一元多项式的加法与乘法运算

题意理解

多项式的表示

有两种表示方法：

数组：                                           链表：

优点：编程简单、调试容易             优点：动态性强

缺点：需要事先确定数组大小          缺点：编程略为复杂、调试比较困难

数据结构设计

typedef struct PolyNode *Polynomial;
struct PolyNode {
int coef;
int expon;  /*指数*/
Polynomial link;
};

程序框架搭建

int main()
{
读入多项式1
读入多项式2
乘法运算并输出
加法运算并输出
return 0;
}

代码

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
typedef struct PolyNode *Polynomial; struct PolyNode { int coef; int expon; /*指数*/ Polynomial link; };
void Attach(int c, int e, Polynomial* pRear)
{
Polynomial P;
P = (struct PolyNode*)malloc(sizeof(struct PolyNode));
P->coef = c; /*对新节点赋值*/
P->expon = e;
P->link = NULL;
(*pRear)->link = P;
(*pRear) = P;
}
Polynomial ReadPoly() /*多项式的输入*/
{
Polynomial P, Rear, t;
int c, e, N;
scanf("%d", &N); /*项数*/
P = (Polynomial)malloc(sizeof(struct PolyNode)); /* 链表头空结点 */
P->link = NULL;
Rear = P;
while ( N-- ) {
scanf("%d%d", &c, &e);
Attach(c, e, &Rear); /* 将当前项插入多项式尾部 */
}
t = P;
P = P->link;
free(t); /* 删除临时生成的头结点 */
return P;
}

Polynomial Add( Polynomial P1, Polynomial P2 )/*多项式的加法*/
{
Polynomial P,Rear,t;
P = (Polynomial)malloc(sizeof(struct PolyNode));
P->link = NULL;
Rear = P;
while(P1&&P2)
{
if( P1->expon > P2->expon ){
Attach(P1->coef,P1->expon,&Rear);
P1 = P1->link;
}
else if( P1->expon < P2->expon ){
Attach(P2->coef,P2->expon,&Rear);
P2 = P2->link;
}
else{
if(P1->coef+P2->coef) /*判断系数和是否为0*/
Attach(P1->coef+P2->coef,P1->expon,&Rear);
P1 = P1->link;
P2 = P2->link;
}
}
while(P1)
{
Attach(P1->coef,P1->expon,&Rear);
P1 = P1->link;
}
while(P2)
{
Attach(P2->coef,P2->expon,&Rear);
P2 = P2->link;
}
t = P;
P = P->link;
free(t);
return P;
}

Polynomial Mult( Polynomial P1, Polynomial P2 )/*多项式的乘法*/
{
Polynomial P, Rear, t1, t2, t;
int c,e;
if (P1==NULL || P2==NULL) return NULL;
t1 = P1;
P = (Polynomial)malloc(sizeof(struct PolyNode));
P->link = NULL;
while(t1)
{
Rear = P;
t2 = P2;
while(t2)
{
c = t1->coef * t2->coef;
e = t1->expon + t2->expon;
while (Rear->link && Rear->link->expon > e)
Rear = Rear->link;
if(Rear->link && Rear->link->expon == e)
{
if (Rear->link->coef + c)
Rear->link->coef += c;
else {
t = Rear->link;
Rear->link = t->link;
free(t);
}
}
else
{
t = (Polynomial)malloc(sizeof(struct PolyNode));
t->coef = c;
t->expon = e;
t->link = Rear->link;
Rear->link = t;
Rear = Rear->link;
}
t2 = t2->link;
}
t1 = t1->link;
}
t = P;
P = P->link;
free(t);
return P;
}

void PrintPoly( Polynomial P ) /* 输出多项式 */
{
int flag = 0; /* 辅助调整输出格式用 */
if (!P) {printf("0 0\n"); return;}
while ( P ) {
if (!flag)
flag = 1;
else
printf(" ");
printf("%d %d", P->coef, P->expon);
P = P->link;
}
printf("\n");
}

int main()
{
Polynomial P1, P2, PP, PS;
P1 = ReadPoly();
P2 = ReadPoly();
PP = Mult( P1, P2 );
PrintPoly( PP );
PS = Add( P1, P2 );
PrintPoly( PS );
return 0;
}