数据结构_多项式相加，相减，相乘

 

经过2天的奋斗终于解决了~~

 

 

 

 

 

Description

 /************************************************************/
  /* 目的：通过一元稀疏多项式的表示和计算，*/

  /* 帮助学生熟练掌握线性表的基本操作，*/
  /*以及用线性链表表示线性表的存储结*/

  /*构和操作的实现。*/
  /* 内容：实现一元稀疏多项式的如下运算：*/
  /* (1)两个一元稀疏多项式相加运算*/
  /* (2)两个一元稀疏多项式相减运算*/
  /* (3)两个一元稀疏多项式相乘运算*/

/************************************************************/
 

 

 code

 

//Author: essence_of_ACMER 
//Time:2011.8.5
//Theme:polynomial_Add_Subtract_Mulitily

#include <stdio.h>
#include <stdlib.h>
#include <iostream>
#include <conio.h>

using namespace std;
typedef struct Item{
  double  coef;
  int     expn;
  struct Item *next;
  }Item,*Polyn;

#define CreateItem(p) p=(Item *)malloc(sizeof(Item));
#define DeleteItem(p) free((void *)p);

int menu(void);
int PolynNotEmpty(Polyn h,char *p);

/************************************************************/
/*                     判断选择函数                         */
/************************************************************/
int Select(char *str)
  { char ch;
    printf("%s\n",str);
    printf("Input Y or N:");
    do{ ch=getch();
    }while(ch!='Y'&&ch!='y'&&ch!='N'&&ch!='n');
    printf("\n");
    if(ch=='Y'||ch=='y') return(1);
    else return(0);
    }
/************************************************************/
/*                插入位置定位函数                          */
/************************************************************/
int InsertLocate(Polyn h,int expn,Item **p)
  { Item *pre,*q;
    pre=h;
    q=h->next;
    while(q&&q->expn<expn)
      { pre=q;
        q=q->next;
    }
    if(!q)
      { *p=pre;
    return(1);
    }
    else if(q->expn==expn)
      { *p=q;
    return(0);
    }
    else//*q->expn>expn
      { *p=pre;
    return(-1);
        }
    }
/************************************************************/
/*                     插入结点函数                         */
/************************************************************/
void insert(Item *pre,Item *p)
{
    p->next=pre->next;
    pre->next=p;
    }
/************************************************************/
/*                     输入多项式                           */
/************************************************************/
Polyn Input(void)
{
  double  coef;
  int     expn;
  Item *h,*p,*pp;
  CreateItem(h);//产生头结点
  h->next=NULL;
  printf("input coef and expn(if end ,expn=-1)\n");
  while(1)
  {
    scanf("%lf%d",&coef,&expn); //输入多项式的系数和指数
    if(expn==-1) break;         //若指数为－1，表示输入结束
    if(InsertLocate(h,expn,&pp))//返回值非0表示插入新结点
     { CreateItem(p);
       p->coef=coef;
       p->expn=expn;
       insert(pp,p);
       }
     else if(Select("has the same expn,Replace older value?"))
      pp->coef=coef;  //指数相同，替换系数
     }
  return h;
  }
/************************************************************/
/*                     撤消多项式                           */
/************************************************************/
void Destroy(Polyn h)
{
  Item *p=h,*q;
  while(p!=NULL)
  {
    q=p;
    p=p->next;
    DeleteItem(q);
    }
  }
/************************************************************/
/*                     输出多项式                           */
/************************************************************/
void Output(Polyn h,char *title)
{
  int flag=1;
  Item *p=h->next;
  printf("%s=",title);
  while(p)
  { 
      if(flag)    //表示是否是多项式的第一项
      { flag=0;
         if(p->expn==0)     
    {printf("%.2lf",p->coef);    
    }
    else printf("%.2lfx^%d",p->coef,p->expn);
    }
    else
      { if(p->coef>0) printf("+");    //good !!!
    if(p->expn==0)     printf("%.2lf",p->coef);
    else printf("%.2lfx^%d",p->coef,p->expn);
    }
    p=p->next;
    }
   if(!p&&flag) printf("0");
 printf("\n");
 }
/************************************************************/
/*                     判断两个多项式项的关系               */
/************************************************************/
int ItemComp(Item x,Item y)
{ if(x.expn<y.expn)
     return(-1);
  else if(x.expn==y.expn)
     return(0);
  else return(1);
  }
/************************************************************/
/*                   两多项式多项式相加                     */
/************************************************************/
Polyn AddPolyn(Polyn h1,Polyn h2)
{
  Item *head,*last,*pa=h1->next,*pb=h2->next,*s,*s0;
  double coef;
  CreateItem(head);
  last=head;
    while(pa&&pb)
    {
        if(!ItemComp(*pa,*pb))
        {
            coef=pa->coef+pb->coef;
            if(coef!=0.0)
            {CreateItem(s);
            s->coef=coef;
            s->expn=pa->expn;
            last->next=s;
            last=s;
            }
            pa=pa->next;
            pb=pb->next;
        }

