多项式运算Cpp程序

1、/=用带表头结点的单链表实现多项式的加-减-乘-除运算的C+程序=/=一元多项式的运算:OOP=/1.降幂建立一个一元多项式并输出-/2.求两个多项式的和并输出(原多项式不变)-/3.利用求和函数，求两个多项式的差并输出(原多项式不变)-/4.利用求和与求差函数，求两个多项式的积并输出(原多项式不变)-/5.利用求和、差、积函数，求两多项式的商并输出(原多项式不变)-#include /getch#include /exit#include /fabs#include/cout,cinusing namespace std;typedef struct/元素类型定义float coef;/系数

2、(Coefficient)int expn;/指数(exponential )EType;/元素类型名(ElementType)typedef struct LNode/链表结点类型定义EType d;/结点数据域struct LNode *next;/结点指针域LNode,*LinkNP;/结点及结点指针类型名typedef struct/表头结点类型LinkNP head,tail;/链表头尾指针int len;/链表长度LHNode;/链表头结点类型名typedef LHNode* polyn;/多项式表头结点指针类型名/=多项式类的定义=/class polynomailprivate

3、:polyn p;/数据成员public:polynomail()/=构造函数：初始化表头结点及其指针=p=new LHNode;if(!p)errExit(New LHNode error!);/检测指针是否为空p-head=NULL,p-tail=NULL,p-len=0;void errExit(char *str)/遇错自动退出程序coutb.expn)return 1;else if(a.expnd=e;/给结点赋值L-next=NULL;return 1;void AppNode(LinkNP L)/=结点链入尾部=if(p-head=NULL)/若表为空p-head=p-tail

4、=L;elsep-tail-next=L;/L连到尾部p-tail=L;/修改头结点的尾指针p-len+=1;/表长增1void InsFirst(LinkNP s)/=s插入链首结点前=if(!p-head)AppNode(s);else s-next=p-head,p-head=s,p-len+=1;void InsSortNode(LinkNP s)/=s所指插入有序链p中=LinkNP h=p-head,t=p-tail;if(!h|s-d.expnd.expn)/若表空或s比尾大.AppNode(s);/.则直接连入尾部else if(s-d.expnh-d.expn)/s比首元素指

5、数大InsFirst(s);/作为首元素插入elsewhile(1)/查找插入位置if(s-d.expnh-next-d.expn)break;/h停在待插点前h=h-next;s-next=h-next;/插入h之后h-next=s;p-len+=1;int LocateElem(EType e,LinkNP& q)/=p中找e且指针入q=LinkNP h=p-head;while(h&CmpElemExpn(h-d,e)/查找是否有eh=h-next;q=h;/指针存入qif(q)return 1;/若有else return 0;/若无void CreatPoly(char *str)/

6、=逐个降幂有序创建=int i=1;LinkNP s,q;EType e;printf(nCreat polyn %s:n,str);while(1)printf(tcoef%d,expn%d=,i,i);scanf(%f,%d,&e.coef,&e.expn);/输入系数及幂次if(e.coef=0&e.expn=0)break;/若全0则结束if(fabs(e.coef)1.0e-30|(e.expn0)/若系数或指数非法coutError!n;continue;/重新输入if(!LocateElem(e,q)/若该项不存在.if(MakeNode(s,e)/若结点创建成功InsSortN

7、ode(s);/将s所指有序插入elsecoutError!n;continue;/.否则重新输入i+;/记录项数void ItemPrint(float a,int n)/输出某项axnif(n=0)couta;/指数为0else if(n=1)/指数为1if(a=1)coutx;else if(a=-1)cout-x;else coutax;else/指数大于1if(a=1)coutxn;else if(a=-1)cout-xn;else coutaxhead;if(L)/若非空则输出首元结点printf(n多项式%s中有%d项: ,str,p-len);ItemPrint(L-d.coe

8、f,L-d.expn);L=L-next;else printf(n多项式%s为空!,str);while(L)/输出之后所有结点if(L-d.coef0)coutd.coef,L-d.expn);L=L-next;/=两多项式类相加=/void AddPoly(polynomail pa,polynomail pb)/求两个多项式的和LinkNP ha,hb,ht;EType ea,eb,ec;ha=pa.p-head,hb=pb.p-head;while(ha&hb)/a,b都非空时循环ea=ha-d,eb=hb-d;switch(CmpElemExpn(ea,eb)/比较大小case 1

