一元多项式计算-白红宇

一元多项式计算

阅读量：6329 次

发布时间：2019-06-22

本文共 14322 字，大约阅读时间需要 47 分钟。

1 #include 
     
        2 #include 
      
         3 #include 
       
          4 #include 
        
           5 #include 
         
            6 #define LIST_INIT_SIZE 100  7 using namespace std;  8 typedef struct{  9         int *elem; 10         int length; 11         int listsize; 12         }Sqlist;//顺序存储结构； 13   14   15   16   17 typedef struct LNode{ 18         int data;//系数  19         int elem;//指数；  20         struct LNode *next; 21          22         }LNode,*LinkList;//动态存储； 23  24           25 void Polyomial_one_input(Sqlist &list)// 顺序存储结构多项式输入 26 {printf("\n%15s","");cout<<"请输入多项式最高次幂"; 27  int n; 28  cin>>n;  29  system("cls"); 30  printf("\n%15s","");cout<<"请输入多项式的各项系数(按指数降序)\n"; 31  int i,j,k; 32  int sum=0; 33  for(i=n;i>=0;i--) 34  {cin>>list.elem[i]; 35  if(list.elem[i]==0) 36  sum++; 37  } 38  list.length=n+1; 39  double x=sum,y=n+1; 40  system("cls"); 41  if(x/y>0.3) 42  {printf("\n%15s","*");cout<<"该多项式是稀疏多项式\n";} 43  else 44  {printf("\n%15s","*");cout<<"该多项式不是稀疏多项式\n";} 45 } 46  47 void Polyomial_one_add(Sqlist list_one,Sqlist list_two,Sqlist &list_three) 48 { 49      int i; 50       51      int n1=list_one.length-1,n2=list_two.length-1,n3=0; 52       53      for(i=0;((i<=n1)&&(i<=n2));i++) 54      {list_three.elem[i]=list_one.elem[i]+list_two.elem[i];} 55      for(i;i<=n1;i++) 56      list_three.elem[i]=list_one.elem[i]; 57      for(i;i<=n2;i++) 58      list_three.elem[i]=list_two.elem[i]; 59      list_three.length=i; 60 } 61  62 void Polyomial_one_multiply(Sqlist list_one,Sqlist list_two,Sqlist &list_three) 63 { 64 int i,j; 65 for(i=0;i
          
           n) 73 n=i+j; 74 } 75 list_three.length=n+1; 76 } 77 78 79 80 81 82 83 84 85 86 void Polyomial_one_output(Sqlist list_three) 87 { 88 int i; 89 cout<<"按指数升序：\n"; 90 int k=0; 91 for(i=0;i
           
            0)102 {cout<<" + "<
            
             =0;i--)118 { if(list_three.elem[i]==0)119 continue;120 121 122 if(k==0)123 {cout<
             
              0)128 {cout<<" + "<
              
               next=NULL;197 L1->data=0;198 L2=(LinkList)malloc(sizeof(LNode));199 L2->next=NULL;200 L2->data=0;201 L3=(LinkList)malloc(sizeof(LNode));202 L3->next=NULL;203 L3->data=0;204 205 printf("%15s","");cout<<"多项式1\n"; 206 Polyomial_two_input(L1);207 cout<<"多项式1:"; Polyomial_two_output(L1);208 printf("%15s","");209 system("PAUSE");210 system("cls");211 printf("%15s","");cout<<"多项式2\n"; 212 Polyomial_two_input(L2);cout<<"多项式2:";213 Polyomial_two_output(L2);214 system("PAUSE");215 system("cls");216 cout<<"多项式和为：\n";217 218 Polyomial_two_add(L1,L2,L3);219 Polyomial_two_output(L3);220 LinkList pp=L3->next,ppp;221 L3->next=NULL;222 while(pp)223 {ppp=pp;224 pp=pp->next;225 free(ppp);226 }227 system("PAUSE");228 system("cls");229 cout<<"多项式乘积为：\n";230 Polyomial_two_multiply(L1,L2,L3);231 Polyomial_two_output(L3);232 233 }234 235 236 void Polyomial_two_output(LinkList L)237 { int i,j;238 cout<<"按指数升序：\n";239 int k=0;240 LinkList p=L->next;241 while(p)242 { if(k==0)243 {cout<
               
