下载文档原格式
#include<stdio.h>#include<stdlib.h>#include<malloc.h>typedef int ElemType;/*单项链表的声明*/typedef struct PolynNode{int coef; // 系数int expn; // 指数struct PolynNode *next;}PolynNode,*PolynList;/*正位序(插在表尾)输入n个元素的值，建立带表头结构的单链线性表*/ /*指数系数一对一对输入*/void CreatePolyn(PolynList &L,int n){int i;PolynList p,q;L=(PolynList)malloc(sizeof(PolynNode)); // 生成头结点L->next=NULL;q=L;printf("成对输入%d个数据\n",n);for(i=1;i<=n;i++){p=(PolynList)malloc(sizeof(PolynNode));scanf("%d%d",&p->coef,&p->expn); //指数和系数成对输入q->next=p;q=q->next;}p->next=NULL;}// 初始条件：单链表L已存在// 操作结果: 依次对L的每个数据元素调用函数vi()。
一旦vi()失败,则操作失败void PolynTraverse(PolynList L,void(*vi)(ElemType, ElemType)){PolynList p=L->next;while(p){vi(p->coef, p->expn);if(p->next){printf(" + "); //“+”号的输出，最后一项后面没有“+” }p=p->next;}printf("\n");}/*ListTraverse()调用的函数(类型要一致)*/void visit(ElemType c, ElemType e){if(c != 0){printf("%dX^%d",c,e); //格式化输出多项式每一项}}/* 多项式相加，原理：归并 *//* 参数：两个已经存在的多项式 *//* 返回值：归并后新的多项式的头结点 */PolynList MergeList(PolynList La, PolynList Lb){PolynList pa, pb, pc, Lc;pa = La->next;pb = Lb->next;Lc = pc = La; // 用La的头结点作为Lc的头结点while(pa&&pb){if(pa->expn < pb->expn){pc->next = pa; //如果指数不相等，pc指针连上指数小的结点，pc = pa;pa = pa->next; //指向该结点的指针后移}else if(pa ->expn > pb->expn ){pc->next = pb; //pc指针连上指数小的结点，pc = pb;pb = pb->next; //指向该结点的指针后移}else//(pa ->expn = pb->expn ){pa->coef = pa->coef + pb->coef; //指数相等时，系数相加 pc->next = pa;pc = pa;pa = pa->next; //两指针都往后移pb = pb->next;}}pc->next = pa ? pa:pb; // 插入剩余段return Lc;}void main(){PolynList ha,hb,hc;printf("非递减输入多项式ha， ");CreatePolyn(ha,5); // 正位序输入n个元素的值printf("非递减输入多项式hb， ");CreatePolyn(hb,5); // 正位序输入n个元素的值printf("多项式ha :");PolynTraverse(ha, visit); printf("\n");printf("多项式hb :"); PolynTraverse(hb, visit); printf("\n");hc = MergeList(ha,hb); PolynTraverse(hc, visit); }。
⼀元多项式加法、减法、乘法实现源代码////链接程序：#include#include#include//using namespace std;#define N 1000//#define INF 65535void link();void shunxu();void Menu();typedef struct{int a[N];//记录多项式int len;//记录多项式的长度}Ploy;typedef struct //项的表⽰{ float coef; //系数int expn; //指数}term;typedef struct LNode{ term data; //term多项式值struct LNode *next;}LNode,*LinkList; //两个类型名typedef LinkList polynomail; //⽤带头结点的有序链表表⽰多项式/*⽐较指数*/int cmp(term a,term b){ if(a.expn>b.expn) return 1;if(a.expn==b.expn) return 0;if(a.expnelse exit(-2);}/*⼜⼩到⼤排列*/void arrange1(polynomail pa){ polynomail h=pa,p,q,r;if(pa==NULL) exit(-2);for(p=pa;p->next!=NULL;p=p->next); r=p;for(h=pa;h->next!=r;)//⼤的沉底{ for(p=h;p->next!=r&&p!=r;p=p->next)if(cmp(p->next->data,p->next->next->data)==1){ q=p->next->next;p->next->next=q->next;q->next=p->next;p->next=q;}r=p;//r指向参与⽐较的最后⼀个，不断向前移动} }/*由⼤到⼩排序*/void arrange2(polynomail pa){ polynomail h=pa,p,q,r;if(pa==NULL) exit(-2);for(p=pa;p->next!=NULL;p=p->next); r=p;for(h=pa;h->next!=r;)//⼩的沉底{ for(p=h;p->next!=r&&p!=r;p=p->next)if(cmp(p->next->next->data,p->next->data)==1){ q=p->next->next;p->next->next=q->next;q->next=p->next;p->next=q;}r=p;//r指向参与⽐较的最后⼀个，不断向前移动} }/*打印多项式,求项数*/int printpolyn(polynomail P){ int i;polynomail q;if(P==NULL) printf("⽆项！