        else
             {  if(ItemComp(*pa,*pb)==1)
                 {s0=pb;
                 pb=pb->next;
                 }

                 else 
                 {
                     s0=pa;
                     pa=pa->next;
                 }

                 CreateItem(s);
                 s->coef=s0->coef;
                 s->expn=s0->expn;
                 last->next=s;
                 last=s;
            }
    }

    s0=pa?pa:pb;
    while(s0)
     {
       CreateItem(s);
       s->coef=s0->coef;
       s->expn=s0->expn;
       last->next=s;
       last=s;
       s0=s0->next;
     }

   
    last->next=NULL;
    return head;
    }
/************************************************************/
/*                   两多项式多项式相减                     */
/************************************************************/
Polyn SubtractPolyn(Polyn h1,Polyn h2)
{   
    Item *head,*last,*pa=h1->next,*pb=h2->next,*s,*s0;
  double coef;
  CreateItem(head);
  CreateItem(s0);
  last=head;
      while(pa&&pb)
      {
          if(!ItemComp(*pa,*pb))
          {
              coef=pa->coef-pb->coef;
              if(coef)
              {
                  CreateItem(s);
                  s->expn=pa->expn;
                  s->coef=coef;
                  last->next=s;
                  last=s;
              }
              pa=pa->next;
              pb=pb->next;
          }

           else
           {if(ItemComp(*pa,*pb)==1)
               {CreateItem(s);
               s->coef=-pb->coef;
               s->expn=pb->expn;
               last->next=s;
               last=s;
                 pb=pb->next;
               }
            if(ItemComp(*pa,*pb)==-1)
            {    CreateItem(s);
                 s->coef=pa->coef;
                 s->expn=pa->expn;
                 last->next=s;
                 last=s;
                 pa=pa->next;
                }
           }
    }
           s0=pa?pa:pb;
           while(s0)
           { CreateItem(s);
              s->coef=s0->coef;
              s->expn=s0->expn;
              last->next=s;
              last=s;
              s0=s0->next;
           }