                data;244 if(p->elem!=0)245 cout<<"X("<
                
                 elem<<")";k++;}246 else247 { if(p->data>0)248 {cout<<" + "<
                 
                  data;249 if(p->elem!=0)250 cout<<"X("<
                  
                   elem<<")";}251 else252 {cout<<" - "<
                   
                    data*(-1);253 if(p->elem!=0)254 cout<<"X("<
                    
                     elem<<")";}255 k++;256 }257 p=p->next;258 }259 260 261 cout<
                     
                      data;i>0;i--)266 { j=1;p=L;267 while(j<=i)268 {p=p->next;j++;}269 270 271 272 if(k==0)273 {cout<
                      
                       data;274 if(p->elem!=0)275 cout<<"X("<
                       
                        elem<<")";k++;}276 else277 { if(p->data>0)278 {cout<<" + "<
                        
                         data;279 if(p->elem!=0)280 cout<<"X("<
                         
                          elem<<")";}281 else282 {cout<<" - "<
                          
                           data*(-1);283 if(p->elem!=0)284 cout<<"X("<
                           
                            elem<<")";}285 k++;286 }287 }288 289 290 291 292 293 }294 void Polyomial_two_multiply(LinkList L1,LinkList L2,LinkList &L3)295 {LinkList p,p1,p2,p3;296 297 298 for(p1=L1->next;p1;p1=p1->next)299 { for(p2=L2->next;p2;p2=p2->next)300 {301 302 for(p3=L3->next,p=L3;p3;p3=p3->next,p=p->next)303 if((p1->elem+p2->elem)<=p3->elem)304 break;305 if(!p3)306 {LinkList pp=(LinkList)malloc(sizeof(LNode));307 pp->next=NULL;308 pp->data=p1->data*p2->data;309 pp->elem=p1->elem+p2->elem;310 p->next=pp;311 }312 else313 { if(p3->elem==(p1->elem+p2->elem))314 p3->data+=(p1->data*p2->data);315 else316 {LinkList pp=(LinkList)malloc(sizeof(LNode));317 pp->next=NULL;318 pp->data=p1->data*p2->data;319 pp->elem=p1->elem+p2->elem;320 pp->next=p->next;321 p->next=pp;322 }323 }324 }}325 p3=L3->next;326 p=L3;327 L3->data=0;328 while(p3)329 { if(p3->data==0)330 {p->next=p3->next;331 free(p3);332 p3=p->next;}333 else334 { L3->data++;p3=p3->next;}335 }336 }337 338 339 340 341 342 343 344 345 346 347 348 void Polyomial_two_add(LinkList L1,LinkList L2,LinkList &L3)349 {LinkList p1,p2,p3;350 351 352 L3->data=0;353 p3=L3;354 for(p1=L1->next,p2=L2->next;p1&&p2;)355 { if(p1->elem
                            
                             elem)356 {p3->next=(LinkList)malloc(sizeof(LNode));357 p3=p3->next;358 p3->next=NULL;359 p3->data=p1->data;360 p3->elem=p1->elem;361 p1=p1->next;L3->data++;362 }363 else if(p1->elem>p2->elem)364 {p3->next=(LinkList)malloc(sizeof(LNode));365 p3=p3->next;366 p3->next=NULL;367 p3->data=p2->data;368 p3->elem=p2->elem;369 p2=p2->next;L3->data++;370 }371 else372 { int n=p1->data+p2->data;373 if(n)374 {p3->next=(LinkList)malloc(sizeof(LNode));375 p3=p3->next;376 p3->next=NULL;377 p3->data=n;378 p3->elem=p2->elem;379 p2=p2->next;p1=p1->next;L3->data++;}380 381 }382 }383 for(p1;p1;p1=p1->next)384 {p3->next=(LinkList)malloc(sizeof(LNode));385 p3=p3->next;386 p3->next=NULL;387 p3->data=p1->data;388 p3->elem=p1->elem;389 L3->data++;390 }391 for(p2;p2;p2=p2->next)392 {p3->next=(LinkList)malloc(sizeof(LNode));393 p3=p3->next;394 p3->next=NULL;395 p3->data=p2->data;396 p3->elem=p2->elem;397 L3->data++;398 }399 400 }401 void Polyomial_two_input(LinkList &L)402 {printf("\n%15s","");cout<<"请输入多项式最高次幂";403 int n;404 cin>>n; 405 system("cls");406 printf("\n%15s","");cout<<"请输入多项式的各项系数(按指数降序)\n";407 int i,k;408 409 LinkList p,p1;410 L->data=0;411 L->next=NULL;412 for(i=n;i>=0;i--)413 {cin>>k;414 if(k==0)415 continue;416 L->data++;417 p1=(LinkList)malloc(sizeof(LNode));418 p1->data=k;419 p1->elem=i;420 p1->next=NULL;421 p1->next=L->next;422 L->next=p1;423 }424 double x=L->data,y=n+1;425 system("cls");426 if(x/y>0.3)427 {printf("\n%15s","*");cout<<"该多项式不是稀疏多项式\n";}428 else429 {printf("\n%15s","*");cout<<"该多项式是稀疏多项式\n";}430 }431 432 433 434 435 436 437 438 int main(int argc, char *argv[])439 {printf("\n%15s","*");cout<<"*************************************************";440 printf("\n%15s","*");cout<<"****************一元多项式计算*******************\n";441 442 printf("\n%15s","*");cout<<"采用顺序结构请按1，动态存储结构请按2\n";443 printf("\n%15s","");444 int n;445 cin>>n;446 while(n<1||n>2)447 { printf("\n%15s","*");cout<<"输入错误，请重新输入";cin>>n;}448 system("cls");449 if(n==1)450 {Polyomial_one();}451 else452 {Polyomial_two();}453 454 system("PAUSE");455 return EXIT_SUCCESS;456 }457 458