\n");else if(P->next==NULL) printf("Y=0\n");else{ printf("该多项式为Y=");q=P->next;i=1;if(q->data.coef!=0&&q->data.expn!=0){ printf("%.2fX^%d",q->data.coef,q->data.expn); i++; }if(q->data.expn==0&&q->data.coef!=0)printf("%.2f",q->data.coef);//打印第⼀项q=q->next;if(q==NULL){printf("\n");return 1;}while(1)//while中，打印剩下项中系数⾮零的项，{ if(q->data.coef!=0&&q->data.expn!=0){ if(q->data.coef>0) printf("+");printf("%.2fX^%d",q->data.coef,q->data.expn); i++;}if(q->data.expn==0&&q->data.coef!=0){ if(q->data.coef>0) printf("+");printf("%f",q->data.coef);}q=q->next;if(q==NULL){ printf("\n"); break; }}}return 1;}/*1、创建并初始化多项式链表*/polynomail creatpolyn(polynomail P,int m){//输⼊m项的系数和指数，建⽴表⽰⼀元多项式的有序链表P polynomail r,q,p,s,Q;int i;P=(LNode*)malloc(sizeof(LNode));r=P;for(i=0;i{s=(LNode*)malloc(sizeof(LNode));printf("请输⼊第%d项的系数和指数：",i+1);scanf("%f%d",&s->data.coef,&s->data.expn);r->next=s;r=s;}r->next=NULL;if(P->next->next!=NULL){for(q=P->next;q!=NULL/*&&q->next!=NULL*/;q=q->next)//合并同类项for(p=q->next,r=q;p!=NULL;)if(q->data.expn==p->data.expn){q->data.coef=q->data.coef+p->data.coef;r->next=p->next;Q=p;p=p->next;free(Q);}else{r=r->next;p=p->next;}}return P;}/*2、两多项式相加*/polynomail addpolyn(polynomail pa,polynomail pb) {//完成多项式相加运算，即：Pa=Pa+Pb polynomail s,newp,q,p,r;int j;p=pa->next;q=pb->next;newp=(LNode*)malloc(sizeof(LNode));r=newp;while(p&&q)//p&&q都不为空{s=(LNode*)malloc(sizeof(LNode));switch(cmp(p->data,q->data)){case -1: s->data.coef=p->data.coef;s->data.expn=p->data.expn;r->next=s;r=s;p=p->next;break;case 0: s->data.coef=p->data.coef+q->data.coef;if(s->data.coef!=0.0){s->data.expn=p->data.expn;r->next=s;r=s;}p=p->next;q=q->next;break;case 1: s->data.coef=q->data.coef;s->data.expn=q->data.expn;r->next=s;r=s;q=q->next;break;}//switch}//while p||q有⼀个跑完就跳出该循环while(p)//p没跑完{s=(LNode*)malloc(sizeof(LNode));s->data.coef=p->data.coef;s->data.expn=p->data.expn;r->next=s;r=s;p=p->next;}//p跑完跳出循环while(q)//q没跑完{s=(LNode*)malloc(sizeof(LNode));s->data.coef=q->data.coef;s->data.expn=q->data.expn;r=s;q=q->next;}//q跑完跳出循环//p&&q都跑完r->next=NULL;for(q=newp->next;q->next!=NULL;q=q->next)//合并同类项{for(p=q;p!=NULL&&p->next!=NULL;p=p->next)if(q->data.expn==p->next->data.expn){q->data.coef=q->data.coef+p->next->data.coef;r=p->next;p->next=p->next->next;free(r);}}printf("升序 1 , 降序 2\n");printf("选择排序⽅式:");scanf("%d",&j);if(j==1)arrange1(newp);elsearrange2(newp);return newp;}/*3、两多项式相减*/polynomail subpolyn(polynomail pa,polynomail pb){//完成多项式相减运算，即：Pa=Pa-Pbpolynomail s,newp,q,p,r,Q; int j;p=pa->next;q=pb->next;newp=(LNode*)malloc(sizeof(LNode));r=newp;while(p&&q){s=(LNode*)malloc(sizeof(LNode));switch(cmp(p->data,q->data)){case -1: s->data.coef=p->data.coef;s->data.expn=p->data.expn;r->next=s;r=s;p=p->next;break;case 0: s->data.coef=p->data.coef-q->data.coef;if(s->data.coef!