一元多项式计算器(链式结构)

Posted 2022-12-15 fulianzhou

//*一元多项式计算器(链式结构)
/*问题描述：
 设有一元多项式Am(x) 和Bn(x).
   Am(x) = A0+A1x1+A2x2+A3x3+… +Amxm
   Bn(x) = B0+B1x1+B2x2+B3x3+… +Bnxn
   试求M(x)= Am(x)+Bn(x)、M(x)= Am(x)-Bn(x)和M(x)= Am(x)×Bn(x)。
 基本要求：
 ⑴首先判定多项式是否稀疏；
 ⑵分别采用顺序和链式结构实现；
 ⑶结果M(x)中无重复阶项和无零系数项；
 ⑷要求输出结果的升幂和降幂两种排列情况。
*/
#include<stdio.h>
#include<stdlib.h>
#include<time.h>

#define OK 1
#define ERROR 0
#define MAXSIZE 30
typedef int Status;
typedef struct

 int coef; //系数
 int expo; //指数
ElemType;
typedef struct LNode

 ElemType data;
 struct LNode *next;
LNode,*LinkList;
typedef LinkList Polynomial;
//初始化
Status InitPolynomial(Polynomial &P)

 P=(Polynomial)malloc(sizeof(LNode));
 P->next=NULL;
 P->data.coef=0;
 P->data.expo=0;
 return OK;

//长度
int PolynomialLength(Polynomial P)

 int l=0;
 while(P->next!=NULL)
 
  l++;
  P=P->next;
 
 return l;

//输出一个多项式
Status PrintPolynomial(Polynomial P)

 bool first=1;
 while(P->next!=NULL)
 
  P=P->next;
  if(first) first=0;
  else printf("+ ");
  printf("%dX%d",P->data.coef,P->data.expo);    
 
 printf("\\n");
 return OK;

//添加
Status AddNode(Polynomial &P,ElemType &e)

 Polynomial s = P;
 while(s->next!=NULL) s=s->next;
 Polynomial Pnew=(Polynomial)malloc(sizeof(LNode));
 Pnew->next=NULL;
 Pnew->data=e;
 s->next=Pnew;
 return OK;

//追加
Status SupperaddNode(Polynomial &P,ElemType e)

 Polynomial pp=P;
 while(pp->next!=NULL) pp=pp->next;
 Polynomial b=(Polynomial)malloc(sizeof(LNode));
 b->data=e;
 b->next=NULL;
 pp->next=b;
 return OK;

//删除结点
Status DeletePolynomial(Polynomial &P,int n)

 int i=1,l=PolynomialLength(P);
 Polynomial Pa=P;
 if(n>l)
 
  printf("n=%d,l=%d\\n",n,l);
  printf("Error!\\n");
  return ERROR;
 
 while(Pa->next!=NULL && i++!=n) Pa=Pa->next;
 Polynomial s = Pa->next;
 Pa->next=s->next;
 printf("Delet:%dX%d\\n",s->data.coef,s->data.expo);
 free(s);
 return OK;

//创建
Status CreatePolynomial(Polynomial &Pa)

 printf("____________ 输入为 0 0 时结束 __________\\n");
 for(int i=0;;i++)
 
  printf("\\t输入系数和指数:");
  int Coeff,Expon;
  ElemType e;
  scanf("%d%d",&Coeff,&Expon);
  if(!Coeff && !Expon) break;
  if(!Coeff) continue;
  e.coef=Coeff; e.expo=Expon;
  SupperaddNode(Pa,e);
 
 return OK;

//调整(类似插入排序)
//成功诀窍:细心细心再细心，画图模拟，一边又一遍，纸上电脑上代码同时进行，相互比较
/********************************************/
Status Addjust(Polynomial &P,bool flag)  //flag==1->小 , flag==0->大

 Polynomial pd=P,pb=P;
 while(pb->next!=NULL && pd->next!=NULL)
 
  Polynomial pe=pd->next;
  Polynomial pc=pb->next;
  if(pc == pe || pd == pb)
  
   pb=pb->next;
   pd=P;
  
  else if((flag == 0 && pc->data.expo < pe->data.expo) || (flag == 1 && pc->data.expo > pe->data.expo))
  
//将pc插入到pd后
  //先处理pb
   pb->next=pc->next;
  //再处理pc
   pc->next=pd->next;
  //再处理pd
   pd->next=pc;
   pd=P;
  
  else if(pc->data.expo == pe->data.expo)
  
