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
照着老师的例程,搞了好久终于弄出来了。
#include <iostream>
#include <cstdlib>
using namespace std;
typedef struct PolyNode *Polynomial;
struct PolyNode{
int coef;//系数
int expon;//指数
Polynomial link;
};
int compare(int e1,int e2)
{
if(e1==e2)return 0;
else if(e1>e2) return 1;
else return -1;
};
void Attach(int c,int e, Polynomial *pRear)
{
Polynomial P;
P=(Polynomial)malloc(sizeof(struct PolyNode));
P->coef=c;//对新结点赋值
P->expon=e;
P->link=NULL;
(*pRear)->link=P;
*pRear=P;// 修改pRear值
}
Polynomial ReadPoly()
{
Polynomial P,Rear,t;
int c,e,N;
cin>>N;
P=(Polynomial)malloc(sizeof(struct PolyNode));//链表头空结点
P->link=NULL;
Rear=P;
while(N--){
cin>>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)
{
Polynomial front,rear,temp;
int sum;
rear=(Polynomial)malloc(sizeof(struct PolyNode));
front=rear; //用front来记录结果多项式的头结点
while(P1&&P2) //当两个多项式都有非零项待处理时
switch(compare(P1->expon,P2->expon)){
case 1:
Attach(P1->coef,P1->expon,&rear);
P1=P1->link;
break;
case -1:
Attach(P2->coef,P2->expon,&rear);
P2=P2->link;
break;
case 0:
sum=P1->coef+P2->coef;
if(sum) Attach(sum,P1->expon,&rear);
P1=P1->link;
P2=P2->link;
break;
}
for(;P1;P1=P1->link) Attach(P1->coef,P1->expon,&rear);
for(;P2;P2=P2->link) Attach(P2->coef,P2->expon,&rear);
rear->link=NULL;
temp=front;
front=front->link;
free(temp);
return front;
}
Polynomial Mult(Polynomial P1,Polynomial P2)
{
Polynomial P,Rear,t1,t2,t;
int c,e;
if(!P1||!P2) return NULL;
t1=P1;
t2=P2;
P=(Polynomial)malloc(sizeof(struct PolyNode));
P->link = NULL;
Rear=P;
while(t2){ //先用P1的第一项乘以P2,得到P
Attach(t1->coef*t2->coef,t1->expon+t2->expon,&Rear);
t2=t2->link;
}
t1=t1->link;//
while(t1){
t2=P2;Rear=P;
while(t2){
e=t1->expon+t2->expon;
c=t1->coef*t2->coef;
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;
}
t2=P;P=P->link;free(t2);
return P;
}
void PrintPoly(Polynomial P)// 输出多项式
{
int flag=0;
if(!P){cout<<"0 0\n";return;}
while(P){
if(!flag)
flag=1;
else
cout<<' ';
cout<<P->coef<<' '<<P->expon;
P=P->link;
}
cout<<endl;
}
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;
}