一元多项式的相乘(代码)

Posted 2020-08-09 XJX

  1 #include <iostream>
  2 #include<stdlib.h>
  3 
  4 using namespace std;
  5 
  6 
  7 #define MAXSIZE 20
  8 
  9 typedef struct LNode
 10 {
 11     int coef;//系数
 12     int expn;//指数
 13     struct LNode *next;
 14 }LNode,*LinkList;
 15 
 16 
 17 int CreateList_L(LinkList &L,int n)
 18 {
 19     LinkList p,q;
 20     for(int i=0;i<n;i++)
 21     {
 22          p=(LinkList)malloc(sizeof(LNode));
 23          cout<<"输入元素系数：";
 24          cin>>p->coef;
 25          cout<<"输入元素指数：";
 26          cin>>p->expn;
 27          if(i==0)L=p;
 28          else q->next=p;
 29          q=p;
 30          p->next=NULL;
 31     }
 32    return 0;
 33 }
 34 
 35 
 36 int LengthPolyn(LinkList L)//判断多项式的项数
 37 {
 38     int s=0;
 39     while(L)
 40     {
 41         s++;
 42         L=L->next;
 43     }
 44     return s;
 45 }
 46 
 47 
 48 int CopyList_L(LinkList La,LinkList &Lb)//开辟一段和La指向的空间一样的新的空间，并把La中各元素的值依次复制到Lb中
 49 {
 50     LinkList p,q,pa=La;
 51     int n=LengthPolyn(La);
 52     for(int i=0;i<n;i++)
 53     {
 54          p=(LinkList)malloc(sizeof(LNode));
 55          p->coef=pa->coef;
 56          p->expn=pa->expn;
 57          if(i==0)Lb=p;
 58          else q->next=p;
 59          q=p;
 60          p->next=NULL;
 61          pa=pa->next;
 62     }
 63    return 0;
 64 }
 65 
 66 
 67 
 68 int Display_L(LinkList L)
 69 {
 70     cout<<"f(x)="<<L->coef;
 71     if(L->expn)cout<<"*"<<"x^"<<L->expn;
 72     L=L->next;
 73     while(L)
 74     {
 75         if(L->coef>0)
 76         {
 77             cout<<"+";
 78             cout<<L->coef<<"*"<<"x^"<<L->expn;
 79         }
 80         else cout<<L->coef<<"*"<<"x^"<<L->expn;
 81         L=L->next;
 82     }
 83     return 0;
 84 }
 85 
 86 
 87 
 88 int AddPolyn(LinkList La,LinkList Lb,LinkList &Lc)
 89 {
 90     LinkList pa,pb,p;
 91     int k=1;
 92     pa=La;pb=Lb;
 93     //确定“和多项式”的头结点
 94     while(k)
 95     {
 96          if(pa->expn<pb->expn){p=Lc=pa;pa=pa->next;k=0;}
 97          else if(pa->expn>pb->expn){p=Lc=pb;pb=pb->next;k=0;}
 98          else
 99          {
100              pa->coef+=pb->coef;
101              if(pa->coef)
102              {
103                   p=Lc=pa;
104                   pa=pa->next;
105                   k=0;
106              }
107              else
108              {
109                  pa=pa->next;
110                  pb=pb->next;
111                  if(!pa||!pb) break;
112              }
113          }
114     }
115     if(!pb&&pa){p=Lc=pa;pa=pa->next;}
116     if(!pa&&pb){p=Lc=pb;pb=pb->next;}
117     if(!pa&&!pb) Lc=NULL;
118     //确定接下来的节点
119     while(pa&&pb)
120     {
121         if(pa->expn<pb->expn){p->next=pa;p=pa;pa=pa->next;}
122         else if(pa->expn>pb->expn){p->next=pb;p=pb;pb=pb->next;}
123         else
124         {
125             pa->coef+=pb->coef;
126             if(pa->coef)
127             {
128                   p->next=pa;
129                   p=pa;
130                   pa=pa->next;
131                   pb=pb->next;
132             }
133             else
134             {
135                   pa=pa->next;
136                   pb=pb->next;
137             }
138 
139         }
140     }
141     while(!pb&&pa)
142     {
143         p->next=pa;
144         p=pa;
145         pa=pa->next;
146     }
147     while(!pa&&pb)
148     {
149         p->next=pb;
150         p=pb;
151         pb=pb->next;
152     }
153     return 0;
154 }
155 
156 
157 
158 int MultiplyPolyn(LinkList La,LinkList Lb,LinkList &Lc)//La指向的多项式乘以Lb指向的多项式
159 {
160     LinkList pa,pb=Lb,l;
161     int i=0,j,n;
162     LNode *L[MAXSIZE];//指针数组，Lb至多MAXSIZE项！
163     while(pb)
164     {
165         CopyList_L(La,L[i]);
166         pa=L[i];
167         while(pa)
168         {
169             pa->coef*=pb->coef;
170             pa->expn+=pb->expn;
171             pa=pa->next;
172         }
173         pb=pb->next;
174         i++;
175     }
176     n=LengthPolyn(Lb);
177     AddPolyn(L[0],L[1],Lc);
178     for(j=2;j<n;j++)
179     {
180         AddPolyn(L[j],l,Lc);
181         l=Lc;
182     }
183     return 0;
184 }
185 
186 
187 
188 int main()
189 {
190     LinkList La,Lb,Lc;
191     int m,n;
192     cout<<"请输入La中的元素个数：";
193     cin>>m;
194     CreateList_L(La,m);
195     cout<<"请输入Lb中的元素个数：";
196     cin>>n;
197     CreateList_L(Lb,n);
198     MultiplyPolyn(La,Lb,Lc);
199     Display_L(Lc);
200     return 0;
201 }