一元多项式的各种运算实现(c++c)

1、一元多项式各种运算本程序可完成一元多项式的加，减，乘，积分，微分运算输入可按习惯书写形式输入各项，输出按指数降序/头文件 ：#include#include#include #include #include #include #include #include #include #include #include #include #include #include #include #include #define TRUE 1 #define FALSE 0 #define OK 1 #define ERROR 0 typedef int status; typedef float ty

2、pe; typedef int fuhaosign;结构体类型定义：typedef struct listtype data; int zhi; struct list* next;list;typedef struct nodeint length; list* next;node;用到的函数：注：各函数参数如是结构体指针，则此指针传入函数之前必将其赋值为NULL否则可能出现错误。void shuoming()cout*endl;cout*各项可以用平时书写习惯输入,若有未知数,必须用x表示,且各项之间必须用空格分隔,支*endl;cout*持:系数是小数,指数是负数的情况,但指数不能是小数

3、,功能选择项: *endl;cout* 1:加法;2:减法;3:乘法;4:积分;5:微分;6:求值;7:原样输出多项式 *endl;cout*endl;cout举例:3 x3 9.3x-3 -x.endl;/求未知数指数是-k时的值float fumi(int k) float a=1.0; for(int i=1;inext) init(toup);/保证赋值前链表有且仅有一个头结点/初始化各变量char c,ch= ;/c接受字符，ch记录上一字符，用于检错int k2=0;/k2标志着+-号前面是否有数值,0时没有,1为有fuhaosign k1=1;/k1是符号位正负的标志,0为负,1

4、为正int k3=0;/小数点的个数int kx=0;/标志前面是否有xlist* p=toup-next,* t;type dat=0.0;/输入c=getchar();int i=0;while(c!=n)if(!p) p=(list*)malloc(sizeof(list); if(!p) cout溢出错误next=p;toup-length+;i+;p-next=NULL;t=p; else t-next=p;t=p;p-next=NULL;toup-length+;if(ch=+|ch=-)&(c=+|c=-)cout未按说明输入,请下次输入前仔细阅读data=k1*1; else

5、p-data=k1*dat;dat=0.0;k1=1;k2=0;k3=0;kx=1;break; case .:k3=1;break; case :if(k2=1) if(kx=1) p-zhi=k1*(int)dat;dat=0.0;p=p-next;else p-data=k1*dat;p-zhi=0;dat=0.0;p=p-next; else if(1=kx) p-zhi=1;p=p-next;k1=1;k2=0;k3=0;kx=0;break; default:if(!k3) dat=c-48+10*dat;/k3=0，即前面没有小数点时 else dat=dat+(c-48)*fu

6、mi(k3);k3+; k2=1;/ switchc=getchar();/ whileif(ch=+|ch=-|ch=.) coutdata =k1*dat;p-zhi=0;else if(k2=0) p-zhi=k1*1;else p-zhi=k1*(int)dat;/初始化,生成单链表表头，参数是指向头结点的指针void init(node *&toup)status destory(node *&toup); if(toup) destory(toup);/假如有头结点或元素节点，销毁结点 toup=(node*)malloc(sizeof(node); if(!toup)cout溢出

7、错误length=0; toup-next=NULL;/销毁全部，包括头结点status destory(node *&toup)if(toup)list* p=toup-next;list* t; while(p) t=p-next; free(p); p=t;/while free(toup);toup=NULL;/if return OK;/找到指数与m相等的元素，返回前一元素的指针，参数是元素指针status equalmi(list *&element,int m,list *&prep)prep=element; list *t=element-next;while(t&t-zhi

8、!=m)prep=t;t=t-next;/while if(t) return 1;/找到了 else return 0;/将toup2原样赋给toup1void copy(node*& toup1,node*& toup2)if(!toup2) cout初始化未成功next,*t1=toup1-next ;while(t2)list* temp=(list*)malloc(sizeof(list);if(!t1)toup1-next =temp;toup1-length+;temp-data =t2-data ;temp-zhi =t2-zhi ;t2=t2-next ;t1=temp;el

