一元多项式的表示及加减乘除运算

例如：如何实现用线性链表表示多项式的加法运算？

根据一元多项式相加的运算规则：对于两个一元多项式中所有指数相同的项，对应系数相加，若其和不为零，则构成“和多项式”中的一项；对于两个一元多项式中所有指数不相同的项，则分别复抄到“和多项式”中去。

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

typedef struct polyn
{
float coef;
int expn;
struct polyn* next;
}PolyNode,*PLinkList;

PLinkList CreatePolyn();//创建一元多项式，使一元多项式呈指数递减
void OutPut(PLinkList head);//输出一元多项式
PLinkList Addition(PLinkList L1,PLinkList L2);//多项式的加法
PLinkList Subtraction(PLinkList L1,PLinkList L2);//多项式的减法
PLinkList Reverse(PLinkList head);//将生成的链表逆置，使一元多项式呈指数递增形式
PLinkList MultiplyPolyn(PLinkList L1,PLinkList L2);//多项式的乘法

#include "test.h"

PLinkList CreatePolyn()//创建一元多项式，使一元多项式呈指数递减
{
PolyNode *p,*q,*s;
PolyNode *head = NULL;
int expn2;
float coef2;
head = (PLinkList)malloc(sizeof(PolyNode));//动态生成头结点
if(!head)
{
return NULL;
}
head->coef = 0.0;//初始化
head->expn = 0;
head->next = NULL;
do
{
printf("输入系数coef(系数和指数都为0结束)");
scanf("%f",&coef2);
printf("输入指数数exp(系数和指数都为0结束)");
scanf("%d",&expn2);
if((long)coef2 == 0 && expn2 == 0)
{
break;
}
s = (PLinkList)malloc(sizeof(PolyNode));
if(!s)
{
return NULL;
}
s->expn = expn2;
s->coef = coef2;
q = head->next ;
p = head;
while(q && expn2 < q->expn)
{
p = q;
q = q->next ;
}
if(q == NULL || expn2 > q->expn)
{
p->next = s;
s->next = q;
}
else
{
q->coef += coef2;
}
}while(1);
return head;
}

void OutPut(PLinkList head)//输出一元多项式
{
PolyNode *p = head->next ;
while(p)
{
printf("%1.1f",p->coef);
if(p->expn)
{
printf("*x^%d",p->expn);
}
if(p->next && p->next->coef > 0)
{
printf("+");
}
p = p->next ;
}
}

PolyNode *Addition(PLinkList L1,PLinkList L2)//多项式的加法
{
PolyNode *pa,*pb,*pc,*u,*head;
head = (PLinkList)malloc(sizeof(PolyNode));
if(!head)
{
return NULL;
}
head->coef = 0.0;
head->expn = 0;
head->next = NULL;
pc = head;
L2 = Reverse(L2);
pa = L1->next ;
pb = L2->next ;
while(pa != NULL && pb != NULL)
{
if(pa->expn == pb->expn)
{
u = (PLinkList)malloc(sizeof(PolyNode));
if(!u)
{
return NULL;
}
u->coef = pa->coef + pb->coef ;
u->expn = pa->expn ;
pa = pa->next ;
pb = pb->next ;
u->next = pc->next ;
pc->next = u;
pc = u;
}
else if(pa->expn > pb->expn)
{
u = (PLinkList)malloc(sizeof(PolyNode));
if(!u)
{
return NULL;
}
u->coef = pa->coef ;
u->expn = pa->expn ;
pa = pa->next ;
u->next = pc->next ;
pc->next = u;
pc = u;
}
else
{
u = (PLinkList)malloc(sizeof(PolyNode));
if(!u)
{
return NULL;
}
u->coef = pb->coef ;
u->expn = pb->expn ;
pb = pb->next ;
u->next = pc->next ;
pc->next = u;
pc = u;
}
}
L2 = Reverse(L2);
return head;
}

PolyNode *Subtraction(PLinkList L1,PLinkList L2)//多项式的减法
{
PolyNode *pa,*pb,*pc,*u,*head;
head = (PLinkList)malloc(sizeof(PolyNode));
if(!head)
{
return NULL;
}
head->coef = 0.0;
head->expn = 0;
head->next = NULL;
pc = head;
pa = L1->next ;
pb = L2->next ;
while(pa != NULL && pb != NULL)
{
if(pa->expn == pb->expn)
{
u = (PLinkList)malloc(sizeof(PolyNode));
if(!u)
{
return NULL;
}
u->coef = pa->coef - pb->coef ;
u->expn = pa->expn ;
pa = pa->next ;
pb = pb->next ;
u->next = pc->next ;
pc->next = u;
pc = u;
}
else if(pa->expn > pb->expn)
{
u = (PLinkList)malloc(sizeof(PolyNode));
if(!u)
{
return NULL;
}
u->coef = pa->coef ;
u->expn = pa->expn ;
pa = pa->next ;
u->next = pc->next ;
pc->next = u;
pc = u;
}
else
{
u = (PLinkList)malloc(sizeof(PolyNode));
if(!u)
{
return NULL;
}
u->coef = pb->coef ;
u->expn = pb->expn ;
pb = pb->next ;
u->next = pc->next ;
pc->next = u;
pc = u;
}
}
return head;
}

PolyNode *Reverse(PLinkList head)//将生成的链表逆置，使一元多项式呈指数递增形式
{
PolyNode *q,*r,*p = NULL;
q = head->next ;
while(q)
{
r = q->next ;
q->next = p;
p = q;
q = r;
}
head->next = p;
return head;
}

PolyNode *MultiplyPolyn(PLinkList L1,PLinkList L2)//多项式的乘法
{
PolyNode *pa,*pb,*pc,*u,*head;
int k,maxExp;
float coef;
head = (PLinkList)malloc(sizeof(PolyNode));
if(!head)
{
return NULL;
}
head->coef = 0.0;
head->expn = 0;
head->next = NULL;
if(L1->next != NULL && L2->next != NULL)
{
maxExp = L1->next->expn +L2->next->expn ;
}
else
{
return head;
}
pc = head;
L2 = Reverse(L2);
for(k = maxExp;k >= 0;k--)
{
pa = L1->next ;
while(pa != NULL && pa->expn > k)
{
pa = pa->next ;
}
pb = L2->next ;
while(pb != NULL && pa != NULL && pa->expn+pb->expn < k)
{
pb= pb->next ;
}
coef = 0.0;
while(pa != NULL && pb != NULL)
{
if(pa->expn +pb->expn == k)
{
coef += pa->coef *pb->coef ;
pa = pa->next ;
pb = pb->next ;
}
else if(pa->expn +pb->expn > k)
{
pa = pa->next ;
}
else
{
pb = pb->next ;
}
}
if(coef != 0.0)
{
u = (PLinkList)malloc(sizeof(PolyNode));
u->coef = coef;
u->expn = k;
u->next = pc->next ;
pc->next = u;
pc = u;
}
}
L2 = Reverse(L2);
return head;
}

#include "test.h"

int main(void)
{
PLinkList A,B,C,D,E;
A = CreatePolyn();
printf("A(x) =");
OutPut(A);
printf("\n");
B = CreatePolyn();
printf("B(x) =");
OutPut(B);
printf("\n");
C = MultiplyPolyn(A,B);
printf("C(x) = A(x)*B(x) =");
OutPut(C);
printf("\n");
D = Addition(A,B);
printf("D(x) = A(x)+B(x) =");
OutPut(D);
printf("\n");
E = Subtraction(A,B);
printf("E(x) = A(x)-B(x) =");
OutPut(E);
printf("\n");
return 0;
}