設計函數分別求兩個一元多項式的乘積與和。
輸入格式:
輸入分2行,每行分別先給出多項式非零項的個數,再以指數遞降方式輸入一個多項式非零項係數和指數(絕對值均爲不超過1000的整數)。數字間以空格分隔。
輸出格式:
輸出分2行,分別以指數遞降方式輸出乘積多項式以及和多項式非零項的係數和指數。數字間以空格分隔,但結尾不能有多餘空格。零多項式應輸出0 0
。
輸入樣例:
4 3 4 -5 2 6 1 -2 0
3 5 20 -7 4 3 1
輸出樣例:
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
分析:這是數據結構中典型的例題,其中加法運算經常遇到,乘法運算不常見,涉及到多項式相乘算法,同類項合併算法以及對於係數爲0時的處理。這道題充分鍛鍊了對了鏈表的理解和操作。
#include<iostream>
using namespace std;
typedef struct PolyNode
{
int coef;
int expon;
struct PolyNode * next;
}*Polynomial;
Polynomial ReadPoly()//輸入(尾插法)
{
int n;
cin >>n;
Polynomial L=new PolyNode;
Polynomial r=L;
L->next=NULL;
while(n--)
{
Polynomial p=new PolyNode;
cin>>p->coef>>p->expon;
if(p->coef==0)//係數爲0,不讀
{
delete p;
continue;
}
p->next=NULL;
r->next=p;
r=p;
}
return L;
}
Polynomial Mult(Polynomial P1,Polynomial P2)
{
Polynomial p1=P1->next;
Polynomial p2=P2->next;
Polynomial P3=new PolyNode;
Polynomial temp=new PolyNode;
temp->coef=1000000001;
temp->expon=10001;
P3->next=temp;
Polynomial temp2=new PolyNode;
temp2->coef=-1000000001;
temp2->expon=-10001;
temp->next=temp2;
temp2->next=NULL;
//while(p1)
for(p1=P1->next;p1!=NULL;p1=p1->next)
{
for(p2=P2->next;p2!=NULL;p2=p2->next)
//while(p2)
{
Polynomial p3=new PolyNode;
p3->coef=(p1->coef)*(p2->coef);
p3->expon=p1->expon+p2->expon;
p3->next=NULL;
if(p3->coef==0)
{
continue;
}
for(Polynomial pp=P3->next;pp->next!=NULL;pp=pp->next)
{
if(pp->expon==p3->expon)
{
pp->coef+=p3->coef;
break;
}
if(p3->expon < pp->expon && p3->expon > pp->next->expon)
{
p3->next=pp->next;
pp->next=p3;
break;
}
}
}
}
P3->next=P3->next->next;
Polynomial pk=P3;
while(pk)//刪除後標誌
{
if(pk->next->next==NULL)
pk->next=NULL;
pk=pk->next;
}
pk=P3->next;
Polynomial pr=P3;
while(pk)
{
if(pk->coef==0)
{
pr->next=pk->next;
pk=pk->next;
}
pk=pk->next;
pr=pr->next;
}
return P3;
}
void PrintPoly(Polynomial p)
{
if(p->next==NULL)
cout<<0<<" "<<0<<endl;
p=p->next;
while(p)
{
cout<<p->coef<<" "<<p->expon;
if(p->next==NULL)
{
cout<<endl;
}
else
cout<<" ";
p=p->next;
}
}
Polynomial Add(Polynomial P1,Polynomial P2)
{
Polynomial p1=P1->next;
Polynomial p2=P2->next;
Polynomial P3=new PolyNode;
Polynomial r3=P3;
P3->next=NULL;
while(p1&&p2)
{
if(p1->expon==p2->expon)
{
if(p1->coef+p2->coef!=0)
{
Polynomial p3=new PolyNode;
p3->coef=(p1->coef)+(p2->coef);
p3->expon=p2->expon;
p3->next=NULL;
r3->next=p3;
r3=p3;
p1=p1->next;
p2=p2->next;
}
else
{
p1=p1->next;
p2=p2->next;
}
}
else if(p1->expon>p2->expon)
{
Polynomial p3=new PolyNode;
p3->coef=p1->coef;
p3->expon=p1->expon;
p3->next=NULL;
r3->next=p3;
r3=p3;
p1=p1->next;
}
else
{
Polynomial p3=new PolyNode;
p3->coef=p2->coef;
p3->expon=p2->expon;
p3->next=NULL;
r3->next=p3;
r3=p3;
p2=p2->next;
}
}
r3->next=p1?p1:p2;
return P3;
}
int main()
{
Polynomial P1,P2,PP,PS;
P1=ReadPoly();
P2=ReadPoly();
PP=Mult(P1,P2);
PrintPoly(PP);
PS=Add(P1,P2);
PrintPoly(PS);
//system("PAUSE");
return 0;
}
運行結果如下
轉載請附上原文鏈接