X' != ch[i-1] && 'x' != ch[i-1] && !isdigit(ch[i+1]) && 'X' != ch[i+1] && 'x' != ch[i+1])
return 0;
if('^' == ch[i] && 'X' != ch[i-1] && 'x' != ch[i-1])
return 0;
if('^' == ch[i] && !isdigit(ch[i+1]))
return 0;
if('.' == ch[i] && !isdigit(ch[i+1]) && !isdigit(ch[i-1]))
return 0;
}
}
}
return 1;
}

void createPoly(polynode **P, char ch[]){
char *t = ch;
int i = 0, j = 1;
int iscoef = 1,isminus = 1;
polyptr Q,L;

if('-' == ch[0]){
isminus = -1;
*t++;
}
while('\0' != *t){
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = 1;
Q->exp = 0;
Q->next = NULL;//申请节点，初始化参数为1.

if(-1 == isminus){
Q->coef *= isminus;
isminus = 1;
}

while('+' != *t && '-' != *t && '*' != *t && '/' != *t && '\0' != *t){
if('x' != *t && 'X' != *t){
while(isdigit(*t)){
i =((int)*t - 48) + i*10;
t++;
j *= i;
}//抽取数字
if(1 == iscoef && 0 != i){
Q->coef *= i;
}
if(0 == iscoef){
Q->exp += i;
iscoef = 1;
}
//如果i=0,则

}
else{
iscoef = 0;
t++;
if('^' == *t)
t++;
else
Q->exp = 1;
}
i = 0;
}//while 遍历到加减乘除,则退出循环,到下一新的节点
iscoef = 1;
if('\0' != *t){
if('-' == *t)
isminus = -1;
t++;
}
if(0 == j){
Q->coef = 0;
j = 1;
}
printf("系数:%d,指数:%d\n",Q->coef,Q->exp);

if(NULL == *P){
*P = Q;
}
else{
L->next = Q;
}
L = Q;

}//while遍历整个字符串

}
void polyAdd(polynode *A,polynode *B){
polyptr P = A, Q,L;
polyptr COPYA = NULL,COPYB = NULL;
if(NULL == A || NULL == B){
printf("多项式未被建立,请先输入多项表达式.\n");
return ;
}

while(NULL != P){//复制A
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = P->coef;
Q->exp = P->exp;
Q->next = NULL;
if(NULL == COPYA)
COPYA = Q;
else
L->next = Q;
L = Q;
P = P->next;
}
P = B;
while(NULL != P){//复制B
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = P->coef;
Q->exp = P->exp;
Q->next = NULL;
if(NULL == COPYB)
COPYB = Q;
else
L->next = Q;
L = Q;
P = P->next;
}

L->next = COPYA;//把COPYA,COPYB两个多项式连接起来,整理一下就OK了.
order(©B);
order(©B);
printf("相加结果为:");
display(COPYB);
destroy(©B);
}
void polyMinus(polynode *A,polynode *B){//相减和相加差不多
polyptr P = A, Q,L;
polyptr COPYA = NULL,COPYB = NULL;
if(NULL == A || NULL == B){
printf("多项式未被建立,请先输入多项表达式.\n");
return ;
}

while(NULL != P){//复制A
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = P->coef;
Q->exp = P->exp;
Q->next = NULL;
if(NULL == COPYA)
COPYA = Q;
else
L->next = Q;
L = Q;
P = P->next;
}
P = B;
while(NULL != P){//复制B
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = -(P->coef);
Q->exp = P->exp;
Q->next = NULL;
if(NULL == COPYB)
COPYB = Q;
else
L->next = Q;
L = Q;
P = P->next;
}

L->next = COPYA;//把COPYA,COPYB两个多项式连接起来,整理一下就OK了.
order(©B);
order(©B);
printf("相减结果为:");
display(COPYB);
destroy(©B);