9、set1-next =temp;toup1-length+;temp-data =t2-data ;temp-zhi =t2-zhi ;t2=t2-next ;t1=temp;if(t1) t1-next=NULL;/按指数绝对值从小到大存放，交换元素值法void paixu(node *&toup)if(!toup) cout初始化失败next; int i=1; while(ilength)list* temp=a; list* p=a; list* t=p-next; while(t) if(abs(p-zhi)abs(t-zhi) p=t;t=t-next; else t=t-next

10、; /while a=a-next; if(p!=temp) float temp1=temp-data;int temp2=temp-zhi;temp-data=p-data;temp-zhi=p-zhi;p-data=temp1;p-zhi=temp2; i+;/while/把指数相等的项合并,也可实现多项式加法void neat(node *&toup) paixu(toup);/先排序 list* p=toup-next; list* pre; while(p) if(equalmi(p,p-zhi,pre)p-data=pre-next-data+p-data; list *temp

11、=pre-next; pre-next=pre-next-next; free(temp); toup-length-;/if else p=p-next;/while，合并幂相等的项 p=toup-next;list* pr=NULL; list* tem=NULL;while(p)if(p-data =0)if(!pr)tem=p;toup-next =p-next ;p=p-next ;toup-length-; free(tem);tem=NULL;elsetem=p;pr-next=p-next ;toup-length -;p=p-next;free(tem);tem=NULL;/

12、ifelsepr=p;p=p-next ;/else/while，将数据为0的项删除pr=NULL;/得到第i个元素的指数/*status get(node *&toup,int i)if(!toup) cout错误:没有头结点endl;exit(-1);if(i(int)toup-data)cout错误:i=0或i大于元素个数0;i-) t=t-next;return (t-zhi);*/把两个多项式连接起来，用newtoup返回void concat(node*& atoup,node*& btoup,node*& newtoup)if(!atoup|!btoup) coutnext;li

13、st* bp=btoup-next;list* temp=NULL;int i=1;while(ap) list* t=(list*)malloc(sizeof(list);if(i=1) newtoup-next=t;newtoup-length+;t-data=ap-data;t-zhi=ap-zhi;ap=ap-next;temp=t;i+;else temp-next=t;newtoup-length+;t-data=ap-data;t-zhi=ap-zhi;temp=t;ap=ap-next; while(bp) list* t=(list*)malloc(sizeof(list);

14、 if(temp) temp-next=t;else temp=t;newtoup-length+;t-data=bp-data;t-zhi=bp-zhi;bp=bp-next;temp=t;if(temp) temp-next=NULL;/链表toup中每个节点的数据域，正变负，负变正,赋给newtoup,toup中的数据不变void qufan(node*& toup,node*& newtoup)if(!toup) cout未初始化，请重新运行。next ;list* newt=NULL;while(t)list* temp=(list*)malloc(sizeof(list);if(!

15、newt)newtoup-next =temp;newtoup-length+;temp-data =t-data *(-1);temp-zhi=t-zhi;newt=temp;elsenewt-next =temp;newtoup-length +;temp-data =t-data *(-1);temp-zhi=t-zhi;newt=temp;t=t-next ;/whileif(newt) newt-next =NULL;/输入x值，计算多项式的值void qiuzhi(node *&toup,node*& resulttoup)init(toup); init(resulttoup);

16、 cout输入各项:endl;couty=next; int x0;cout请输入x的值:x0; float sum=0.0,x1; int x=1,i=1; while(p) for(;izhi);i+) x=x*x0; if(p-zhi0) x1=x; else if(p-zhi=0) x1=1; else x1=(float)1/x; sum=sum+(p-data)*x1; p=p-next; /while list* temp=(list*)malloc(sizeof(list); resulttoup-next=temp; resulttoup-length+; temp-data

17、=sum; temp-zhi =0; temp-next =NULL; neat(resulttoup); /两个多项式相加，toup1+toup2,resulttoup返回void jia(node *&toup1,node*& toup2,node*& resulttoup)init(toup1);init(toup2); cout输入各项:endl;couty1=endl;fuzhi(toup1); couty2=endl;fuzhi(toup2);concat(toup1,toup2,resulttoup);neat(resulttoup);/两个多项式相减，toup1-toup2,r