#include <cstdlib>

#include <iostream>

#include <conio.h>

#include <string.h>

#include <stdio.h>

#define LIST_INIT_SIZE 100

using namespace std;

typedef struct{

int *elem;

int length;

int listsize;

}Sqlist;//顺序存储结构；

typedef struct LNode{

int data;//系数

int elem;//指数；

struct LNode *next;

}LNode,*LinkList;//动态存储；

void Polyomial_one_input(Sqlist &list)// 顺序存储结构多项式输入

{printf("\n%15s","");cout<<"请输入多项式最高次幂

int n;

cin>>n;

system("cls");

printf("\n%15s","");cout<<"请输入多项式的各项系数(按指数降序)

\n";

int i,j,k;

int sum=0;

for(i=n;i>=0;i--)

{cin>>list.elem[i];

if(list.elem[i]==0)

sum++;

}

list.length=n+1;

double x=sum,y=n+1;

system("cls");

if(x/y>0.3)

{printf("\n%15s","*");cout<<"该多项式是稀疏多项式\n";}

else

{printf("\n%15s","*");cout<<"该多项式不是稀疏多项式\n";}

}

void Polyomial_one_add(Sqlist list_one,Sqlist list_two,Sqlist &list_three)

{

int i;

int n1=list_one.length-1,n2=list_two.length-1,n3=0;

for(i=0;((i<=n1)&&(i<=n2));i++)

{list_three.elem[i]=list_one.elem[i]+list_two.elem[i];}

for(i;i<=n1;i++)

list_three.elem[i]=list_one.elem[i];

for(i;i<=n2;i++)

list_three.elem[i]=list_two.elem[i];

list_three.length=i;

}

void Polyomial_one_multiply(Sqlist list_one,Sqlist list_two,Sqlist &list_three)

{

int i,j;

for(i=0;i<list_one.length+list_two.length;i++)

list_three.elem[i]=0;

list_three.length=0;

int n=0;

for(i=0;i<list_one.length;i++)

for(j=0;j<list_two.length;j++)

{list_three.elem[i+j]+=list_one.elem[i]*list_two.elem[j];

if((i+j)>n)

n=i+j;

}

list_three.length=n+1;

}

void Polyomial_one_output(Sqlist list_three)

{

int i;

cout<<"按指数升序：\n";

int k=0;

for(i=0;i<list_three.length;i++)

{ if(list_three.elem[i]==0)

continue;

if(k==0)

{cout<<list_three.elem[i];

if(i!=0)

cout<<"X("<<i<<")";k++;}

else

{

if(list_three.elem[i]>0)

{cout<<" + "<<list_three.elem[i];

if(i!=0)

cout<<"X("<<i<<")";}

else

{cout<<" - "<<list_three.elem[i]*(-1);

if(i!=0)

cout<<"X("<<i<<")";}

k++;

}

cout<<endl;

k=0;

cout<<"按指数降序：\n";

for(i=list_three.length-1;i>=0;i--)

{ if(list_three.elem[i]==0)

continue;

if(k==0)

