无偿 链表的应用：一元多项式相加（C语言）
#include <stdio.h>#include <malloc.h>
typedef struct node
{ float coef; /*序数*/
int expn; /*指数*/
struct node *next; /*指向下一个结点的指针*/
} PolyNode;
void InitList(PolyNode *&L) /*初始化多项式单链表*/
{
L=(PolyNode *)malloc(sizeof(PolyNode)); /*建立头结点*/
L->next=NULL;
}
int GetLength(PolyNode *L) /*求多项式单链表的长度*/
{
int i=0;
PolyNode *p=L->next;
while (p!=NULL) /*扫描单链表L，用i累计结点个数*/
{
i++;p=p->next;
}
return i;
}
PolyNode *GetElem(PolyNode *L,int i) /*返回多项式单链表中第i个结点的指针*/
{
int j=1;
PolyNode *p=L->next;
if (i<1 || i>GetLength(L))
return NULL;
while (j<i) /*沿next域找第i个结点*/
{
p=p->next;j++;
}
return p;
}
PolyNode *Locate(PolyNode *L,float c,int e) /*在多项式单链表中按值查找*/
{
PolyNode *p=L->next;
while (p!=NULL && (p->coef!=c ||p->expn!=e))
p=p->next;
return p;
}
int InsElem(PolyNode *&L,float c,int e,int i) /*在多项式单链表中插入一个结点*/
{
int j=1;
PolyNode *p=L,*s;
s=(PolyNode *)malloc(sizeof(PolyNode));
s->coef=c;s->expn=e;s->next=NULL;
if (i<1 || i>GetLength(L)+1)
return 0;
while (j<i) /*查找第i-1个结点*p*/
{
p=p->next;j++;
}
s->next=p->next;
p->next=s;
return 1;
}
int DelElem(PolyNode *L,int i) /*在多项式单链表中删除一个结点*/
{
int j=1;
PolyNode *p=L,*q;
if (i<1 || i>GetLength(L))
return 0;
while (j<i) /*在单链表中查找第i-1个结点，由p指向它*/
{
p=p->next;j++;
}
q=p->next; /*q指向被删结点*/
p->next=q->next; /*删除*q结点*/
free(q);
return 1;
}
void DispList(PolyNode *L) /*输出多项式单链表的元素值*/
{
PolyNode *p=L->next;
while (p!=NULL)
{
printf("(%g,%d) ",p->coef,p->expn);
p=p->next;
}
printf("\n");
}
void CreaPolyList(PolyNode *&L,float C[],int E[],int n)
{
int i;
InitList(L);
for (i=0;i<n;i++)
InsElem(L,C[i],E[i],i+1);
}
void SortPloy(PolyNode *&L) /*对L的多项式单链表按expn域递增排序*/
{
PolyNode *p=L->next,*q,*pre;
L->next=NULL;
while (p!=NULL)
{
if (L->next==NULL) /*处理第1个结点*/
{
L->next=p;p=p->next;
L->next->next=NULL;
}
else /*处理其余结点*/
{
pre=L;q=pre->next;
while (q!=NULL && p->expn>q->expn) /*找q->expn刚大于或等于p->expn的结点*q的前驱结点*pre*/
{
pre=q;q=q->next;
}
q=p->next; /*在*pre结点之后插入*p*/
p->next=pre->next;
pre->next=p;
p=q;
}
}
}
PolyNode *AddPoly(PolyNode *pa,PolyNode *pb)
{
PolyNode *pc,*p1=pa->next,*p2=pb->next,*p,*tc,*s;
pc=(PolyNode *)malloc(sizeof(PolyNode)); /*新建头结点*pc*/
pc->next=NULL; /*pc为新建单链表的头结点*/
tc=pc; /*tc始终指向新建单链表的最后结点*/
while (p1!=NULL && p2!=NULL)
{
if (p1->expn<p2->expn) /*将*p1结点复制到*s并链到pc尾*/
{
s=(PolyNode *)malloc(sizeof(PolyNode));
s->coef=p1->coef;s->expn=p1->expn;s->next=NULL;
tc->next=s;tc=s;
p1=p1->next;
}
else if (p1->expn>p2->expn) /*将*p2结点复制到*s并链到pc尾*/
{
s=(PolyNode *)malloc(sizeof(PolyNode));
s->coef=p2->coef;s->expn=p2->expn;s->next=NULL;
tc->next=s;tc=s;
p2=p2->next;
}
else /*p1->expn=p2->expn的情况*/
{
if (p1->coef+p2->coef!=0) /*序数相加不为0时新建结点*s并链到pc尾*/
{
s=(PolyNode *)malloc(sizeof(PolyNode));
s->coef=p1->coef+p2->coef;s->expn=p1->expn;
s->next=NULL;
tc->next=s;tc=s;
}
p1=p1->next;p2=p2->next;
}
}
if (p1!=NULL) p=p1; /*将尚未扫描完的余下结点复制并链接到pc单链表之后*/
else p=p2;
while (p!=NULL)
{
s=(PolyNode *)malloc(sizeof(PolyNode));
s->coef=p->coef;s->expn=p->expn;s->next=NULL;
tc->next=s;tc=s;
p=p->next;
}
tc->next=NULL; /*新建单链表最后结点的next域置空*/
return pc;
}
void main()
{
PolyNode *L1,*L2,*L3;
float C1[]={3,7,5,9},C2[]={-9,8,22};
int E1[]={1,0,17,8},E2[]={8,1,7};
InitList(L1);
InitList(L2);
InitList(L3);
CreaPolyList(L1,C1,E1,4);
CreaPolyList(L2,C2,E2,3);
printf("两多项式相加运算\n");
printf(" 原多项式A:");DispList(L1);
printf(" 原多项式B:");DispList(L2);
SortPloy(L1);
SortPloy(L2);
printf("排序后的多项式A:");DispList(L1);
printf("排序后的多项式B:");DispList(L2);
L3=AddPoly(L1,L2);
printf("多项式相加结果:");DispList(L3);
}
