多项式【数据结构课设一枚，671原创】
帮别人写的。。先是在网上找了一个。。但是发现错误百出。。然后又找不到更好的。。于是就改了下。。。将就着看。。。完全c语言，。。。木有任何c++~~~~不过倒是很别扭。。。学了java之后。。。感觉自己被面向过程残害匪浅。。。。面向对象和多线程的思路完全屡不清头绪。。。。哎。。。ACM害我一生么难道？
主要实现了以下功能
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. 多项式求导
6. 代数求值
7. 积分计算
8. 打印多项式
9. 清空多项式
以下是代码：
#include <stdlib.h>
#include <stdio.h>
#include <iostream.h>
#include <math.h>
#define NULL 0
#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;
void printPloyn(polynomial*p);
int PloynStatus(polynomial*p) //判断多项式的状态
{
if(p==NULL)
{
return -1;
}
else if(p->last==-1)
{
return 0;
}
else
{
return 1;
}
}
polynomial* Init_Polynomial() //初始化空的多项式
{
polynomial*P;
P=new polynomial;
if(P!=NULL)
{
P->last=-1;
return P;
}
else
{
return NULL;
}
}
void Reset_Polynomial(polynomial*p)
{
if(PloynStatus(p)==1)
{
p->last=-1;
}
}
int Location_Element(polynomial*p,term x) //在多项式p中查找与x项指数相同的项是否存在
{
int i=0;
if(PloynStatus(p) == -1)
return 0;
while(i<=p->last && p->terms[i].expn!=x.expn)
{
i++;
}
if(i > p->last)
{
return 0;
}
else
{
return 1;
}
}
int Insert_ElementByOrder(polynomial*p,term x) //在多项式p中插入一个指数项x
{
int j;
if(PloynStatus(p)==-1)
return 0;
if(p->last==MAXSIZE-1)
{
printf("The polym is full!\n");
return 0;
}
j=p->last;
while(p->terms[j].expn<x.expn && j>=0)
{
p->terms[j+1]=p->terms[j];
j--;
}
p->terms[j+1]=x;
p->last++;
return 1;
}
int CreatePolyn(polynomial *P, int m) //输入m项系数和指数，建立表示一元多项式的有序表p
{
float coef;
int expn;
term x;
if(PloynStatus(P) == -1)
return 0;
if(m > MAXSIZE)
{
printf("顺序表溢出\n");
return 0;
}
else
{
printf("请依次输入%d对系数和指数...\n",m);
for(int i=0;i<m;i++)
{
scanf("%f%d",&coef,&expn);
x.coef = coef;
x.expn = expn;
if(!Location_Element(P,x))
{
Insert_ElementByOrder(P,x);
}
}
}
return 1;
}
char compare(term term1,term term2) //比较指数项term1和指数项term2
{
if(term1.expn>term2.expn)
{
return'>';
}
else if(term1.expn<term2.expn)
{
return'<';
}
else
{
return'=';
}
}
polynomial*addPloyn(polynomial*p1,polynomial*p2) //将多项式p1和多项式p2相加，生成一个新的多项式
{
int i=0, j=0, k=0;
if((PloynStatus(p1)==-1)||(PloynStatus(p2)==-1))
{
return NULL;
}
polynomial*p3 = Init_Polynomial();
while(i <= p1->last && j <= p2->last)
{
switch(compare(p1->terms[i], p2->terms[j]))
{
case'>':
p3->terms[k++] = p1->terms[i++];
p3->last++;
break;
case'<':
p3->terms[k++] = p2->terms[j++];
p3->last++;
break;
case'=':
if(p1->terms[i].coef + p2->terms[j].coef != 0)
{
p3->terms[k].coef = p1->terms[i].coef + p2->terms[j].coef;
p3->terms[k].expn = p1->terms[i].expn;
k++;
p3->last++;
}
i++;
j++;
}
}
while(i<=p1->last)
