duoxiangshijisuan.cpp

一元多项式计算

#include"stdio.h"
#include"malloc.h"
#include"conio.h"
#include"stdlib.h"
#include"process.h"

#define TRUE 1
#define FALSE 0
#define OK 1
#define ERROR 0
#define NULL 0
#define MAX 20 //多项式最多项数

typedef struct //定义存放多项式的数组类型
{
 float coef; //系数
 int expn; //指数
}Polyn[MAX];

typedef struct LNode //定义单链表结点类型
{
 float coef; //系数
 int expn; //指数
 struct LNode *next;
}Polynomial;

void PrintPolyn(Polynomial *P) //打印输出一元多项式P
{
 Polynomial *L;
 L=P->next;
 while(L!=NULL)
 {
  printf("%gx^%d ",L->coef,L->expn);
  L=L->next;
 }
 printf("\n");
}

void CreatPolyn(Polynomial *&P,Polyn a,int n) 
//输入n项的系数和指数，建立表示一元多项式的有序链表P
{
 Polynomial *e,*L;int i;
 P=(Polynomial *)malloc(sizeof(Polynomial)); //创建头结点
 P->next=NULL;
 L=P; //L始终指向尾结点，开始时指向头结点
 for(i=0;i<n;i++)
 {
  e=(Polynomial *)malloc(sizeof(Polynomial)); //创建新结点
  e->coef=a[i].coef;
  e->expn=a[i].expn;
  L->next=e; //将*e插入*r之后
  L=e;
 }
 L->next=NULL; //尾结点next域置为NULL
}

void Sort(Polynomial *&head) //按指数递减排序
{
 Polynomial *p,*q,*r;
 p=head->next;
 if(p!=NULL) //若原单链表中有一个或以上的数据结点
 {
  r=p->next; //r保存*p结点后继结点的指针
  p->next=NULL; //构造只含一个数据结点的有序表
  p=r;
  while(p!=NULL)
  {
   r=p->next; //r保存*p结点后继结点的指针
   q=head;
   while(q->next!=NULL&&q->next->expn>p->expn)  q=q->next; 
   //在有序表中找插入*p的前驱结点*q
   p->next=q->next; //将*p插入到*q之后
   q->next=p;
   p=r;
  }
 }
}

void AddPolyn(Polynomial *pa,Polynomial *pb,Polynomial *&pc)
//完成多项式相加运算
{
 float c;
 Polynomial *ha=pa->next,*hb=pb->next,*s,*hc;
 pc=(Polynomial *)malloc(sizeof(Polynomial)); //创建头结点
 hc=pc;
 while(ha!=NULL&&hb!=NULL) //当链表ha,hb不为空时
 {
  if(ha->expn>hb->expn) //当链表ha的指数大于hb的指数时
  {
   s=(Polynomial *)malloc(sizeof(Polynomial)); //复制头结点
   s->expn=ha->expn;s->coef=ha->coef; //链表ha的系数和指数赋给s
   hc->next=s;hc=s;
   ha=ha->next; //把链表ha指向的下一个元素赋给ha
  }
  else if(ha->expn<hb->expn) //当链表ha的指数小于hb的指数时
  {
   s=(Polynomial *)malloc(sizeof(Polynomial)); //复制头结点
   s->expn=hb->expn;s->coef=hb->coef; //链表hb的系数和指数赋给s 
   hc->next=s;hc=s;
   hb=hb->next; //把链表hb指向的下一个元素赋给hb
  }
  else //当链表ha的指数等于hb的指数时
  {
   c=ha->coef+hb->coef; //系数相加
   if(c!=NULL) //系数之和不为0时创建新结点
   {
    s=(Polynomial *)malloc(sizeof(Polynomial)); //复制结点
	s->expn=ha->expn;s->coef=c;
	hc->next=s;hc=s;
   }
   ha=ha->next; //把链表ha指向的下一个元素赋给ha
   hb=hb->next; //把链表hb指向的下一个元素赋给hb
  }
 }
 if(hb!=NULL) ha=hb; //复制余下的结点
 while(ha!=NULL)
 {
  s=(Polynomial *)malloc(sizeof(Polynomial)); //复制结点
  s->expn=ha->expn;s->coef=ha->coef;
  hc->next=s;hc=s;
  ha=ha->next; //把链表ha指向的下一个元素赋给ha
 }
 hc->next=NULL;
}

