📄 一元多项式.cpp
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#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);
}
/*小到大排列*/
void arrange(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;)
{
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
}
}
/*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，
{ //同时，指数为零的项只输出系数，系数为负的不输出+号
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("%.2f",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;
arrange(P);
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;
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);
}
return newp;
}
/*3、两多项式相减*/
polynomail subpolyn(polynomail pa,polynomail pb)
{
polynomail s,newp,q,p,r,Q;
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;
if(newp->next!=NULL&&newp->next->next!=NULL)//合并同类项
{
for(q=newp->next;q!=NULL;q=q->next)
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 newp;
}
/*4两多项式相乘*/
polynomail mulpolyn(polynomail pa,polynomail pb)
{
polynomail s,newp,q,p,r;
newp=(LNode*)malloc(sizeof(LNode));
r=newp;
for(p=pa->next;p!=NULL;p=p->next)
for(q=pb->next;q!=NULL;q=q->next)
{
s=(LNode*)malloc(sizeof(LNode));
s->data.coef=p->data.coef*q->data.coef;
s->data.expn=p->data.expn+q->data.expn;
r->next=s;
r=s;
}
r->next=NULL;
arrange(newp);
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);
}
return newp;
}
void main()
{
polynomail pa=NULL,pb=NULL;
polynomail p,q;
polynomail addp=NULL,subp=NULL,mulp=NULL;
int n,m;
char sign='y';
printf("1、输入一元多项式\n");
printf("2、相加\n");
printf("3、相减\n");
printf("4、相乘\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;
}
subp=subpolyn(pa,pb);
printpolyn(subp);
break;
case 4:
if(pa==NULL)
{
printf("请先创建两个一元多项式！\n");
break;
}
mulp=mulpolyn(pa,pb);
printpolyn(mulp);
break;
}//switch
}//while
}
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