}
void polyMulti(polynode *A,polynode *B){
polyptr R = A, P = B, Q, L = NULL, T;

if(NULL == A || NULL == B){
printf("多项式未被建立,请先输入多项表达式.\n");
return ;
}
if(0 == A->coef || 0 == B->coef){
printf("多项式乘积为:0\n");
return ;
}

while(NULL != R){
while(NULL != P){
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = P->coef * R->coef;
Q->exp = P->exp + R->exp;
Q->next = NULL;

if(NULL == L)
L = Q;
else
T->next = Q;
T = Q;
P = P->next;
}
P = B;
R = R->next;
}
order(&L);
order(&L);
printf("多项式乘积为:\n");
display(L);
destroy(&L);
}
void polyDiv(polynode *A,polynode *B){//多项式除法
polyptr P = A, Q,L,R,T,C,D;
polyptr COPYA = NULL,COPYB = NULL;
if(NULL == A || NULL == B){
printf("多项式未被建立,请先输入多项表达式.\n");
return ;
}
if(A->coef == 0){
printf("0.\n");
return ;
}
if(B->coef == 0){
printf("除数为0,错误!\n");
return ;
}
if(A->coef < B->coef){
printf("商:0,余数为:");
display(A);
return ;
}
while(NULL != P){//复制A
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = P->coef;
Q->exp = P->exp;
Q->next = NULL;
if(NULL == COPYA)
COPYA = Q;
else
L->next = Q;
L = Q;
P = P->next;
}
P = B;
while(NULL != P){//复制B
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = -(P->coef);
Q->exp = P->exp;
Q->next = NULL;
if(NULL == COPYB)
COPYB = Q;
else
L->next = Q;
L = Q;
P = P->next;
}
C = P = Q = L = R = T = NULL;

//------------------开始计算
while(COPYA->exp >= COPYB->exp){
D = COPYA;
while(NULL != D->next)
D = D->next;
R = COPYB;
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = (-COPYA->coef) / R->coef;
Q->exp = COPYA->exp - R->exp;
Q->next = NULL;
if(NULL == L)
L = Q;
else
P->next = Q;
P = Q;

while(NULL != R){
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = P->coef * R->coef;
Q->exp = P->exp + R->exp;
Q->next = NULL;

if(NULL == T)
T = Q;
else
C->next = Q;
C = Q;

R = R->next;
}
D->next = T;
order(©A);
order(©A);
T = NULL;
C = NULL;
}
order(&L);
order(©A);
printf("A除以B,商:");
display(L);
printf("余数:");
display(COPYA);

destroy(&L);
destroy(©A);
destroy(©B);
}

void display(polynode *P){
//考虑情况有系数为1,指数为1,0,一般数;系数为系数不为1,指数为1,0,一般数;
//系数为负数,指数为1,0,一般数,主要考虑中间符号问题.
if(NULL == P){
printf("多项式为空.\n");
return ;
}
if(1 == P->coef){
if(0 == P->exp)
printf("1");
else if(1 == P->exp) printf("x");
else printf("x^%d",P->exp);
}
else{
if(-1 == P->coef){
if(0 == P->exp)
printf("-1");
else if(1 == P->exp) printf("-x");
else printf("-x^%d",P->exp);
}
else if(0 == P->exp)
printf("%d",P->coef);
else if(1 == P->exp) printf("%dx",P->coef);
else
printf("%dx^%d",P->coef,P->exp);
}
P = P->next;
while(NULL != P){
if(0 < P->coef){
if(1 == P->coef){
if(0 == P->exp)
printf("+1");
else if(1 == P->exp) printf("+x");
else printf("+x^%d",P->exp);
}
else{
if(0 == P->exp)
printf("+%d",P->coef);
else if(1 == P->exp) printf("+%dx",P->coef);
else
printf("+%dx^%d",P->coef,P->exp);
}
}
else{
if(-1 == P->coef){
if(0 == P->exp)
printf("-1");
else if(1 == P->exp) printf("-x");
else printf("-x^%d",P->exp);
}
else{
if(0 == P->exp)
printf("%d",P->coef);
else if(1 == P->exp) printf("%dx",P->coef);
else
printf("%dx^%d",P->coef,P->exp);
}
}
P = P->next;
}
printf("\n");
}

void destroy(polynode **P){
polyptr Q = *P;
if(NULL == *P)
return ;
while(*P != NULL){
Q = *P;
*P = (*P)->next;
delete Q;
}