    last->next=NULL;
    return head;
    }
/************************************************************/
/*                   两多项式多项式相乘                     */
/************************************************************/
Polyn MultPolyn(Polyn h1,Polyn h2)  //两个多项式相乘
{ int expn;
  Item *head,*pa,*pb=h2->next,*s,*pp;
  double coef;
  CreateItem(head);
  head->next=NULL;
while(pb)
{
    pa=h1->next;
    while(pa)
    {
       expn=pa->expn+pb->expn;
       coef=pa->coef*pb->coef;
       if(InsertLocate(head,expn,&pp))
         {
             CreateItem(s);
             s->coef=coef;
             s->expn=expn;
             insert(pp,s);
          }
        else pp->coef=pp->coef+coef;
        pa=pa->next;
    }
    pb=pb->next;
}
    return head;
    }
/************************************************************/
/*                      菜单选择                            */
/************************************************************/
int menu(void)
  { int num;
    printf("%20c1--create P(x)\n",' ');
    printf("%20c2--create Q(x)\n",' ');
    printf("%20c3--p(x)+Q(x)\n",' ');
    printf("%20c4--P(x)-Q(x)\n",' ');
    printf("%20c5--p(x)*Q(x)\n",' ');
    printf("%20c6--print P(x)\n",' ');
    printf("%20c7--print Q(x)\n",' ');
    printf("%20c8--print P(x)+Q(x)\n",' ');
    printf("%20c9--print P(x)-Q(x)\n",' ');
    printf("%20c10--print P(x)*Q(x)\n",' ');
    printf("%20c11--Quit\n",' ');
    printf("         please select 1,2,3,4,5,6,7,8,9,10,11:");
      do{
      scanf("%d",&num);
      }while(num<1 || num>11);   //good manial thought!!
    return(num);
    }
/************************************************************/
/*                  判断多项式是否存在                      */
/************************************************************/
int PolynNotEmpty(Polyn h,char *p)
  { if(h==NULL)
      { printf("%s is not exist!\n",p);
        getchar();
    return(0);
    }
     else return(1);
     }
/************************************************************/
/*                        主函数                            */
/************************************************************/
void main()
{ int num;
  Polyn  h1=NULL; //p(x)
  Polyn  h2=NULL; //Q(x)
  Polyn  h3=NULL; //P(x)+Q(x)
  Polyn  h4=NULL; //P(x)-Q(x)
  Polyn  h5=NULL; //P(x)*Q(x)
  while(1)
    { num=menu();
      getchar();
      switch(num)
       {
     case 1:  //输入第一个多项式，若多项式存在，首先撤消然后再输入
        if(h1!=NULL)
          { if(Select("P(x) is not Empty,Create P(x) again?"))
         { Destroy(h1);
           h1=Input();
           }
        }
        else h1=Input();
            break;
     case 2:  //输入第二个多项式，若多项式存在，首先撤消然后再输入
        if(h2!=NULL)
          { if(Select("Q(x) is not Empty,Create Q(x) again?"))
         { Destroy(h2);
           h2=Input();
           }
        }
        else h2=Input();
        break;
     case 3:  //两多项式相加
        if(PolynNotEmpty(h1,"p(x)")&&PolynNotEmpty(h2,"Q(X)"))
          {h3=AddPolyn(h1,h2);
           Output(h3,"P(x)+Q(X)");
               printf("P(x)+Q(x) has finished!\n");
           getchar();
               }
        break;
     case 4:  //两多项式相减
        if(PolynNotEmpty(h1,"p(x)")&&PolynNotEmpty(h2,"Q(X)"))
          { h4=SubtractPolyn(h1,h2);
            Output(h4,"Px)-Q(x)");
                printf("P(x)-Q(x) has finished!\n");
        getchar();
        }
        break;
     case 5:  //两多项式相乘
            if(PolynNotEmpty(h1,"p(x)")&&PolynNotEmpty(h2,"Q(X)"))
          { h5=MultPolyn(h1,h2);
                Output(h5,"P(x)*Q(x)");
            printf("P(x)*Q(x) has finished!\n");
            getchar();
                }
        break;
         case 6: //显示第一个多项式
        if(PolynNotEmpty(h1,"p(x)"))
           { Output(h1,"P(x)");
         getchar();
         }
        break;
     case 7: //显示第二个多项式
        if(PolynNotEmpty(h2,"Q(x)"))
          { Output(h2,"Q(x)");
        getchar();
        }
        break;
     case 8: //显示相加结果多项式
        if(PolynNotEmpty(h3,"P(x)+Q(x)"))
          { Output(h3,"P(x)+Q(x)");
        getchar();
        }
        break;
     case 9: //显示相减结果多项式
        if(PolynNotEmpty(h4,"P(x)-Q(x)"))
          { Output(h4,"P(x)-Q(x)");
        getchar();
        }
        break;
     case 10: //显示相乘结果多项式
        if(PolynNotEmpty(h5,"P(x)*Q(x)"))
          { Output(h5,"P(x)*Q(x)");
        getchar();
        }
        break;
     case 11: //结束程序运行。结束前应先撤消已存在的多项式
        if(h1!=NULL) Destroy(h1);
        if(h2!=NULL) Destroy(h2);
        if(h3!=NULL) Destroy(h3);
        if(h4!=NULL) Destroy(h4);
        if(h4!=NULL) Destroy(h4);
        if(h4!=NULL) Destroy(h5);
     }
      if(num==11) break;
      }
  getch();
  }