9、:/若ea大则将ea加入ecif(MakeNode(ht,ea)AppNode(ht);ha=ha-next;/a表指针后移break;case 0:/若ea与ec相等则将和加入ecec.coef=ea.coef+eb.coef;ec.expn=ea.expn;if(ec.coef)/若系数不为0if(MakeNode(ht,ec)/若开辟结点成功AppNode(ht);/将结点指针L链入cha=ha-next,hb=hb-next;/a,b两表指针同时后移break;case -1:/若eb大则将eb加入ecif(MakeNode(ht,eb)AppNode(ht);hb=hb-next;/

10、b表指针后移break;while(ha)/若ea有剩余,则将剩余加入ea=ha-d;if(MakeNode(ht,ea)AppNode(ht);ha=ha-next;while(hb)/若eb有剩余,则将剩余加入eb=hb-d;if(MakeNode(ht,eb)AppNode(ht);hb=hb-next;void CopyPoly(polynomail s)/拷贝多项式LinkNP np=s.p-head,q;while(np)if(MakeNode(q,np-d)AppNode(q);np=np-next;void RevSignPoly(polynomail &pn)/系数反号Lin

11、kNP p=pn.p-head;while(p)p-d.coef=-p-d.coef;/反号p=p-next;/=两多项式类相减=/void SubPoly(polynomail a,polynomail b)/将b反号与a相加polynomail pn;pn.CopyPoly(b);RevSignPoly(pn);AddPoly(a,pn);/=两多项式类相乘=/void MulPoly(polynomail a,polynomail b,polynomail &c)/a与b相乘存入cLinkNP ha=a.p-head,hb=b.p-head;polynomail pa,pb,pc,pt;

12、if(!ha|!hb)c=pt;return;/空多项式即0while(ha)/取多项式的某项pb.CopyPoly(b);hb=pb.p-head;while(hb)/与多项式b相乘hb-d.coef*=ha-d.coef;hb-d.expn+=ha-d.expn;hb=hb-next;pt.CopyPoly(c);/c复制到ptc.Destroy();/c清零c.AddPoly(pt,pb);/pt与pb之和存入cpt.Destroy();/pt清零pb.Destroy();ha=ha-next;/=两多项式类相除=/void DivPoly(polynomail a,polynomail

13、 b,polynomail &q,polynomail &r)/a与b相除商存入q余存入rpolynomail pa,pb,pt;LinkNP ep,h,ha=a.p-head,hb=b.p-head;if(!ha)q=r=pt;return;if(!hb)errExit(n多项式b不能为零);/除式不能为0pa.CopyPoly(a);while(ha&hb&ha-d.expn=hb-d.expn)/a比b首项指数大ep=new LNode;ep-next=NULL;ep-d.coef=ha-d.coef/hb-d.coef;ep-d.expn=ha-d.expn-hb-d.expn;q.A

14、ppNode(ep);/商式因子连入qpb.CopyPoly(b);h=pb.p-head;while(h)/商式与除式相乘h-d.coef*=ep-d.coef;h-d.expn+=ep-d.expn;h=h-next;pt.SubPoly(pa,pb);/再与被除式相减pa.Destroy();pb.Destroy();pa.CopyPoly(pt);pt.Destroy();ha=pa.p-head;r.CopyPoly(pa);void Destroy()/释放内存空间=LinkNP px=p-head,pt;while(px)pt=px;px=px-next;delete pt;/释放内存空间p-head=NULL;p-tail=NULL;p-len=0;/=多项式类的测试=/void main() polynomail a,b,c,r;/创建对象a,b,c空多项式a.CreatPoly(a);/有序创建多项式a并输出a.PrintPoly(a);b.CreatPoly(b);/有序创建多项式b并输出b.PrintPoly(b);c.AddPoly(a,b);/a与b相加其和存入c并输出c.PrintPoly(和式);c.Destroy();/清除cc.SubPoly(a,b);/a与b相减其