}

void order(polynode **P){
//首先 系数为零的要清掉,其次指数从高到低排序,再者系数相同的要合并.
polyptr prev,curr,OUT,INcurr;//前一节点和当前节点
int temp;

//出去第一节点系数为0的项
while(NULL != *P){
if(0 != (*P)->coef)
break;
else{
if(NULL == (*P)->next)
return;
curr = *P;
(*P) = (*P)->next;
delete curr;
}
}
if(NULL == *P || NULL == (*P)->next)//如果只剩1项或空,则不需要整理,退出函数
return;
//冒泡排序
OUT = INcurr = *P;
while(NULL != OUT->next){//外循环
while(NULL != INcurr->next){//内循环
prev = INcurr;
INcurr = INcurr->next;
if(prev->exp < INcurr->exp){
temp = prev->coef;
prev->coef = INcurr->coef;
INcurr->coef = temp;//交换系数

temp = prev->exp;
prev->exp = INcurr->exp;
INcurr->exp = temp;//交换指数
}
}
OUT = OUT->next;
INcurr = *P;
}

//去除0项
prev = curr = *P;
curr = curr->next;
while(NULL != curr){
if(0 == curr->coef){
prev->next = curr->next;
delete curr;
curr = prev->next;
}
else{
prev = curr;
curr = curr->next;
}
}
//合并同类项
OUT = INcurr = *P;
while(NULL != OUT->next){
while(NULL != INcurr->next){
prev = INcurr;
INcurr = INcurr->next;
if(INcurr->exp == OUT->exp){
OUT->coef += INcurr->coef;
prev->next = INcurr->next;
delete INcurr;
INcurr = prev;
}
}
INcurr = OUT = OUT->next;
if(NULL == OUT)
return;
}

}

void main(){
int choice;
// int i;
char ch[100];
polynode *polyA,*polyB;

polyA = polyB = NULL;

menu();
scanf("%d",&choice);
while(!IsChoice(choice)){
menu();
printf("输入错误,重新输入.\n");
scanf("%d",&choice);
}
while(8 != choice){
switch(choice){
case 1:
if(NULL != polyA || NULL != polyB){
destroy(&polyA);
destroy(&polyB);
printf("原多项式被销毁.\n");
}
printf("多项式输入格式:4x^3+7x^2+x+6--x不分大小写.\n输入多项式A:\n");
scanf("%s",&ch);

while(!isPut(ch)){
printf("输入错误!重新输.\n");
scanf("%s",&ch);
}
createPoly(&polyA,ch);//建立多项式A链表

printf("输入多项式B:\n");
scanf("%s",&ch);
while(!isPut(ch)){
printf("输入错误!重新输.\n");
scanf("%s",&ch);
}
createPoly(&polyB,ch);//建立多项式B链表
order(&polyB);
order(&polyA);//整理排序多项式,默认降幂

printf("建立多项式成功!多项式:\nA为:");
display(polyA);
printf("B为:");
display(polyB);
break;
case 2:
polyAdd(polyA,polyB);
break;
case 3:
polyMinus(polyA,polyB);
break;
case 4:
polyMulti(polyA,polyB);
break;
case 5:
printf("PS:系数只支持整数,计算除法存在误差;\n如果除数所有项系数为1,能得到正确答案,或者某些情况系数刚好被整除.");
polyDiv(polyA,polyB);
break;
case 6:
printf("------显示多项式------\nA :");
display(polyA);
printf("B :");
display(polyB);
break;
case 7:
destroy(&polyA);
destroy(&polyB);
printf("此多项式已被清空.\n");
break;
default:
return ;
}
choice = 0;
menu();
scanf("%d",&choice);
while(!IsChoice(choice) || 0 == choice){
menu();
printf("输入错误,重新输入.\n");
scanf("%d",&choice);
}
}
}

