一元多项式的建立及其运算

• 一元多项式的数据结构
• 输入一元多项式的函数
• 输出保存在单链表中的一元多项式
• 运算一元多项式并输出结果
• main函数中的内容

一元多项式的数据结构

#ifndef __POLYNOMIAL_H__
#define __POLYNOMIAL_H__
#include <bits/stdc++.h>
using namespace std;

typedef int DataType;
typedef struct node
{
    double coef;
    int exp;
    struct node *link;
}Term, *Polynomial;

#endif

输入一元多项式的函数

此函数会把键入的多项式，按照降幂顺序排列

void Input(Polynomial& PL){
    //从系数C[] 和 指数E[]中输入一元多项式的各项，建立一个按降幂方式排列的
    //一元多项式PL。
    double coef; int exp;
    while (true)
    {
        Term *p = PL ->link, *pr = PL;
        cin >> coef >> exp;
        if(exp < 0) break;
        else{ 
            Term *newTerm = (Term *)malloc(sizeof(Term));
            newTerm ->coef = coef; newTerm ->exp = exp;
            while (p != NULL && exp < p ->exp) 
            {
                pr = p;
                p = p ->link;
            }

            if( p != NULL && p ->exp == exp){cout << "已存在exp相同的项，该项作废\n";}
            else{
                newTerm ->link = p;
                pr ->link = newTerm;
            }
        }
    }
     
}

输出保存在单链表中的一元多项式

void Output(Polynomial& PL){
    //输出带头结点的一元多项式链表PL
    Term *p = PL ->link;
    bool flag = true;
    while(p != NULL){
        if(p ->coef < 0) {cout << '-'; flag = false;}
        if(p ->coef > 0 && !flag ){cout << '+'; flag = false;}

        if(p ->exp == 0 || fabs(p ->coef) != 1){cout << fabs(p ->coef);}
        flag = false;
        switch (p ->exp)
        {
        case 0:
            break;
        case 1:
            cout << 'X' ;
            break;
        default:
            cout << "X^" << p ->exp; 
            break;
        }
        p = p ->link;
    }
}

运算一元多项式并输出结果

double calcValue(Polynomial& PL, double x){
    Term *p = PL ->link;
    if(p == NULL) return -1;
    double consequence = p ->coef;
    while (p != NULL)
    {
        if(p ->link != NULL){
            consequence = consequence*pow(x,p ->exp - p ->link ->exp) + p ->link ->coef;
        }
        else{
            consequence = consequence*pow(x,p ->exp);
        }
        p = p ->link;
    }
     return consequence;
}

main函数中的内容

int main(){
    Polynomial PL;
    PL = (Term *)malloc(sizeof(Term));
    PL ->link = NULL;
    Input(PL);
    Output(PL);
    cout << endl;
    cout << calcValue(PL, 1);
    cout << endl;
    system("pause");
}