=0.0){s->data.expn=p->data.expn;r->next=s;r=s;}p=p->next;q=q->next;break;case 1: s->data.coef=-q->data.coef;s->data.expn=q->data.expn;r->next=s;r=s;}//switch}//whilewhile(p){s=(LNode*)malloc(sizeof(LNode));s->data.coef=p->data.coef;s->data.expn=p->data.expn;r->next=s;r=s;p=p->next;}while(q){s=(LNode*)malloc(sizeof(LNode));s->data.coef=-q->data.coef;s->data.expn=q->data.expn;r->next=s;r=s;q=q->next;}r->next=NULL;if(newp->next!=NULL&&newp->next->next!=NULL)//合并同类项{for(q=newp->next;q!=NULL;q=q->next)for(p=q->next,r=q;p!=NULL;)if(q->data.expn==p->data.expn){q->data.coef=q->data.coef+p->data.coef;r->next=p->next;Q=p;p=p->next;free(Q);}else{r=r->next;p=p->next;}}printf("升序 1 , 降序 2\n");printf("选择:");scanf("%d",&j);if(j==1)arrange1(newp);elsearrange2(newp);return newp;}/*4两多项式相乘*/polynomail mulpolyn(polynomail pa,polynomail pb){//完成多项式相乘运算，即：Pa=Pa*Pbpolynomail s,newp,q,p,r;int i=20,j;newp=(LNode*)malloc(sizeof(LNode));r=newp;for(p=pa->next;p!=NULL;p=p->next)for(q=pb->next;q!=NULL;q=q->next){s=(LNode*)malloc(sizeof(LNode));s->data.coef=p->data.coef*q->data.coef;s->data.expn=p->data.expn+q->data.expn;r->next=s;r=s;}r->next=NULL;printf("升序 1 , 降序 2\n");printf("选择:");scanf("%d",&j);if(j==1)arrange1(newp);elsearrange2(newp);for(;i!=0;i--){for(q=newp->next;q->next!=NULL;q=q->next)//合并同类项for(p=q;p!=NULL&&p->next!=NULL;p=p->next)if(q->data.expn==p->next->data.expn){q->data.coef=q->data.coef+p->next->data.coef;r=p->next;p->next=p->next->next;free(r);}}return newp;}/*5、销毁已建⽴的两个多项式*/void delpolyn(polynomail pa,polynomail pb){polynomail p,q;p=pa;while(p!=NULL){q=p;p=p->next;free(q);}p=pb;while(p!=NULL){q=p;p=p->next;free(q);}printf("两个多项式已经销毁\n");}void Menulink(){printf("\n");printf(" ********⼀元多项式链式存储的基本运算********\n"); printf(" 1、创建两个⼀元多项式请按1\n");printf(" 2、两多项式相加得⼀新多项式请按2\n");printf(" 3、两多项式相减得⼀新多项式请按3\n");printf(" 4、两多项式相乘得⼀新多项式请按4\n");printf(" 5、销毁已建⽴的两个多项式请按5\n");printf(" 6、退出该⼦系统返回主菜单请按6\n");printf(" 7、退出该系统请按7\n");printf(" ********************************************\n");printf("\n");}void link() //⼀元多项式链式存储的实现{polynomail pa=NULL,pb=NULL;polynomail p,q;polynomail addp=NULL,subp=NULL,mulp=NULL; int n,m;printf("已进⼊链式存储⼀元多项式运算的⼦系统\n"); Menulink();while(1){printf("请选择你想进⾏的链式存储运算操作：\n"); scanf("%d",&n);switch(n){case 1:if(pa!=NULL){printf("已建⽴两个⼀元多项式，请选择其他操作!"); break;}printf("请输⼊第⼀个多项式：\n");printf("要输⼊⼏项：");scanf("%d",&m);while(m==0){printf("m不能为0，请重新输⼊m：");scanf("%d",&m);}pa=creatpolyn(pa,m);printpolyn(pa);printf("请输⼊第⼆个多项式：\n");printf("要输⼊⼏项：");scanf("%d",&m);while(m==0){printf("m不能为0，请重新输⼊m：");scanf("%d",&m);}pb=creatpolyn(pb,m);printpolyn(pb);break;case 2:if(pa==NULL){printf("请先创建两个⼀元多项式!\n");break;}addp=addpolyn(pa,pb);printpolyn(addp);break;case 3:if(pa==NULL){printf("请先创建两个⼀元多项式!\n");break;}subp=subpolyn(pa,pb);printpolyn(subp);break;case 4:if(pa==NULL){printf("请先创建两个⼀元多项式!\n"); break;}mulp=mulpolyn(pa,pb);printpolyn(mulp);break;case 5:if(pa==NULL){printf("请先创建两个⼀元多项式!\n"); break;}delpolyn(pa,pb);pa=pb=NULL;printf("两个⼀元多项式的销毁成功!\n"); break;case 6:if(addp!=NULL){p=addp;while(p!=NULL){q=p;p=p->next;free(q);}}if(subp!=NULL){p=subp;while(p!=NULL){q=p;p=p->next;free(q);}}printf("返回主菜单\n");Menu();break;case 7:if(addp!=NULL){p=addp;while(p!=NULL){q=p;p=p->next;free(q);}}if(subp!