一元多项式计算
1 #include <cstdlib> 2 #include <iostream> 3 #include <conio.h> 4 #include <string.h> 5 #include <stdio.h> 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<list_one.length+list_two.length;i++) 66 list_three.elem[i]=0; 67 list_three.length=0; 68 int n=0; 69 for(i=0;i<list_one.length;i++) 70 for(j=0;j<list_two.length;j++) 71 {list_three.elem[i+j]+=list_one.elem[i]*list_two.elem[j]; 72 if((i+j)>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<list_three.length;i++) 92 { if(list_three.elem[i]==0) 93 continue; 94 95 96 if(k==0) 97 {cout<<list_three.elem[i]; 98 if(i!=0) 99 cout<<"X("<<i<<")";k++;} 100 else 101 {if(list_three.elem[i]>0) 102 {cout<<" + "<<list_three.elem[i]; 103 if(i!=0) 104 cout<<"X("<<i<<")";} 105 else 106 {cout<<" - "<<list_three.elem[i]*(-1); 107 if(i!=0) 108 cout<<"X("<<i<<")";} 109 k++; 110 } 111 112 113 } 114 cout<<endl; 115 k=0; 116 cout<<"按指数降序：\n"; 117 for(i=list_three.length-1;i>=0;i--) 118 { if(list_three.elem[i]==0) 119 continue; 120 121 122 if(k==0) 123 {cout<<list_three.elem[i]; 124 if(i!=0) 125 cout<<"X("<<i<<")";k++;} 126 else 127 {if(list_three.elem[i]>0) 128 {cout<<" + "<<list_three.elem[i]; 129 if(i!=0) 130 cout<<"X("<<i<<")";} 131 else 132 {cout<<" - "<<list_three.elem[i]*(-1); 133 if(i!=0) 134 cout<<"X("<<i<<")";} 135 k++; 136 } 137 } 138 } 139 140 141 142 143 144 145 void Polyomial_one()//顺序存储； 146 { Sqlist list_one,list_two,list_three; 147 list_one.elem=(int *)malloc(sizeof(int)*LIST_INIT_SIZE); 148 list_one.length=0; 149 list_one.listsize=LIST_INIT_SIZE; 150 list_two.elem=(int *)malloc(sizeof(int)*LIST_INIT_SIZE); 151 list_two.length=0; 152 list_two.listsize=LIST_INIT_SIZE; 153 list_three.elem=(int *)malloc(sizeof(int)*LIST_INIT_SIZE); 154 list_three.length=0; 155 list_three.listsize=LIST_INIT_SIZE; 156 157 printf("%15s","");cout<<"多项式1"; 158 Polyomial_one_input(list_one); 159 cout<<"多项式1:"; Polyomial_one_output(list_one); 160 printf("%15s",""); 161 system("PAUSE"); 162 system("cls"); 163 printf("%15s","");cout<<"多项式2"; 164 Polyomial_one_input(list_two);cout<<"多项式2:"; 165 Polyomial_one_output(list_two); 166 system("PAUSE"); 167 system("cls"); 168 cout<<"多项式和为：\n"; 169 170 Polyomial_one_add(list_one,list_two,list_three); 171 Polyomial_one_output(list_three); 172 system("PAUSE"); 173 system("cls"); 174 cout<<"多项式乘积为：\n"; 175 Polyomial_one_multiply(list_one,list_two,list_three); 176 Polyomial_one_output(list_three); 177 178 } 179 180 181 182 183 184 185 186 187 188 void Polyomial_two_output(LinkList L); 189 void Polyomial_two_multiply(LinkList L1,LinkList L2,LinkList &L3); 190 void Polyomial_two_add(LinkList L1,LinkList L2,LinkList &L3); 191 void Polyomial_two_input(LinkList &L); 192 193 void Polyomial_two()//动态存储； 194 {LinkList L1,L2,L3; 195 L1=(LinkList)malloc(sizeof(LNode)); 196 L1->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<<p->data; 244 if(p->elem!=0) 245 cout<<"X("<<p->elem<<")";k++;} 246 else 247 {if(p->data>0) 248 {cout<<" + "<<p->data; 249 if(p->elem!=0) 250 cout<<"X("<<p->elem<<")";} 251 else 252 {cout<<" - "<<p->data*(-1); 253 if(p->elem!=0) 254 cout<<"X("<<p->elem<<")";} 255 k++; 256 } 257 p=p->next; 258 } 259 260 261 cout<<endl; 262 k=0; 263 264 cout<<"按指数降序：\n"; 265 for(i=L->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<<p->data; 274 if(p->elem!=0) 275 cout<<"X("<<p->elem<<")";k++;} 276 else 277 {if(p->data>0) 278 {cout<<" + "<<p->data; 279 if(p->elem!=0) 280 cout<<"X("<<p->elem<<")";} 281 else 282 {cout<<" - "<<p->data*(-1); 283 if(p->elem!=0) 284 cout<<"X("<<p->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 else 313 {if(p3->elem==(p1->elem+p2->elem)) 314 p3->data+=(p1->data*p2->data); 315 else 316 {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 else 334 { 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<p2->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 else 372 {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 else 429 {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 else 452 {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 100using 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;}
