多项式c语言编程.docx

#include "stdlib.h"
#include "stdio.h"

typedef struct node{
double coef; //系数
int exp; //指数
struct node *next;
}Polynode,*Polynomial;

void error(char *s){
fprintf(stderr,"%s\n",s);
exit(1);
}

Polynode* createNode(double coef,int exp){
// 为结点分配空间
Polynode *p=(Polynode*)malloc(sizeof(Polynode));
if(!p)
error("分配失败");
p->coef=coef;
p->exp=exp;
p->next=NULL;
return p;
}

void insertNode(Polynomial p,Polynode *newnode){
Polynode *q=p;
//找到链表的末尾,循环结束时,p指向最后一个结点
while(q->next!=NULL)
q=q->next;
q->next=newnode;
}

Polynomial createPolynomial(int m){
double coef;
int exp,i=1;
Polynode *newnode;
Polynomial p;
// 创建头结点
newnode=createNode(0,0);
// p指向头结点
p=newnode;
// 依次创建多项式各项对应的结点
while(i<=m){
printf("系数=");scanf("%lf",&coef);
printf("指数=");scanf("%d",&exp);
newnode=createNode(coef,exp);
insertNode(p,newnode);
i=i+1;
}
return p;
}

void append(Polynomial p,Polynode *currentnode){
Polynode *newnode,*q;
// 找到链表p的尾结点q
q=p;
while(q->next)
q=q->next;

// 复制currentnode指向的每一个结点，链入p的末尾
while(currentnode){
newnode=createNode(currentnode->coef,currentnode->exp);
q->next=newnode;
q=q->next;
currentnode=currentnode->next;
}
}

void outputPolynomial(Polynomial p){
Polynode *currentnode;
currentnode=p->next;
if(!currentnode)
error("Polynomial is null");
// 输出第一项
printf("%lfx^%d",currentnode->coef,currentnode->exp);
currentnode=currentnode->next;

while(currentnode){
if(currentnode->coef>0)
printf("+");
printf("%lfx^%d",currentnode->coef,currentnode->exp);
currentnode=currentnode->next;
}
printf("\n");
}

void freePolynomial(Polynomial p){
Polynode *q;
while(p){
q=p;p=p->next;
free(q);
}
}

Polynomial addPolynomial(Polynomial pa,Polynomial pb){
Polynomial pc;
Polynode *currenta,*currentb,*newnode;
double coef;
currenta=pa->next;
currentb=pb->next;
newnode=createNode(0,0); // 创建链表pc的头结点
pc=newnode; //pc指向头结点
while(currenta&&currentb){
if(currenta->exp>currentb->exp){
newnode=createNode(currentb->coef,currentb->exp);
insertNode(pc,newnode);
currentb=currentb->next;
}else if(currenta->exp<currentb->exp){
newnode=createNode(currenta->coef,currenta->exp);
insertNode(pc,newnode);
currenta=currenta->next;
}else{
// 代表currenta->exp==currentb->exp
coef=currenta->coef+currentb->coef;
if(coef!=0){
newnode=createNode(coef,currenta->exp);
insertNode(pc,newnode);
}
currenta=currenta->next;currentb=currentb->next;
}
}
// 将pa中剩余的节点加入pc中
if(currenta)
append(pc,currenta);
// 将pb中剩余的节点加入pc中
if(currentb)
append(pc,currentb);
return pc;
}

void derivate(Polynomial p){
Polynode *currentnode=p->next;
while(currentnode){
currentnode->coef=currentnode->coef*currentnode->exp;
currentnode->exp=currentnode->exp-1;
currentnode=currentnode->next;
}
}

void showMenu(){
printf("--------------------------\n");
printf(" 1.求和\n");
printf(" 2.求导\n");
printf(" 3.退出\n");
printf("--------------------------\n");
printf("请输入要进行的操作[1或2或3]:");
}

void main() {
Polynomial pa,pb,pc;
int choice,num;
while(true){
showMenu(); scanf("%d",&choice); printf("\n");
switch(choice){
// 求和
case 1:
printf("请输入多项式1的项数:"); scanf("%d",&num);
printf("按照指数从小到大的次序，输入多项式1的系数和指数\n");
pa=createPolynomial(num);
printf("请输入多项式2的项数:"); scanf("%d",&num);
printf("按照指数从小到大的次序，输入多项式2的系数和指数\n");
pb=createPolynomial(num); pc=addPolynomial(pa,pb);
printf("多项式1:"); outputPolynomial(pa);
printf("多项式2:"); outputPolynomial(pb);
printf("求和的结果:"); outputPolynomial(pc);
// 释放空间
freePolynomial(pa); freePolynomial(pb); freePolynomial(pc);
break;
// 求导
case 2:
printf("请输入多项式的项数:"); scanf("%d",&num);
printf("按照指数从小到大的次序，输入多项式的系数和指数\n");
pc=createPolynomial(num);
printf("输入的多项式:"); outputPolynomial(pc);
derivate(pc);
printf("求导的结果:"); outputPolynomial(pc);
freePolynomial(pc);
break;
// 退出
case 3:
exit(0);
// 错误的输入
default:
printf("输入错误\n");
exit(0);
}
}
}