=NULL){p=subp;while(p!=NULL){q=p;p=p->next;free(q);}}printf("已成功退出该系统，谢谢你的使⽤！\n");exit(-2);break;}//switch}//while}//2、顺序程序：void ADD(Ploy A,Ploy B,Ploy *M)/*多项式A与多项式B相加，得到多项式M*/{int la=A.len,lb=B.len,i;M->len=la>lb?la:lb;for(i=0;i<=la&&i<=lb;i++){M->a[i]=A.a[i]+B.a[i];}while(i<=la){M->a[i]=A.a[i];i++;}while(i<=lb){M->a[i]=B.a[i];i++;}return;}void SUB(Ploy A,Ploy B,Ploy *M)/*多项式A与多项式B相减（A-B），得到多项式M*/{int la=A.len,lb=B.len,i;M->len=la>lb?la:lb;for(i=0;i<=la&&i<=lb;i++){M->a[i]=A.a[i]-B.a[i];}while(i<=la) {M->a[i]=A.a[i];i++;}while(i<=lb) {M->a[i]=0-B.a[i];i++;}return ;}void MUL(Ploy A,Ploy B,Ploy *M)/*多项式A与多项式B相乘，得到多项式M*/{int i,j;for(i=0;i<=A.len+B.len+1;i++) M->a[i]=0;for(i=0;i<=A.len;i++)for(j=0;j<=B.len;j++){M->a[i+j]+=A.a[i]*B.a[j];}M->len=A.len+B.len;return ;}void GetPloy(Ploy *A){int i,coef,ex,maxe=0;//ex指指数，maxe指最⼤指数char ch;printf("请输⼊每个项的系数及对应的指数，指数为负数时标志输⼊结束！\n");for(i=0;iA->a[i]=0;scanf("%d%d",&coef,&ex);while(ex>=0){if(ex>maxe)maxe=ex;if(A->a[ex]!=0){printf("你输⼊的项已经存在，是否更新原数据？（Y/N）"); cin>>ch;if(ch=='Y'||ch=='y'){A->a[ex]=coef;printf("更新成功，请继续输⼊！\n");}elseprintf("请继续输⼊！\n");;}elseA->a[ex]=coef;scanf("%d%d",&coef,&ex);}A->len=maxe;return ;}void PrintPloy1(Ploy A)//降序输出顺序⼀元多项式{int i;printf(" %dx^%d ",A.a[A.len],A.len);for(i=A.len-1;i>=1;i--){if(A.a[i]==0) ;else if(A.a[i]==1) printf(" + x^%d ",i);else if(A.a[i]==-1) printf(" - x^%d ",i);else{if(A.a[i]>0)printf("+ %dx^%d ",A.a[i],i);elseprintf("- %dx^%d ",-A.a[i],i);}}if(A.a[0]==0) ;else if(A.a[0]>0)printf(" + %d",A.a[0]);//打印x的0次项elseprintf(" - %d",-A.a[0]);printf("\n");return ;}void PrintPloy2(Ploy A)//升序输出顺序⼀元多项式{int i=0;while(A.a[i]==0)++i;if(i==0)printf("%d",A.a[i]);else{if(A.a[i]==1)printf("x^%d",i);else if(A.a[i]==-1)printf("-x^%d",i);elseprintf("%dx^%d",A.a[i],i);}for(++i;i<=A.len;i++){if(A.a[i]==0) ;else if(A.a[i]==1)printf(" + x^%d",i);else if(A.a[i]==-1)printf(" - x^%d",i);else if(A.a[i]>1)printf(" + %dx^%d",A.a[i],i);else if(A.a[i]<-1)printf(" - %dx^%d",-A.a[i],i);}}void Menushunxu(){printf("\n");printf(" ********⼀元多项式顺序存储的基本运算********\n");printf(" 1、更新两个多项式⼀元多项式请按1\n");printf(" 2、两多项式相加得⼀新多项式请按2\n");printf("3、两多项式相减得⼀新多项式请按3\n");printf(" 4、两多项式相乘得⼀新多项式请按4\n");printf(" 5、退出该⼦系统，返回主菜单请按5\n");printf(" 6、退出该系统请按6\n");printf(" ********************************************\n");printf("\n");return ;}void shunxu() //⼀元多项式顺序存储的实现{Ploy A,B,M;int n,m;printf("进⼊顺序存储⼀元多项式运算⼦系统\n");printf("请输⼊多项式A：\n");GetPloy(&A);printf("请输⼊多项式B：\n");GetPloy(&B);printf("输出两个⼀元多项式A、B，降幂输出请按1，升幂输出请按2！\n"); cin>>m;while(m<1&&m>m){printf("你输⼊的输出新创⼀元多项式的操作号不合法，请重新输⼊\n"); cin>>m;}switch(m){case 1:if(m==1){printf("A降=");PrintPloy1(A);printf("\n");printf("B降=");PrintPloy1(B);break;case 2:if(m==2){printf("A升=");PrintPloy1(A);printf("\n");printf("B升=");PrintPloy1(B);}break;}Menushunxu();while(1){printf("请选择你想进⾏的顺序存储运算操作：\n");cin>>n;while(n<1&&n>6){printf("输⼊的顺序操作号不对，请重新输⼊\n");cin>>n;}switch(n){case 1:if(n==1)printf("更新两个多项式：\n");printf("请输⼊多项式A：\n");GetPloy(&A);printf("请输⼊多项式B：\n");GetPloy(&B);printf("输出两个更新的⼀元多项式A、B，降幂输出请按1，升幂输出请按2！