{cout<<list_three.elem[i];

if(i!=0)

cout<<"X("<<i<<")";k++;}

else

{

if(list_three.elem[i]>0)

{cout<<" + "<<list_three.elem[i];

if(i!=0)

cout<<"X("<<i<<")";}

else

{cout<<" - "<<list_three.elem[i]*(-1);

if(i!=0)

cout<<"X("<<i<<")";}

k++;

}

void Polyomial_one()//顺序存储；

{ Sqlist list_one,list_two,list_three;

list_one.elem=(int *)malloc(sizeof(int)*LIST_INIT_SIZE);

list_one.length=0;

list_one.listsize=LIST_INIT_SIZE;

list_two.elem=(int *)malloc(sizeof(int)*LIST_INIT_SIZE);

list_two.length=0;

list_two.listsize=LIST_INIT_SIZE;

list_three.elem=(int *)malloc(sizeof(int)*LIST_INIT_SIZE);

list_three.length=0;

list_three.listsize=LIST_INIT_SIZE;

printf("%15s","");cout<<"多项式1

Polyomial_one_input(list_one);

cout<<"多项式1:"; Polyomial_one_output(list_one);

printf("%15s","");

system("PAUSE");

system("cls");

printf("%15s","");cout<<"多项式2

Polyomial_one_input(list_two);cout<<"多项式2:";

Polyomial_one_output(list_two);

system("PAUSE");

system("cls");

cout<<"多项式和为：\n";

Polyomial_one_add(list_one,list_two,list_three);

Polyomial_one_output(list_three);

system("PAUSE");

system("cls");

cout<<"多项式乘积为：\n";

Polyomial_one_multiply(list_one,list_two,list_three);

Polyomial_one_output(list_three);

}

void Polyomial_two_output(LinkList L);

void Polyomial_two_multiply(LinkList L1,LinkList L2,LinkList &L3);

void Polyomial_two_add(LinkList L1,LinkList L2,LinkList &L3);

void Polyomial_two_input(LinkList &L);

void Polyomial_two()//动态存储；

{LinkList L1,L2,L3;

L1=(LinkList)malloc(sizeof(LNode));

L1->next=NULL;

L1->data=0;

L2=(LinkList)malloc(sizeof(LNode));

L2->next=NULL;

L2->data=0;

L3=(LinkList)malloc(sizeof(LNode));

L3->next=NULL;

L3->data=0;

printf("%15s","");cout<<"多项式1

\n";

Polyomial_two_input(L1);

cout<<"多项式1:"; Polyomial_two_output(L1);

printf("%15s","");

system("PAUSE");

system("cls");

printf("%15s","");cout<<"多项式2

\n";

Polyomial_two_input(L2);cout<<"多项式2:";

Polyomial_two_output(L2);

system("PAUSE");

system("cls");

cout<<"多项式和为：\n";

Polyomial_two_add(L1,L2,L3);

Polyomial_two_output(L3);

LinkList pp=L3->next,ppp;

L3->next=NULL;

while(pp)

{ppp=pp;

pp=pp->next;

free(ppp);

}

system("PAUSE");

system("cls");

cout<<"多项式乘积为：\n";

Polyomial_two_multiply(L1,L2,L3);

Polyomial_two_output(L3);

}

void Polyomial_two_output(LinkList L)

{

int i,j;

cout<<"按指数升序：\n";

int k=0;

LinkList p=L->next;

while(p)

{ if(k==0)

{cout<<p->data;

if(p->elem!=0)

cout<<"X("<<p->elem<<")";k++;}

else

{

if(p->data>0)

{cout<<" + "<<p->data;

if(p->elem!=0)

cout<<"X("<<p->elem<<")";}

else

{cout<<" - "<<p->data*(-1);

if(p->elem!=0)

cout<<"X("<<p->elem<<")";}

k++;

}

p=p->next;

}

cout<<endl;

k=0;

cout<<"按指数降序：\n";

for(i=L->data;i>0;i--)

{ j=1;p=L;

while(j<=i)

{p=p->next;j++;}

if(k==0)

{cout<<p->data;

if(p->elem!=0)

cout<<"X("<<p->elem<<")";k++;}

else

{

if(p->data>0)

{cout<<" + "<<p->data;

if(p->elem!=0)

cout<<"X("<<p->elem<<")";}

else

{cout<<" - "<<p->data*(-1);

if(p->elem!=0)

cout<<"X("<<p->elem<<")";}

k++;