Answer 2

#include<stdio.h>
#include<stdlib.h>
typedef struct
{ float coef; //系数
int expn; //指数
}term;
typedef struct LNode
{ term data; //term多项式值
struct LNode *next;
}LNode,*LinkList;
typedef LinkList polynomail;
/*比较指数*/
int cmp(term a,term b)
{ if(a.expn>b.expn) return 1;
if(a.expn==b.expn) return 0;
if(a.expn<b.expn) return -1;
else exit(-2);
}
/*又小到大排列*/
void arrange1(polynomail pa)
{ polynomail h=pa,p,q,r;
if(pa==NULL) exit(-2);
for(p=pa;p->next!=NULL;p=p->next); r=p;
for(h=pa;h->next!=r;)//大的沉底
{ for(p=h;p->next!=r&&p!=r;p=p->next)
if(cmp(p->next->data,p->next->next->data)==1)
{ q=p->next->next;
p->next->next=q->next;
q->next=p->next;
p->next=q;
}
r=p;//r指向参与比较的最后一个，不断向前移动
} }
/*由大到小排序*/
void arrange2(polynomail pa)
{ polynomail h=pa,p,q,r;
if(pa==NULL) exit(-2);
for(p=pa;p->next!=NULL;p=p->next); r=p;
for(h=pa;h->next!=r;)//小的沉底
{ for(p=h;p->next!=r&&p!=r;p=p->next)
if(cmp(p->next->next->data,p->next->data)==1)
{ q=p->next->next;
p->next->next=q->next;
q->next=p->next;
p->next=q;
}
r=p;//r指向参与比较的最后一个，不断向前移动
} }
/*打印多项式,求项数*/
int printpolyn(polynomail P)
{ int i;
polynomail q;
if(P==NULL) printf("无项！\n");
else if(P->next==NULL) printf("Y=0\n");
else
{ printf("该多项式为Y=");q=P->next;i=1;
if(q->data.coef!=0&&q->data.expn!=0)
{ printf("%.2fX^%d",q->data.coef,q->data.expn); i++; }
if(q->data.expn==0&&q->data.coef!=0)
printf("%.2f",q->data.coef);//打印第一项
q=q->next;
if(q==NULL)
{printf("\n");return 1;}
while(1)//while中，打印剩下项中系数非零的项，
{ if(q->data.coef!=0&&q->data.expn!=0)
{ if(q->data.coef>0) printf("+");
printf("%.2fX^%d",q->data.coef,q->data.expn); i++;
}
if(q->data.expn==0&&q->data.coef!=0)
{ if(q->data.coef>0) printf("+");
printf("%f",q->data.coef);
}
q=q->next;
if(q==NULL)
{ printf("\n"); break; }
}
}
return 1;
}
/*1、创建并初始化多项式链表*/
polynomail creatpolyn(polynomail P,int m)
{ polynomail r,q,p,s,Q;
int i;
P=(LNode*)malloc(sizeof(LNode));
r=P;
for(i=0;i<m;i++)
{ s=(LNode*)malloc(sizeof(LNode));
printf("请输入第%d项的系数和指数：",i+1);
scanf("%f%d",&s->data.coef,&s->data.expn);
r->next=s; r=s;
}
r->next=NULL;
if(P->next->next!=NULL)
{ for(q=P->next;q!=NULL/*&&q->next!=NULL*/;q=q->next)//合并同类项
for(p=q->next,r=q;p!=NULL;)
if(q->data.expn==p->data.expn)
{ q->data.coef=q->data.coef+p->data.coef;
r->next=p->next;
Q=p;p=p->next;
free(Q);
}
else
{ r=r->next;
p=p->next;
}
}
return P;
}
/*2、两多项式相加*/