\n"); cin>>m;while(m<1&&m>2){printf("你输⼊的输出排序操作号不合法，请重新输⼊\n");cin>>m;}switch(m){case 1:if(m==1){printf("A降=");PrintPloy1(A);printf("\n");printf("B降=");PrintPloy1(B);}break;case 2:if(m==2){printf("A升=");PrintPloy1(A);printf("\n");printf("B升=");PrintPloy1(B);}break;break;case 2:if(n==2)ADD(A,B,&M);printf("降幂输出请按1，升幂输出请按2！\n");cin>>m;while(m<1&&m>2){printf("你输⼊的输出排序操作号不合法，请重新输⼊\n"); cin>>m;}switch(m){case 1:if(m==1){printf("ADD降=");PrintPloy1(M);printf("\n");}break;case 2:if(m==2){printf("ADD升=");PrintPloy2(M);printf("\n");}break;}break;case 3:if(n==3)SUB(A,B,&M);printf("降幂输出请按1，升幂输出请2！\n");cin>>m;while(m<1&&m>2){printf("你输⼊的输出排序操作号不合法，请重新输⼊\n"); cin>>m;}switch(m){case 1:if(m==1){printf("SUB降=");PrintPloy1(M);printf("\n");}break;case 2:if(m==2){printf("SUB升=");PrintPloy2(M);printf("\n");}break;}break;case 4:if(n==4)MUL(A,B,&M);printf("降幂输出请按1，升幂输出请2！\n");cin>>m;while(m<1&&m>3){printf("你输⼊输出排序操作号不合法，请重新输⼊\n"); cin>>m;}switch(m){case 1:if(m==1){printf("MUL降=");PrintPloy1(M);printf("\n");}break;case 2:if(m==2){printf("MUL升=");PrintPloy2(M);printf("\n");}break;}break;case 5:if(n==5)printf("返回主菜单\n");Menu();break;case 6:if(n==6)printf("已成功退出该系统，谢谢你的使⽤！\n");exit(-2);break;}}}void Menu(){printf("\n");printf(" ************⼀元多项式的基本运算系统************\n"); printf(" 1、⼀元多项式顺序存储的⼦系统请按1\n");printf(" 2、⼀元多项式链式存储的基本运算请按2\n"); printf(" 3、退出系统请按3\n");printf(" ************************************************\n"); printf("\n");printf("请输⼊你想进⾏的操作号：\n");int n;scanf("%d",&n);while(n!=1 && n!=2 && n!=3){printf("对不起，你的输⼊不正确，请重新输⼊！\n"); scanf("%d",&n);}switch(n){case 1:if(n==1)shunxu();break;case 2:if(n==2)link();break;case 3:if(n==3)printf("已成功退出该系统，谢谢你的使⽤！\n"); exit(-2);}}void main(){Menu();}。
#include <iostream>#include <stdio.h>using namespace std;class Node{public:int Coe;int Exp;Node *next;};class List{public://初始化构造函数，别忘了初始化Node *InsertNode(Node *Head,Node *Ipt); //声明一个输入节点函数Node *InsertTerm(); //声明一个输入项函数void ShowPloy(Node *Head); //显示多项式的函数Node *AddPloy(Node *Head1,Node *Head2); //声明一个加法函数Node *SubPloy(Node *Head1,Node *Head2); //声明一个减法函数Node *MulPloy(Node *Head1,Node *Head2); //声明一个乘法函数void MainShow(); //程序界面设计};Node *List::InsertNode(Node *Head,Node *Ipt) //插入节点函数，返回值为空{int Flag=0; //初始化一个信号，便于我后面的判断Node *pre,*now; //定义两个指针，分别代表我们之前的位置以及现在的位置pre=Head; //将头指针赋给pre，即我们之前的位置在头结点if (pre->next==NULL){pre->next=Ipt; //此时的Ipt就是我们传入的ptr指针，他是我们要插入的那个指针，这行语句是在我们已经判断了头指针后面为空的情况下，我们将Ipt赋给头指针的后一项}else{now=pre->next; //如果头指针后面的值不为空，那么代表着这个链表已经开始存储数据，所以我们需要遍历链表，同时我们将现在的位置定在头指针的后面，然后开始依次比较，看插入的节点的幂数与现在指针的幂数哪个大，若比现在大，那么插到现在位置的前面，若小，那么继续比较，若相同，那么合并这两项///接下来会是一系列if的判断语句，OK，如果你现在有点头晕那么先休息片刻，再来看这段程序，当然这还不算什么while(Flag==0){if ((Ipt->Exp)<(now->Exp)) //判断结果为插入指针的幂数小于现在指针的幂数，执行花括号里面的语句{if (now->next==NULL) //如果现在指针后面的指针值为空，执行花括号里面的语句{now->next=Ipt;Flag=1; //标记Flag变为1，跳出while 循环}else //看清楚，这个else是表示如果现在指针后面指针的值不为空的情况，那么执行花括号的语句{pre=now; //如果接下来还有值得话，那么我就将现在的指针定义为我之前的指针now=pre->next; //而我的位置将向后移动一位，我现在的位置变成了now之后的那个指针，然后我继续做判断}}else if(Ipt->Exp>now->Exp) //这个else表示的是插入节点的幂数大于现在节点的幂数时，执行花括号内的语句{Ipt->next=now; //当插入的幂数大于现在的幂数时，我们就只需将插入的节点放到现在节点的前面即可，那么我们就将插入节点的后面的指针定义为现在的指针pre->next=Ipt; //之前的指针指向我们现在的插入指针Flag=1; //标记Flag变为1，,跳出while循环}else //这个else表示我们的插入节点幂数既不大于也不小于现在的节点幂数，那么很显然，这个表示的是幂数相同的情况。
