比如：怎样实现用线性链表表示多项式的加法运算？

依据一元多项式相加的运算规则：对于两个一元多项式中全部指数同样的项。相应系数相加，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全部指数不同样的项，则分别复抄到“和多项式”中去。

#include

#include

#include

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;

}