void SubtractPolyn(Polynomial *pa,Polynomial *pb,Polynomial *&pc)
//完成多项式相减运算
{
 float c;
 Polynomial *ha=pa->next,*hb=pb->next,*s,*hc;
 pc=(Polynomial *)malloc(sizeof(Polynomial)); //创建头结点
 hc=pc;
 while(ha!=NULL&&hb!=NULL) //当链表ha,hb不为空时
 {
  if(ha->expn>hb->expn) //当链表ha的指数大于hb的指数时
  {
   s=(Polynomial *)malloc(sizeof(Polynomial)); //复制头结点
   s->expn=ha->expn;s->coef=ha->coef; //链表ha的系数和指数赋给s
   hc->next=s;hc=s;
   ha=ha->next; //把链表ha指向的下一个元素赋给ha
  }
  else if(ha->expn<hb->expn) //当链表ha的指数小于hb的指数时
  {
   s=(Polynomial *)malloc(sizeof(Polynomial)); //复制头结点
   s->expn=hb->expn;s->coef=-(hb->coef); //链表hb的系数和指数赋给s
   hc->next=s;hc=s;
   hb=hb->next; //把链表hb指向的下一个元素赋给hb
  }
  else //当链表ha的指数等于hb的指数时
  {
   c=ha->coef-hb->coef; //系数相减
   if(c!=NULL) //系数之差不为0时创建新结点
   {
    s=(Polynomial *)malloc(sizeof(Polynomial)); //复制结点
	s->expn=ha->expn;s->coef=c;
	hc->next=s;hc=s;
   }
   ha=ha->next; //把链表ha指向的下一个元素赋给ha
   hb=hb->next; //把链表hb指向的下一个元素赋给hb
  }
 }
 if(hb!=NULL) ha=hb; //复制余下的结点
 while(ha!=NULL)
 {
  s=(Polynomial *)malloc(sizeof(Polynomial)); //复制结点
  s->expn=ha->expn;s->coef=-ha->coef;
  hc->next=s;hc=s;
  ha=ha->next; //把链表ha指向的下一个元素赋给ha
 }
 hc->next=NULL;
}

Print() //屏幕输出
{
 int i;
 printf("\n\n         --------------------多项式运算器--------------------\n\n");
 printf("             1.多项式加法                   2.多项式减法\n");
 printf("             3.退出                                   \n\n");
 printf("         ----------------------------------------------------\n\n");
 printf("请选择你要进行的操作:");
 scanf("%d",&i);
 return i;
}

void main()
{
 int i,j,n=0,m=0;
 Polynomial *ha,*hb,*hc,*hd;
 Polyn a,b;
 
 printf("\n\n       --------------------欢迎使用多项式运算器--------------------\n\n");
 printf("         请先依次输入多项式A、B的系数和指数,然后选择多项式的运算\n\n");
 printf("       ------------------------------------------------------------\n\n");
 printf("请输入多项式A的系数和指数,按ESC键结束:\n");
 for(i=0;i<=MAX;i++) //输入多项式A的系数和指数
 {
 scanf("%g,%d",&a[i].coef,&a[i].expn);
 n++;
 if(getch()==0x1b) goto flag1; //当按ESC时跳到flag1
 }
 flag1:printf("请输入多项式B的系数和指数,按ESC键结束:\n");
 for(j=0;j<=MAX;j++) //输入多项式B的系数和指数
 {
 scanf("%g,%d",&b[j].coef,&b[j].expn);
 m++;
 if(getch()==0x1b) goto flag2; //当按ESC时跳到flag2
 }
 flag2:CreatPolyn(ha,a,n); //建立表示一元多项式的有序链表ha
 CreatPolyn(hb,b,m); //建立表示一元多项式的有序链表hb
 system("cls.exe"); //清屏
 printf("多项式A的项数:%d",n);printf("     多项式A:");PrintPolyn(ha);
 printf("多项式B的项数:%d",m);printf("     多项式B:");PrintPolyn(hb);
 printf("\n");
 Sort(ha); //按指数递减排序ha
 Sort(hb); //按指数递减排序hb
 printf("有序多项式A:");PrintPolyn(ha);
 printf("有序多项式B:");PrintPolyn(hb);
 printf("\n");
 AddPolyn(ha,hb,hc); //完成多项式相加运算
 SubtractPolyn(ha,hb,hd); //完成多项式相减运算
 flag:switch(Print())
 {
  case 1:PrintPolyn(hc);goto flag;break;
  case 2:PrintPolyn(hd);goto flag;break;
  case 3:break;
  default:printf("操作错误!请重新选择!\n");goto flag;
 }
}