一元多项式的计算代码：#include<iostream.h>#include <stdlib.h>#include <math.h>typedef struct Polynomial{float coe; //系数float exp;//指数struct Polynomial *next;}*Polyn,Polynomial;Polyn ma,mb;void Insert(Polyn p,Polyn h){if(p->coe==0) delete p;else{Polyn q1,q2;q1=h;q2=h->next;while(q2&&p->exp<q2->exp){q1=q2;q2=q2->next;}if(q2&&p->exp==q2->exp){q2->coe+=p->coe;delete p;if(!q2->coe){q1->next=q2->next;delete q2;}}else{p->next=q2;q1->next=p;}}}Polyn CreatePolyn(Polyn head,int m) {int i;Polyn p;p=head=new Polynomial;head->next=NULL;for(i=0;i<m;i++){p=new Polynomial;;cout<<"请输入第"<<i+1<<"项的系数:";cin>>p->coe;cout<<" 指数:";cin>>p->exp;Insert(p,head);}return head;}void DestroyPolyn(Polyn p){Polyn t;while(p!=NULL){t=p;p=p->next;delete t;}}void PrintPolyn(Polyn Pm){Polyn qa=Pm->next;int flag=1;if(!qa){cout<<"0";cout<<endl;return;}while (qa){if(qa->coe>0&&flag!=1) cout<<"+";if(qa->coe!=1&&qa->coe!=-1){cout<<qa->coe;if(qa->exp==1) cout<<"X";else if(qa->exp) cout<<"X^"<<qa->exp;}else{if(qa->coe==1){if(!qa->exp) cout<<"1";else if(qa->exp==1) cout<<"X";else cout<<"X^"<<qa->exp;}if(qa->coe==-1){if(!qa->exp) cout<<"-1";else if(qa->exp==1) cout<<"-X";else cout<<"-X^"<<qa->exp;}}qa=qa->next;flag++;}cout<<endl;}int compare(Polyn a,Polyn b){if(a&&b){if(!b||a->exp>b->exp) return 1;else if(!a||a->exp<b->exp) return -1;else return 0;}else if(!a&&b) return -1;else return 1;}Polyn AddPolyn(Polyn pa,Polyn pb){Polyn qa=pa->next;Polyn qb=pb->next;Polyn headc,hc,qc;hc=new Polynomial;hc->next=NULL;headc=hc;while(qa||qb){qc=new Polynomial;switch(compare(qa,qb)){case 1:{qc->coe=qa->coe;qc->exp=qa->exp;qa=qa->next;break;}case 0:{qc->coe=qa->coe+qb->coe;qc->exp=qa->exp;qa=qa->next;qb=qb->next;break;}case -1:{qc->coe=qb->coe;qc->exp=qb->exp;qb=qb->next;break;}}if(qc->coe!=0){qc->next=hc->next;hc->next=qc;hc=qc;}else delete qc;}return headc;}Polyn SubtractPolyn(Polyn pa,Polyn pb){Polyn h=pb;Polyn p=pb->next;Polyn pd;while(p){p->coe*=-1;p=p->next;pd=AddPolyn(pa,h);for(p=h->next;p;p=p->next)p->coe*=-1;return pd;}Polyn MultiplyPolyn(Polyn pa,Polyn pb){Polyn hf,pf;//Polyn qa=pa->next; //新建一个结点作为pa的后继结点Polyn qb=pb->next; //新建一个结点作为pb的后继结点hf=new Polynomial;hf->next=NULL;while(qa)//使用while循环，使得多项式的每项得以运算{qb=pb->next;while(qb){pf=new Polynomial;pf->coe=qa->coe*qb->coe;pf->exp=qa->exp+qb->exp;Insert(pf,hf);//调用插入函数，将新的结点插入到新建链表中，并合并同类项qb=qb->next;}qa=qa->next;}return hf;//返回所得链表的头指针}void DevicePolyn(Polyn pa,Polyn pb){Polyn quotient,remainder,temp1,temp2;Polyn qa=pa->next;Polyn qb=pb->next;quotient=new Polynomial; //建立头结点,存储商quotient->next=NULL;remainder=new Polynomial; //建立头结点，存储余数remainder->next=NULL;temp1=new Polynomial;temp1->next=NULL;temp2=new Polynomial;temp2->next=NULL;temp1=AddPolyn(temp1,pa);while(qa!