{
p3->terms[k++] = p1->terms[i++];
p3->last++;
}
while(j<=p2->last)
{
p3->terms[k++] = p2->terms[j++];
p3->last++;
}
return p3;
}
polynomial*subStractPloyn(polynomial*p1,polynomial*p2) //多项式p1和多项式p2相减，生成一个新的多项式
{
int i=0;
if((PloynStatus(p1)!=1)||(PloynStatus(p2)!=1))
{
return NULL;
}
polynomial*p3=Init_Polynomial();
p3->last=p2->last;
for(i=0;i<=p2->last;i++)
{
p3->terms[i].coef=-p2->terms[i].coef;
p3->terms[i].expn=p2->terms[i].expn;
}
p3=addPloyn(p1,p3);
return p3;
}
polynomial* mulitPloyn(polynomial*p1,polynomial*p2) //多项式p1和多项式p2相乘，生成一个新的多项式
{
int i=0, j, k;
if((PloynStatus(p1)!=1)||(PloynStatus(p2)!=1))
{
return NULL;
}
polynomial*p3=Init_Polynomial();
polynomial**p=new polynomial*[p2->last+1];
for(k=0; k<=p2->last; k++)
{
p[k]=Init_Polynomial();
p[k]->last=p1->last;
for(j=0; j<=p1->last; j++)
{
p[k]->terms[j].coef = p1->terms[j].coef * p2->terms[k].coef;
p[k]->terms[j].expn = p1->terms[j].expn + p2->terms[k].expn;
}
p3=addPloyn(p[k], p3);
}
return p3;
}
void printPloyn(polynomial*p) //输出在顺序存储结构的多项式p
{
int i;
for(i=0;i<=p->last;i++)
{
if(p->terms[i].coef>0 && i>0)
printf("+%.2f", p->terms[i].coef);
else
printf("%.2f", p->terms[i].coef);
printf("x^%d", p->terms[i].expn);
}
puts("");
}
void menu()
{
printf("\n\t\t*******数据结构综合性实验*********\n");
printf("\t\t***一、多项式的加、减、乘法运算***\n");
printf("\t\t******* 1.多项式创建 *********\n");
printf("\t\t******* 2.多项式相加 *********\n");
printf("\t\t******* 3.多项式相减 *********\n");
printf("\t\t******* 4.多项式相乘 *********\n");
printf("\t\t******* 5.多项式求导 *********\n");
printf("\t\t******* 6.代数求值 *********\n");
printf("\t\t******* 7.积分计算 *********\n");
printf("\t\t******* 8.打印多项式 *********\n");
printf("\t\t******* 9.清空多项式 *********\n");
printf("\t\t******* 0.退出系统 *********\n");
printf("\t\t****** 请选择(0-9) ********\n");
printf("\t\t**********************************\n");
}
polynomial* derivative(polynomial* p1) //多项式求导
{
int i=0, k;
if((PloynStatus(p1)!=1))
{
return NULL;
}
polynomial*p3=Init_Polynomial();
polynomial*tmp;
for(k=0; k<=p1->last; k++)
{
tmp=Init_Polynomial();
tmp->last = 0;
if (p1->terms[k].expn != 0)
{
tmp->terms[0].coef = p1->terms[k].expn * p1->terms[k].coef;
tmp->terms[0].expn = p1->terms[k].expn - 1;
p3=addPloyn(tmp, p3);
}
}
return p3;
}
polynomial* Rederivative(polynomial* p1) //多项式原函数（积分要用）。。。。。太麻烦了 *.*||
{
int i=0, k;
if((PloynStatus(p1)!=1))
{
return NULL;
}
polynomial*p3=Init_Polynomial();
polynomial*tmp;
for(k=0; k<=p1->last; k++)
{
tmp=Init_Polynomial();
tmp->last = 0;