polynomail addpolyn(polynomail pa,polynomail pb)
{ polynomail s,newp,q,p,r;int j;
p=pa->next;q=pb->next;
newp=(LNode*)malloc(sizeof(LNode));
r=newp;
while(p&&q)
{ s=(LNode*)malloc(sizeof(LNode));
switch(cmp(p->data,q->data))
{case -1: s->data.coef=p->data.coef;
s->data.expn=p->data.expn;
r->next=s; r=s;
p=p->next;
break;
case 0: s->data.coef=p->data.coef+q->data.coef;
if(s->data.coef!=0.0)
{ s->data.expn=p->data.expn;
r->next=s;
r=s;
}
p=p->next;
q=q->next;
break;
case 1: s->data.coef=q->data.coef;
s->data.expn=q->data.expn;
r->next=s; r=s;
q=q->next;
break;
}//switch
}//while
while(p)
{ s=(LNode*)malloc(sizeof(LNode));
s->data.coef=p->data.coef;
s->data.expn=p->data.expn;
r->next=s; r=s;
p=p->next;
}
while(q)
{ s=(LNode*)malloc(sizeof(LNode));
s->data.coef=q->data.coef;
s->data.expn=q->data.expn;
r->next=s; r=s;
q=q->next;
}
r->next=NULL;
for(q=newp->next;q->next!=NULL;q=q->next)//合并同类项
for(p=q;p!=NULL&&p->next!=NULL;p=p->next)
if(q->data.expn==p->next->data.expn)
{ q->data.coef=q->data.coef+p->next->data.coef;
r=p->next;
p->next=p->next->next;
free(r);
}
printf("升序 1 , 降序 2\n");
printf("选择:");
scanf("%d",&j);
if(j==1) arrange1(newp);
else arrange2(newp);
return newp;
}
void delpolyn(polynomail pa,polynomail pb)
{ polynomail p,q;
p=pa;
while(p!=NULL)
{ q=p;
p=p->next;
free(q);
}
p=pb;
while(p!=NULL)
{ q=p;
p=p->next;
free(q);
}
printf("两个多项式已经销毁\n");
}
void main()
{ polynomail pa=NULL,pb=NULL;
polynomail p,q;
polynomail addp=NULL;
int n,m;
int sign='y';
printf("1、创建两个一元多项式\n");
printf("2、两多项式相加得一新多项式\n");
printf("3、销毁已建立的两个多项式\n");
printf("4、退出\n");
printf("\n");
while(sign!='n')
{ printf("请选择：");
scanf("%d",&n);
switch(n)
{case 1:
if(pa!=NULL)
{ printf("已建立两个一元多项式，请选择其他操作！");
break;
}
printf("请输入第一个多项式：\n");
printf("要输入几项：");
scanf("%d",&m);
while(m==0)
{ printf("m不能为0，请重新输入m:");
scanf("%d",&m);
}
pa=creatpolyn(pa,m);
printpolyn(pa);
printf("请输入第二个多项式：\n");
printf("要输入几项：");
scanf("%d",&m);
pb=creatpolyn(pb,m);
printpolyn(pb);
break;
case 2:
if(pa==NULL)
{ printf("请先创建两个一元多项式！\n");
break;
}
addp=addpolyn(pa,pb);
printpolyn(addp);
break;
case 3:
if(pa==NULL)
{ printf("请先创建两个一元多项式！\n");
break;
}
delpolyn(pa,pb);
pa=pb=NULL;
break;
case 4:
if(addp!=NULL)
{ p=addp;
while(p!=NULL)
{ q=p;
p=p->next;
free(q);
}
}
if(subp!=NULL)
{ p=subp;
while(p!=NULL)
{ q=p;
p=p->next;
free(q);
}
}
exit(-2);
}//switch
}//while
}