=NULL&&qa->exp>=qb->exp)temp2->next=new Polynomial;temp2->next->coe=(qa->coe)/(qb->coe);temp2->next->exp=(qa->exp)-(qb->exp);Insert(temp2->next,quotient);pa=SubtractPolyn(pa,MultiplyPolyn(pb,temp2));qa=pa->next;temp2->next=NULL;}remainder=SubtractPolyn(temp1,MultiplyPolyn(quotient,pb));pb=temp1;cout<<endl<<"shang"<<endl;//printf("\t商：");PrintPolyn(quotient);cout<<"yushu"<<endl;//printf("\t余数：");PrintPolyn(remainder);}float ValuePolyn(Polyn head,float x){Polyn p;p=head->next;float result=0;while(p!=NULL){result+=(p->coe)*(float)pow(x,p->exp);p=p->next;}return result;}void desktop(){system("cls");cout<<endl<<endl<<endl<<" 一元多项式的计算"<<endl;cout<<"**********************************************"<<endl;cout<<" ** 1.输出多项式a和 b **"<<endl;cout<<" ** 2.建立多项式a+b **"<<endl;cout<<" ** 3.建立多项式a-b **"<<endl;cout<<" ** 4.建立多项式a*b **"<<endl;cout<<" ** 5.建立多项式a/b**"<<endl;cout<<" ** 6.计算多项式a的值**"<<endl;cout<<" ** 7.退出**"<<endl;cout<<"**********************************************"<<endl<<endl;cout<<" 执行操作:";}void input(){int m,n;//Polyn pa,pb;cout<<"请输入多项式a的项数:";cin>>m;ma=CreatePolyn(ma,m);cout<<endl;cout<<"请输入多项式b的项数:";cin>>n;mb=CreatePolyn(mb,n);}void main(){//int m,n;float x,result;char key;//Polyn pa,pb;cout<<endl<<endl<<endl<<endl<<" 欢迎您的使用！"<<endl;cout<<" 系统正在初始化数据，请稍后..."<<endl;_sleep(3*1000);system("cls");while(key){desktop();cin>>key;switch (key){case'1':input();cout<<"多项式a：";PrintPolyn(ma);cout<<"多项式b：";PrintPolyn(mb);break;case'2':input();//pc=AddPolyn(pa,pb);cout<<"多项式a：";PrintPolyn(ma);cout<<"多项式b：";PrintPolyn(mb);cout<<"多项式a+b：";PrintPolyn(AddPolyn(ma,mb));//DestroyPolyn(pc);break;case'3':input();//pd=SubtractPolyn(pa,pb);cout<<"多项式a：";PrintPolyn(ma);cout<<"多项式b：";PrintPolyn(mb);cout<<"多项式a-b：";PrintPolyn(SubtractPolyn(ma,mb));//DestroyPolyn(pd);break;case'4':input();//pd=SubtractPolyn(pa,pb);cout<<"多项式a：";PrintPolyn(ma);cout<<"多项式b：";PrintPolyn(mb);cout<<"多项式a*b：";PrintPolyn(MultiplyPolyn(ma,mb));//DestroyPolyn(pd);break;case'5':input();//pd=SubtractPolyn(pa,pb);cout<<"多项式a：";PrintPolyn(ma);cout<<"多项式b：";PrintPolyn(mb);cout<<"多项式a/b：";DevicePolyn(ma,mb);//DestroyPolyn(pd);break;case'6':input();cout<<"多项式a：";PrintPolyn(ma);cout<<"输入x的值：x=";cin>>x;result=ValuePolyn(ma,x);cout<<"多项式a的值:"<<result<<endl;break;case'7':DestroyPolyn(ma);DestroyPolyn(mb);exit(0);break;default:cout<<"Error!!!"<<endl;}cout<<endl<<endl;system("pause");}}。
C语言实现一元多项式相加（源代码）#include<stdio.h>#include<malloc.h>//动态申请空间的函数的头文件typedef struct node //定义节点类型{float coef; //多项式的系数int expn; //多项式的指数struct node * next; //结点指针域}PLOYList;void insert(PLOYList *head,PLOYList *input) //查找位置插入新链节的函数，且让输入的多项式呈降序排列{PLOYList *pre,*now;int signal=0;pre=head;if(pre->next==NULL) {pre->next=input;} //如果只有一个头结点，则把新结点直接连在后面else{now=pre->next;//如果不是只有一个头结点，则设置now指针while(signal==0){if(input->expn < now->expn){if(now->next==NULL){now->next=input;signal=1;}else{pre=now;now=pre->next;//始终让新输入的数的指数与最后一个结点中的数的指数比较，小于则插在其后面}}else if( input->expn > now->expn ){input->next=now;pre->next=input;signal=1;}//若新结点中指数比最后一个结点即now中的指数大，则插入now之前else//若指数相等则需合并为一个结点，若相加后指数为0则释放该结点{now->coef=now->coef+input->coef;signal=1;free(input);if(now->coef==0){pre->next=now->next;free(now);}}//else} //while}//else}//voidPLOYList *creat(char ch) //输入多项式{PLOYList *head,*input;float x;int y;head=(PLOYList *)malloc(sizeof(PLOYList)); //创建链表头head->next=NULL;scanf("%f %d",&x,&y);//实现用户输入的第一个项，包括其指数和系数while(x!