多项式算法

#include<stdio.h>#include<iostream.h>#include<stdlib.h>#include<malloc.h>#include<string.h>#define NULL 0//************************************************** typedef struct LNode{float coef;//系数int exp;//指数struct LNode *next;}LNode, *Polyn;//**************************************************//销毁传递过来的链表【多项式】void DestroyPolyn(Polyn &L){Polyn p;p=L->next;while(p){L->next=p->next;free(p);p=L->next;}free(L);}//**************************************************/*判断指数是否与多项式中已存在的某项相同*/int JudgeExp(Polyn L,Polyn e){Polyn p;p=L->next;while(p!=NULL&&(e->exp!=p->exp))p=p->next;if(p==NULL)return 0;elsereturn 1;}//******************************************************** //创建一个项数为n的多项式,有头结点void CreatePolyn(Polyn &L,int n)int i=1;Polyn prep;if(L!=NULL)DestroyPolyn(L);Polyn p,newp;L=(LNode*)malloc(sizeof(LNode));L->next=NULL;L->coef=0; //创建头结点for(i=1;i<=n;i++){newp=(LNode*)malloc(sizeof(LNode));printf("输入第%d项的系数和指数:\n",i);printf("系数:\n");scanf("%f",&newp->coef);printf("指数:\n");scanf("%d",&newp->exp);newp->next=NULL;//定位插入位置prep=L;p=L->next;while(p&&p->exp<newp->exp){prep=p;p=p->next;}if(p)//找到一项指数更大的项{prep->next=newp;newp->next=p;}else{prep->next=newp;}if(JudgeExp(L,newp)==0) //调用JudgeExp函数判断是否输入了同指数项{newp->next=p->next;p->next=newp;}}}//********************************************************//******************************************************** //输出函数void Output(Polyn h){Polyn L=h->next;if(h->next==NULL)printf("0");else{printf("%f*X^%d",L->coef,L->exp);while(L->next!=NULL){L=L->next;if(L->coef>0)printf("+%f*X^%d",L->coef,L->exp);elseprintf("%f*X^%d",L->coef,L->exp);}}}//******************************************************** //复制函数void CopyPolyn(Polyn &pc,Polyn pa){Polyn p,q,r;pc=(LNode*)malloc(sizeof(LNode));pc->next=NULL;r=pc;p=pa;while(p->next!=NULL){q=(LNode*)malloc(sizeof(LNode));q->coef=p->next->coef;q->exp=p->next->exp;r->next=q;q->next=NULL;r=q;p=p->next;}}//******************************************************** //加法函数void Add(Polyn &pc,Polyn pa,Polyn pb)Polyn p1,p2,p,pd;CopyPolyn(p1,pa);CopyPolyn(p2,pb);pc=(LNode*)malloc(sizeof(LNode)); pc->next=NULL;p=pc;p1=p1->next;p2=p2->next;while(p1!=NULL&&p2!=NULL){if(p1->exp<p2->exp){p->next=p1;p=p->next;p1=p1->next;}else if(p1->exp>p2->exp){p->next=p2;p=p->next;p2=p2->next;}else{p1->coef=p1->coef+p2->coef;if(p1->coef!=0){p->next=p1;p=p->next;p1=p1->next;p2=p2->next;}else{pd=p1;p1=p1->next;p2=p2->next;free(pd);}}}if(p1!=NULL){p->next=p1;}if(p2!=NULL){p->next=p2;}}//************************************************}//减法函数void Sub(Polyn &pc,Polyn pa,Polyn pb){Polyn p,pt;CopyPolyn(pt,pb);p=pt;while(p!=NULL){p->coef=(-(p->coef));p=p->next;}Add(pc,pa,pt);DestroyPolyn(pt);}//****************************************************** //乘法函数void Mul(Polyn &pc,Polyn pa,Polyn pb){Polyn pl,p2,p,pd,newp,t;pc=(LNode*)malloc(sizeof(LNode));pc->next=NULL;pl=pa->next;p2=pb->next;while(pl!