02-线性结构2 一元多项式的乘法与加法运算 (20分)
设计函数分别求两个一元多项式的乘积与和。
输入格式:
输入分2行,每行分别先给出多项式非零项的个数,再以指数递降方式输入一个多项式非零项系数和指数(绝对值均为不超过1000的整数)。数字间以空格分隔。
输出格式:
输出分2行,分别以指数递降方式输出乘积多项式以及和多项式非零项的系数和指数。数字间以空格分隔,但结尾不能有多余空格。零多项式应输出0 0。
输入样例:
4 3 4 -5 2 6 1 -2 0
3 5 20 -7 4 3 1
输出样例:
15 24 -25 22 30 21 -10 20 -21 8 35 6 -33 5 14 4 -15 3 18 2 -6 1
5 20 -4 4 -5 2 9 1 -2 0
求解思路
1.多项式表示
2. 程序框架
3. 读多项式
4. 加法实现:指数相同,系数相加
5. 乘法实现:指数相加,系数相乘
6. 多项式输出
#include<stdio.h>
#include<stdlib.h>
//链表的数据结构设计
typedef struct PolyNode *Polynomial;
struct PolyNode{
int coef;
int expon;
Polynomial link;
};
void Attach(int c,int e, Polynomial *pRear)
{
Polynomial P;
P=(Polynomial)malloc(sizeof(struct PolyNode));
P->coef=c;
P->expon = e;
P->link = NULL;
(*pRear)->link = P;
*pRear = P;
}
Polynomial ReadPoly()
{
Polynomial P,Rear,t;
int c,e,N;
scanf("%d",&N);
P = (Polynomial)malloc(sizeof(struct PolyNode)); //表头空结点
P->link =NULL ;
Rear=P;
while(N--){
scanf("%d%d",&c,&e); //输入保存
Attach(c,e,&Rear); //链表中加入此数据
}
t= P; P =P->link; free(t); //删除零时生成的头节点
return P;
}
Polynomial Add(Polynomial P1, Polynomial P2)
{
Polynomial t1,t2,P,Rear;
if(!P1&&!P2) return NULL;
t1 = P1; //跳过头指针
t2 = P2;
P = (Polynomial)malloc(sizeof(struct PolyNode)); P->link = NULL; //新建表头,下一个指向null
Rear= P;
while(t1&&t2)
{
if(t1->expon == t2->expon) //相等
{
if(t1->coef+t2->coef){
Attach(t1->coef+t2->coef,t1->expon,&Rear);
t1=t1->link;
t2=t2->link;
}
else{
t1=t1->link;
t2=t2->link;
}
}
else if (t1->expon > t2->expon){
Attach(t1->coef,t1->expon,&Rear);
t1=t1->link;
}
else{
Attach(t2->coef,t2->expon,&Rear);
t2=t2->link;
}
}
while(t1){
Attach(t1->coef,t1->expon,&Rear);
t1=t1->link;
}
while(t2){
Attach(t2->coef,t2->expon,&Rear);
t2=t2->link;
}
Rear=P;P=P->link;free(Rear);
return P;
}
Polynomial Mult(Polynomial P1, Polynomial P2)
{
Polynomial P,Rear,t1 ,t2,t;
int c,e;
if (!P1||!P2) return NULL; //有一个为空就不乘了
t1= P1;
t2 = P2;
P= (Polynomial)malloc(sizeof(struct PolyNode));P->link = NULL; //新建p,指向null
Rear = P;
while (t2){ //系数相乘,指数相加
Attach(t1->coef*t2->coef, t1->expon+t2->expon, & Rear); //让t1的第一项乘以t2的每一项——而得到P
t2=t2->link;
}
t1=t1->link;
while(t1){
t2 = P2;
Rear = P;
while(t2){
e = t1->expon+t2->expon; //逐个相乘
c= t1->coef * t2 ->coef;
while(Rear->link && Rear->link -> expon >e) Rear = Rear->link; //找到插入的位置
//这时Rear中下一个不大于e
if(Rear->link&&Rear->link->expon ==e){
//相等则coef相加
if(Rear->link->coef +c )
Rear->link->coef+=c;
else{ //系数相加为0
t=Rear->link;
Rear->link=t->link; //略过下一项
free(t);
}
}
else //小于e,则插入link之前
{
t = (Polynomial)malloc(sizeof(struct PolyNode));
t->coef = c;
t->expon = e;
t->link = Rear->link;
Rear->link=t;
Rear=Rear->link; //加了一项进去
}
t2=t2->link;
}
t1=t1->link;
}
t2=P;P=P->link; free(t2); //free(t2)就把P内存delete了
return P;
}
void PrintPoly(Polynomial P)
{
int flag = 0;
if(!P){printf("0 0\n"); return;}
while(P){
if(!flag) flag=1; //输出头部不加空格,后面要加空格
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;
}
关于链表表头问题
attach函数是将一个结构链表加到表头后面,即表头为空,
所以mult和add函数返回的链表需要略过表头——即return p->link;
头节点为新申请的动态内存,不要忘记释放;