=0)//当用户没有输入结束标志0时可一直输入多项式的项，且输入一个创建一个结点{input=(PLOYList *)malloc(sizeof(PLOYList)); //创建新链节input->coef=x;input->expn=y;input->next=NULL;insert(head,input); //每输入一项就将其排序，是的链表中多项式呈降序排列scanf("%f %d",&x,&y);}return head;}PLOYList *add(PLOYList *head,PLOYList *pre) //多项式相加，head为第一个多项式建立的链表表头，pre 为第二个多项式建立的链表表头{PLOYList *input;int flag=0;while(flag==0){if(pre->next==NULL)flag=1; //若该链表为空，则无需进行加法运算，跳出循环else{pre=pre->next;input=(PLOYList *)malloc(sizeof(PLOYList));//申请空间input->coef=pre->coef;input->expn=pre->expn;input->next=NULL;insert(head,input); // 把g(x)插入到f(x）中，相当于两者相加，结果保存于f(x) }}return head;}void print(PLOYList *fun) //输出多项式，fun指要输出的多项式链表的表头{PLOYList *printing;int flag=0;printing=fun->next;if(fun->next==NULL)//若为空表，则无需输出{printf("0\n");return;}while(flag==0){if(printing->coef>0&&fun->next!=printing)printf("+");if(printing->coef==1);else if(printing->coef==-1)printf("-");elseprintf("%f",printing->coef);if(printing->expn!=0) printf("x^%d",printing->expn);else if((printing->coef==1)||(printing->coef==-1))printf("1");if(printing->next==NULL)flag=1;elseprinting=printing->next;}printf("\n");}void start() //用户选择界面{printf(" * 1.两个一元多项式相加*\n");printf(" * 0.退出系统*\n");printf(" \n");printf(" 注：输入多项式格式为：系数1 指数1 系数2 指数2 ……，并以0 0 结束：\n");printf(" \n");printf(" 请选择操作: ");}void main(){PLOYList *f,*g,*pf,*hf,*p;int sign=-1;start();while(sign!=0){scanf("%d",&sign);switch(sign){case 0:break;case 1://多项式相加{printf(" 你选择的操作是多项式相加:\n");printf(" 请输入第一个多项式f(x)：");f=creat('f');printf(" 第一个多项式为：f(x)=");print(f);printf(" 请输入第二个多项式g(x)：");g=creat('g');printf(" 第二个多项式为：g(x)=");print(g);printf(" 结果为：F(x)=f(x)+g(x)=");f=add(f,g);print(f);printf("\n\n");printf(" 继续请选择相应操作，退出请按0. ");break;}}}}。
1。
一元多项式加法、减法、乘法运算的实现1。
1设计内容及要求1)设计内容（1）使用顺序存储结构实现多项式加、减、乘运算。
例如：10321058)(2456+-+-+=x x x x x x f ,x x x x x x g +--+=23451020107)(求和结果:102220128)()(2356++-+=+x x x x x g x f(2）使用链式存储结构实现多项式加、减、乘运算，10305100)(1050100+-+=x x x x f ，x x x x x x g 320405150)(10205090+++-=求和结果：1031040150100)()(102090100++-++=+x x x x x x g x f2)设计要求（1）用C 语言编程实现上述实验内容中的结构定义和算法。
（2）要有main()函数，并且在main()函数中使用检测数据调用上述算法.（3）用switch 语句设计如下选择式菜单.***＊＊*＊＊＊＊＊*＊＊＊数据结构综合性实验＊＊*＊＊＊**＊*＊*＊＊****＊*＊**一、多项式的加法、减法、乘法运算＊＊*＊**＊**＊＊*＊＊＊*＊ 1。
多项式创建 **＊*＊＊＊*＊＊＊**＊＊＊＊ 2。
多项式相加 *＊＊＊＊＊*＊＊＊＊＊*＊*＊* 3.多项式相减 ＊*＊＊＊*＊＊*＊*＊＊＊*** 4。
多项式相乘 *＊******＊**＊＊*＊** 5。
清空多项式 **＊＊*＊＊**＊＊*＊＊＊＊* 0.退出系统 ***＊＊＊＊*＊**＊＊＊*＊* 请选择（0—5） ＊＊＊*＊**＊*****＊＊＊*＊＊＊**＊*＊＊＊****＊**＊*＊＊＊****＊*＊＊*＊*******＊**＊请选择（0—5）：1.2数据结构设计根据下面给出的存储结构定义:＃define MAXSIZE 20 //定义线性表最大容量//定义多项式项数据类型typedef struct｛float coef; //系数int expn； //指数｝term，elemType;typedef struct{term terms[MAXSIZE］； //线性表中数组元素int last； //指向线性表中最后一个元素位置}SeqList；typedef SeqList polynomial；1。