//如果相等就相加
   pe->data.coef+=pc->data.coef;
//删除pc所指的结点
   Polynomial t1=pc;
   pb->next=t1->next;
   pc=pb->next;
   free(t1);
//如果相加为零，删除该点
   if(pe->data.coef == 0)
   
    Polynomial t2=pe;
    pd->next=pe->next;
    free(t2);
    pe=pd->next;
   
   pd=P;
  
  else if((flag == 0 && pc->data.expo > pe->data.expo) || (flag == 1 && pc->data.expo < pe->data.expo))
   pd=pd->next; 
 
 PrintPolynomial(P);
 return OK;

/********************************************/
//随机生成多项式
Status RandomCreate(Polynomial &P)

 printf("\\n产生多少项:");
 int n,m;
 scanf("%d",&n);
 printf("\\n输入 系数 和 指数 的 范围 m。将产生[-m,m]之间的系数和指数,输入m:");
 scanf("%d",&m);
 int M=m*2;
 for(int i=0;i<n;i++)
 
  ElemType e;
  int C=rand()%M-m;
  int E=rand()%M-m;
  if(!C) i--; continue;
  e.coef=C; e.expo=E;
  SupperaddNode(P,e);
 
 return OK;

//多项式相加,相加后的值给P1
Status Polynomial_add(Polynomial &P1,Polynomial &P2)

 Polynomial p=P1;
 printf("\\nA(x)=");
 PrintPolynomial(P1);
 printf("\\nB(x)=");
 PrintPolynomial(P2);
 while(p->next!=NULL) p=p->next;
 p->next=P2;
 Polynomial s=p->next;
 p->next=s->next;
 free(s);
 printf("\\n由 M(x) = A(x) + B(x) \\n\\nM(x)=");
 PrintPolynomial(P1);
 printf("\\n调整后\\n\\nM(x)=");
 Addjust(P1,0);
 P1->next=NULL;
 P2->next=NULL;
 printf("\\n\\t\\t多项式A(x),B(x)已置空，请重新创建.\\n");
 system("pause");
 system("cls");
 return OK;

//多项式相减 P1 - P2
//方法:P2系数全部取反，再相加
Status Polynomial_sub(Polynomial &P1,Polynomial &P2)

 Polynomial p=P2;
 printf("\\nM(x) = A(x) + ( - B(x) )\\n");
 printf("\\nB(x)=");
 PrintPolynomial(P2);
 while(p->next!=NULL)
 
  p=p->next;
  p->data.coef=-p->data.coef;
 
 printf("\\n-B(x)=");
 PrintPolynomial(P2);
 printf("\\n令 B(x) = - B(x)\\n");
 system("pause");
 Polynomial_add(P1,P2);
 return OK;

//生成菜单
int Create_menu()

 printf("\\t\\t 生成两个一元多项式\\n");
 printf("\\t\\t_____________________\\n\\n");
 printf("\\t\\t     1.手动输入.     \\n\\n");
 printf("\\t\\t     2.自动生成.     \\n\\n");
 printf("\\t\\t_____________________\\n");
 printf("-----------请选择:");
 char chi[5];
 scanf("%s",chi);
 return atoi(chi);

//生成多项式
Status Create(Polynomial &A,Polynomial &B)

 int chiose=Create_menu();
 if(chiose == 1)
 
  printf("\\n建立多项式 A(x)\\n");
  CreatePolynomial(A);
  printf("\\nA(x)=");
  PrintPolynomial(A);
  system("pause");
  printf("\\n建立多项式 B(x)\\n");  
  CreatePolynomial(B);
  printf("\\nB(x)=");
  PrintPolynomial(B);
 
 else if(chiose == 2)
 
  printf("_________________________\\n");
  printf("\\n随机生成多项式 A(x) \\n");
  RandomCreate(A);
  printf("\\n已产生随机多项式.\\nA(x)=");
  PrintPolynomial(A);
  printf("\\n整理后\\nA(x)=");
  Addjust(A,0);
  system("pause");
  printf("_________________________\\n");
  printf("\\n随机生成多项式 B(x) \\n");
  RandomCreate(B);
  printf("\\n已产生随机多项式.\\nB(x)=");
  PrintPolynomial(B);
  printf("\\n整理后\\nB(x)=");
  Addjust(B,0);
  printf("_________________________\\n");
 
 return OK;