=NULL){pd=(LNode*)malloc(sizeof(LNode));pd->next=NULL;p=(LNode*)malloc(sizeof(LNode));p->next=NULL;t=p;while(p2){newp=(LNode*)malloc(sizeof(LNode));newp->next=NULL;newp->coef=pl->coef*p2->coef;newp->exp=pl->exp+p2->exp;t->next=newp;t=t->next;p2=p2->next;}Add(pd,pc,p);CopyPolyn(pc,pd);pl=pl->next;p2=pb->next;DestroyPolyn(p);DestroyPolyn(pd);}}Polyn poly(){Polyn Head;Head=new LNode;Head->next=NULL;return Head;}//***********求导************Polyn disp(Polyn Head)//disp{Polyn p;p=Head->next;while(p!=NULL){if(p->coef>0)cout<<"+"<<p->coef<<"x^"<<p->exp<<'\t';elsecout<<p->coef<<"x^"<<p->exp<<'\t';p=p->next;}return Head;}Polyn create(Polyn Head){Polyn p;int a; float b;Head=NULL;while(a){p=new LNode;cout<<"输入系数和指数（例如23 3，输入0 0则输出） "<<endl;cin>>a>>b;p->coef=a;p->exp=b;p->next=Head;Head=p;}return Head;}Polyn qiudao(Polyn Head){Polyn p;p=Head->next ;while(p!=NULL){if(p->exp!=0) //系数不为零时进行求导{p->coef=p->coef*p->exp;p->exp=p->exp-1; //求导后系数变为原来的系数乘以指数 指数变为原来的指数减一}else p->coef=0;p=p->next;}return Head;}//********************************************************//菜单函数void Menu(){printf("\n");printf("***************************************\n");printf("l.新建两个多项式f1(x)和f2(x)\n");printf("2.输出两个多项式f1(x)和f2(x)\n");printf("3.两个多项式f1(x)和f2(x)相加为F(x)\n");printf("4.两个多项式相减：F(x)=f1(x)-f2(x)\n");printf("5.两个多项式相乘: F(x)=f1(x)*f2(x)\n");printf("6.退出\n");printf("***************************************\n");printf("请输入(1-6):");}//********************************************************//清屏函数void Clear(){system("pause");system("cls");}//********************************************************//主函数void main(){system("color 4A");int n, choose;Polyn L,L1=NULL,L2=NULL;while(1){Menu();scanf("%d",&choose);switch(choose){case 1:printf("输入第一个一元多项式的项数:");scanf("%d",&n);CreatePolyn(L1,n);printf("输入第二个一元多项式的项数:");scanf("%d",&n);CreatePolyn(L2,n);Clear();break;case 2:if(L1==NULL||L2==NULL){printf("多项式为空，请重新选择……");Clear();break;}printf("己输入多项式为:\n第一个一元多项式为:\n f1(X)=");Output(L1);printf("\n第二个一元多项式为:\n f2(X)=");Output(L2);//printf("");Clear();break;case 3:if(L1==NULL||L2==NULL){printf("多项式创建错误，请重新选择……");Clear();break;}Add(L,L1,L2);printf("待相加的两个一元多项式为:\n");//cout<<""<<endl;printf("多项式1为:\n f1(X)=");Output(L1);//cout<<""<<endl;printf("\n多项式2为:\n f2(X)=");Output(L2);//cout<<""<<endl;printf("\n相加后的结果为:F(x)=\n");Output(L);//cout<<""<<endl;Clear();DestroyPolyn(L);break;case 4:if(L1==NULL||L2==NULL){printf("多项式创建错误，请重新选择……");Clear();break;}printf("相减的两个一元多项式为:\n");printf("多项式1为:\n f1(X)=");Output(L1);//cout<<""<<endl;printf("\n多项式2为:\n f2(X)=");Output(L2);printf("\n");Sub(L, L1, L2);printf("相减后的结果为:F(x)=\n");Output(L);//cout<<""<<endl;Clear();DestroyPolyn(L);break;case 5:if(L1==NULL||L2==NULL){printf("多项式创建错误，请重新选择……");Clear();break;}Mul(L,L1 ,L2);printf("相乘的两个一元多项式为:\n");//cout<<""<<endl;printf("多项式1为:\n f1(X)=");Output(L1);//cout<<""<<endl;printf("\n多项式2为:\n f2(X)=");Output(L2);printf("\n");printf("相乘后的结果为:F(x)=\n");Output(L);DestroyPolyn(L);//cout<<" "<<endl;Clear();break;default:printf("输入错误，请重新选择操作……");Clear();case 6:exit(0); //终止止程序}// Switch}// While}// main。