}

void Polyomial_two_multiply(LinkList L1,LinkList L2,LinkList &L3)

{LinkList p,p1,p2,p3;

for(p1=L1->next;p1;p1=p1->next)

{

for(p2=L2->next;p2;p2=p2->next)

{

for(p3=L3->next,p=L3;p3;p3=p3->next,p=p->next)

if((p1->elem+p2->elem)<=p3->elem)

break;

if(!p3)

{LinkList pp=(LinkList)malloc(sizeof(LNode));

pp->next=NULL;

pp->data=p1->data*p2->data;

pp->elem=p1->elem+p2->elem;

p->next=pp;

}

else

{

if(p3->elem==(p1->elem+p2->elem))

p3->data+=(p1->data*p2->data);

else

{LinkList pp=(LinkList)malloc(sizeof(LNode));

pp->next=NULL;

pp->data=p1->data*p2->data;

pp->elem=p1->elem+p2->elem;

pp->next=p->next;

p->next=pp;

}

}}

p3=L3->next;

p=L3;

L3->data=0;

while(p3)

{

if(p3->data==0)

{p->next=p3->next;

free(p3);

p3=p->next;}

else

{ L3->data++;p3=p3->next;}

}

void Polyomial_two_add(LinkList L1,LinkList L2,LinkList &L3)

{LinkList p1,p2,p3;

L3->data=0;

p3=L3;

for(p1=L1->next,p2=L2->next;p1&&p2;)

{

if(p1->elem<p2->elem)

{p3->next=(LinkList)malloc(sizeof(LNode));

p3=p3->next;

p3->next=NULL;

p3->data=p1->data;

p3->elem=p1->elem;

p1=p1->next;L3->data++;

}

else if(p1->elem>p2->elem)

{p3->next=(LinkList)malloc(sizeof(LNode));

p3=p3->next;

p3->next=NULL;

p3->data=p2->data;

p3->elem=p2->elem;

p2=p2->next;L3->data++;

}

else

{

int n=p1->data+p2->data;

if(n)

{p3->next=(LinkList)malloc(sizeof(LNode));

p3=p3->next;

p3->next=NULL;

p3->data=n;

p3->elem=p2->elem;

p2=p2->next;p1=p1->next;L3->data++;}

}

for(p1;p1;p1=p1->next)

{p3->next=(LinkList)malloc(sizeof(LNode));

p3=p3->next;

p3->next=NULL;

p3->data=p1->data;

p3->elem=p1->elem;

L3->data++;

}

for(p2;p2;p2=p2->next)

{p3->next=(LinkList)malloc(sizeof(LNode));

p3=p3->next;

p3->next=NULL;

p3->data=p2->data;

p3->elem=p2->elem;

L3->data++;

}

void Polyomial_two_input(LinkList &L)

{printf("\n%15s","");cout<<"请输入多项式最高次幂

int n;

cin>>n;

system("cls");

printf("\n%15s","");cout<<"请输入多项式的各项系数(按指数降序)

\n";

int i,k;

LinkList p,p1;

L->data=0;

L->next=NULL;

for(i=n;i>=0;i--)

{cin>>k;

if(k==0)

continue;

L->data++;

p1=(LinkList)malloc(sizeof(LNode));

p1->data=k;

p1->elem=i;

p1->next=NULL;

p1->next=L->next;

L->next=p1;

}

double x=L->data,y=n+1;

system("cls");

if(x/y>0.3)

{printf("\n%15s","*");cout<<"该多项式不是稀疏多项式\n";}

else

{printf("\n%15s","*");cout<<"该多项式是稀疏多项式\n";}

}

int main(int argc, char *argv[])

{printf("\n%15s","*");cout<<"*************************************************";

printf("\n%15s","*");cout<<"****************一元多项式计算*******************\n";

printf("\n%15s","*");cout<<"采用顺序结构请按1，动态存储结构请按2\n";

printf("\n%15s","");

int n;

cin>>n;

while(n<1||n>2)

{ printf("\n%15s","*");cout<<"输入错误，请重新输入

";cin>>n;}

system("cls");

if(n==1)

{Polyomial_one();}

else

{Polyomial_two();}

system("PAUSE");

return EXIT_SUCCESS;

}

转载于:https://www.cnblogs.com/zjushuiping/archive/2012/05/30/2527002.html

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