//多项式升幂
Status Polynomial_ascend(Polynomial &A,Polynomial &B)

 printf("________________________________\\n");
 printf("\\n原来:\\nA(x)=");
 PrintPolynomial(A);
 printf("\\n调整后:\\n");
 printf("A(x)=");
 Addjust(A,0);
 printf("\\n原来:\\nB(x)=");
 PrintPolynomial(B);
 printf("\\n调整后:\\n");
 printf("B(x)=");
 Addjust(B,0);
 printf("________________________________\\n");
 return OK;

//多项式降幂
Status Polynomial_decline(Polynomial &A,Polynomial &B)

 printf("________________________________\\n");
 printf("\\n原来:\\nA(x)=");
 PrintPolynomial(A);
 printf("\\n调整后:\\n");
 printf("A(x)=");
 Addjust(A,1);
 printf("\\n原来:\\nB(x)=");
 PrintPolynomial(B);
 printf("\\n调整后:\\n");
 printf("B(x)=");
 Addjust(B,1);
 printf("________________________________\\n");
 return OK;

//乘法
Status Polynomial_multiply(Polynomial &A,Polynomial &B)

 Polynomial M,pa=A;
 InitPolynomial(M);
 printf("乘法运算方法: \\nA(x)=A1(x)+A2(x)+....+An(x)\\n");
 printf("\\nB(x)=B1(x)+B2(x)+....+Bn(x)\\n\\n");
 printf("M(x)=B(x)*A1(x)+B(x)*A2(x)+....+B(x)*An(x)\\n");
 system("pause");
 int i=0;
 while(pa->next!=NULL)
 
  pa=pa->next;
  ElemType Ea=pa->data;
  Polynomial pb=B;
  printf("\\nM%d(x) = A%d(x) * B(x)\\n",++i,i+1);
  printf("\\nA%d(x)=%dX%d\\n",i,Ea.coef,Ea.expo);
  int j=0;
  printf("\\nB(x)=");
  PrintPolynomial(B);
  printf("\\n");
  while(pb->next!=NULL)
  
   pb=pb->next;
   ElemType Eb=pb->data;
   ElemType Em;
   Em.coef=Ea.coef*Eb.coef;
   Em.expo=Ea.expo+Eb.expo;
   AddNode(M,Em);
  
  printf("M%d(x)=",i);
  Addjust(M,0);
  system("pause");
 
 printf("\\n运算结果为\\nM(x)=");
 PrintPolynomial(M);
 printf("\\n");
 A->next=NULL;
 B->next=NULL;
 printf("\\n\\t\\t多项式A(x),B(x)已置空，请重新创建.\\n");
 system("pause");
 system("cls");
 return OK;

//主菜单
int Main_menu()

 printf("\\t\\t_____________________________________\\n");
 printf("\\t\\t              主菜单                 \\n");
 printf("\\t\\t_____________________________________\\n");
 printf("\\t\\t    1.     生成多项式                \\n");
 printf("\\t\\t_____________________________________\\n");
 printf("\\t\\t    2.     多项式升幂                \\n");
 printf("\\t\\t_____________________________________\\n");
 printf("\\t\\t    3.     多项式降幂                \\n");
 printf("\\t\\t_____________________________________\\n");
 printf("\\t\\t    4.   M(x) = A(x) + B(x)          \\n");
 printf("\\t\\t_____________________________________\\n");
 printf("\\t\\t    5.   M(x) = A(x) - B(x)          \\n");
 printf("\\t\\t_____________________________________\\n");
 printf("\\t\\t    6.   M(x) = A(x) * B(x)           \\n");
 printf("\\t\\t_____________________________________\\n");
 printf("\\t\\t    7.        退出                   \\n");
 printf("\\t\\t_____________________________________\\n");
 printf("---------请选择:");
 char select[5];
 scanf("%s",select);
 return atoi(select);

int main()

 srand(time(0));
 Polynomial A,B;
 InitPolynomial(A);
 InitPolynomial(B);
 printf("\\t***********  欢迎使用一元多项式计算器软件  ***********\\n");
 while(true)
 
  switch(Main_menu())
  
  case 1:Create(A,B);break;
  case 2:Polynomial_ascend(A,B);break;
  case 3:Polynomial_decline(A,B);break;
  case 4:Polynomial_add(A,B);break;
  case 5:Polynomial_sub(A,B);break;
  case 6:Polynomial_multiply(A,B);break;
  case 7:printf("谢谢使用，再见!\\n");return 0;
  default:printf("Error! Input Again!\\n");break;
  
  system("pause");
 
 return 0;