tmp->terms[0].coef = p1->terms[k].coef / (float)(p1->terms[k].expn + 1);
tmp->terms[0].expn = p1->terms[k].expn + 1;
p3=addPloyn(tmp, p3);
}
return p3;
}
double getanswer(polynomial* p1, double x) //求值
{
double ans = 0.0;;
int i=0, k;
if((PloynStatus(p1)!=1))
{
return NULL;
}
for(k=0; k<=p1->last; k++)
{
ans += pow(x, p1->terms[k].expn) * p1->terms[k].coef;
}
return ans;
}
int choose() //选择。。方便省代码。。
{
int tmp;
printf("\n请输入要操作的多项式编号(1/2):");
scanf("%d", &tmp);
if (tmp != 1 && tmp != 2)
{
puts("输入有误，结束操作。\n");
return 0;
}
return tmp;
}
void main()
{
int sel, tmp;
double ans;
polynomial*p1=NULL;
polynomial*p2=NULL;
polynomial*p3=NULL;
while(1)
{
menu();
printf("\t\t*请选择(0-9):");
scanf("%d", &sel);
switch(sel)
{
case 1:
p1=Init_Polynomial();
p2=Init_Polynomial();
int m;
printf("请输入第一个多项式的项数:\n");
scanf("%d",&m);
CreatePolyn(p1,m);
printf("第一个多项式的表达式为p1=");
printPloyn(p1);
printf("请输入第二个多项式的项数:\n");
scanf("%d",&m);
CreatePolyn(p2,m);
printf("第二个多项式的表达式为p2=");
printPloyn(p2);
break;
case 2:
printf("p1+p2=");
if((p3 = addPloyn(p1,p2)) != NULL)
printPloyn(p3);
break;
case 3:
printf("\np1-p2=");
if((p3 = subStractPloyn(p1,p2)) != NULL)
printPloyn(p3);
break;
case 4:
printf("\np1*p2=");
if((p3 = mulitPloyn(p1,p2)) != NULL)
printPloyn(p3);
break;
case 5:
if (!(tmp = choose()))
break;
printf("p%d导数为:", tmp);
switch(tmp)
{
case 1:
if ((p3=derivative(p1)) != NULL)
printPloyn(p3);
break;
case 2:
if ((p3=derivative(p2)) != NULL)
printPloyn(p3);
break;
}
break;
case 6:
if (!(tmp = choose()))
break;
printf("请输入x的值:\n");
double tmp2;
scanf("%lf", &tmp2);
switch(tmp)
{
case 1:
ans = getanswer(p1, tmp2);
printf("当x=%.2lf时，p1的值为：%.2lf\n", tmp2, ans);
break;
case 2:
ans = getanswer(p2, tmp2);
printf("当x=%.2lf时，p2的值为：%.2lf\n", tmp2, ans);
break;
}
break;
case 7:
if (!(tmp = choose()))
break;
double a, b;
printf("请输入下限与上限:");
scanf("%lf %lf", &a, &b);
if (a > b)
{
a = a + b;
b = a - b;
a = a - b;
}
if (tmp == 1)
ans = getanswer(Rederivative(p1), b) - getanswer(Rederivative(p1), a);
if (tmp == 2)
ans = getanswer(Rederivative(p2), b) - getanswer(Rederivative(p2), a);
printf("结果为:%.2lf", ans);
break;
case 8:
if (!(tmp = choose()))
break;
printf("p%d=", tmp);
if (tmp == 1)
printPloyn(p1);
if (tmp == 2)
printPloyn(p2);
break;
case 9:
Reset_Polynomial(p1);
Reset_Polynomial(p2);
Reset_Polynomial(p3);
puts("\n清空成功！\n");
getchar();
printf("是否清空屏幕？y/n\t");
char tmpa;
scanf("%c", &tmpa);
if (tmpa == 'y')
{
system("cls");
}
break;
case 0:
return;
default:
puts("输入错误，请重新输入:");
}
}
return;
}