18、esulttoup返回void jian(node *&toup1,node*& toup2,node*& resulttoup) init(toup1);init(toup2); cout输入各项:endl;couty1=endl;fuzhi(toup1); couty2=endl;fuzhi(toup2);node* fantoup=NULL;qufan(toup2,fantoup);concat(toup1,fantoup,resulttoup);neat(resulttoup);/两个多项式相乘void cheng(node*& atoup,node*& btoup,node*& re

19、sulttoup)init(atoup);init(btoup);init(resulttoup); cout输入各项:endl;couty1=endl;fuzhi(atoup); couty2=next ,*t=NULL; list* b=btoup-next;if(!a)copy(resulttoup,btoup);else if(!b)copy(resulttoup,atoup);elsewhile(a) b=btoup-next;while(b)list* temp=(list*)malloc(sizeof(list);if(!t)t=temp;resulttoup-next =tem

20、p;resulttoup-length +;elset-next =temp;resulttoup-length +;t=temp;t-data =a-data *b-data ;t-zhi =a-zhi +b-zhi ;b=b-next ;/while(b)a=a-next ;/while(a) t-next =NULL;/elseneat(resulttoup);/求积分void jifen(node*& toup,node*& resulttoup)init(toup); init(resulttoup); cout输入各项:endl;couty=next ,*t=NULL;while(

21、p)list* temp=(list*)malloc(sizeof(list);if(!resulttoup-next )resulttoup-next =temp;resulttoup-length +;t=temp;t-next =NULL;elset-next =temp;resulttoup-length +;t=temp;t-next =NULL;if(p-zhi =-1)t-zhi =p-zhi; t-data =p-data;elset-zhi =p-zhi +1; t-data =p-data /t-zhi;p=p-next ;/whileneat(resulttoup);/微

22、分void weifen(node*& toup,node*& resulttoup)init(toup); init(resulttoup); cout输入各项:endl;couty=next,* p=NULL;while(t)list* temp=(list*)malloc(sizeof(list);if(!resulttoup-next )resulttoup-next =temp;resulttoup-length +;p=temp;p-next =NULL;elsep-next =temp;resulttoup-length +;p=temp;p-next =NULL;p-data

23、=t-data *(t-zhi );p-zhi =t-zhi -1;t=t-next ;neat(resulttoup);/按指数从大到小存放status outxu(node*& toup,node*& newtoup)if(!toup) cout初始化失败next) return 1;copy(newtoup,toup); list *p=newtoup-next; while(p-next ) list* t=p; list* hou=p-next; while(hou) if(t-zhizhi) t=hou; hou=hou-next; /while list* temp=(list*

24、)malloc(sizeof(list);if(t!=p)float temp1=t-data;int temp2=t-zhi;t-data=p-data;t-zhi=p-zhi;p-data=temp1;p-zhi=temp2; p=p-next; /whilereturn 1;/输出多项式status out(node*& toup)extern yunsuan;if(!toup) cout要输出的链表未初始化,请重新运行endl;exit(-1); node* outresult=NULL;outxu(toup,outresult);cout结果是:next;int i=1; couts

25、etprecision(3);if(!temp)if(yunsuan=4)cout任意常数endl;elsecout0zhi)case 0:if(1=i) coutdata;i+; /if else if(temp-data=0) cout+data; else coutdata ; /else break;case 1:if(1=i) if(temp-data0) if(1=temp-data ) coutx; else coutdata data ) cout-x; else coutdata data 0) if(1=temp-data) cout+x; else cout+data d

26、ata ) cout-x; else coutdata data 0)if(1=temp-data ) coutxzhi ;else coutdata xzhi ;elseif(-1=temp-data ) cout-xzhi ;else coutdata xzhi ;i+;/if elseif(temp-data 0)if(1=temp-data ) cout+xzhi ;else cout+data xzhi;elseif(-1=temp-data ) cout-xzhi ;else coutdata xzhi ;/else/switchtemp=temp-next ;/while if(yunsuan=4