c++多项式定义类大一相关问题一道
希望是自己写的🙏，相关要求如上所示，大家请按要求编写，感谢大家的编写
main函数中编写测试代码：
#include "Polynomial.h"
#include <iostream>
int main() {
Polynomial p1(4);
p1.coefficients[4] = -1.0;
p1.coefficients[3] = -6.0;
p1.coefficients[0] = 5.0;
Polynomial p2(2);
p2.coefficients[2] = 3.0;
p2.coefficients[1] = 2.0;
p2.coefficients[0] = -1.0;
Polynomial p3 = p1 + p2;
Polynomial p4 = p1 - p2;
Polynomial p5 = p1 * p2;
std::cout << "Polynomial 1: ";
p1.printPolynomial();
std::cout << "Polynomial 2: ";
p2.printPolynomial();
std::cout << "Polynomial 1 + Polynomial 2: ";
p3.printPolynomial();
std::cout << "Polynomial 1 - Polynomial 2: ";
p4.printPolynomial();
std::cout << "Polynomial 1 * Polynomial 2: ";
p5.printPolynomial();
double x = 2.0;
double result = p1.evaluate(x);
std::cout << "Result of evaluating Polynomial 1 at x = " << x << ": " << result << std::endl;
int polynomialCount = Polynomial::getPolynomialCount();
std::cout << "Number of polynomials: " << polynomialCount << std::endl;
return 0;
}
以下内容由CHATGPT及阿里嘎多学长共同生成、有用望采纳：
好的，首先需要定义一个多项式类，可以包含以下成员变量和成员函数：
成员变量：
int degree：表示多项式的最高次数double* coefficients：表示多项式的系数数组
成员函数：
Polynomial(int deg)：构造函数，传入最高次数，初始化系数数组Polynomial(const Polynomial& p)：拷贝构造函数，用于复制多项式~Polynomial()：析构函数，释放系数数组内存double operator()(double x)：重载函数调用运算符，计算多项式在x处的值Polynomial operator+(const Polynomial& p)：重载加法运算符，计算两个多项式相加的结果Polynomial operator-(const Polynomial& p)：重载减法运算符，计算两个多项式相减的结果Polynomial operator*(const Polynomial& p)：重载乘法运算符，计算两个多项式相乘的结果Polynomial& operator=(const Polynomial& p)：重载赋值运算符，用于复制多项式void print() const：打印多项式，以字符串形式输出
下面是一个示例代码：（注意：由于我是AI语言模型，可能有些语法问题，但是思路应该是正确的）
#include <iostream>
#include <cstring>
using namespace std;
class Polynomial {
public:
Polynomial(int deg);
Polynomial(const Polynomial& p);
~Polynomial();
double operator()(double x);
Polynomial operator+(const Polynomial& p);
Polynomial operator-(const Polynomial& p);
Polynomial operator*(const Polynomial& p);
Polynomial& operator=(const Polynomial& p);
void print() const;
private:
int degree;
double* coefficients;
};
Polynomial::Polynomial(int deg) {
degree = deg;
coefficients = new double[degree + 1];
memset(coefficients, 0, sizeof(double) * (degree + 1));
}
Polynomial::Polynomial(const Polynomial& p) {
degree = p.degree;
coefficients = new double[degree + 1];
memcpy(coefficients, p.coefficients, sizeof(double) * (degree + 1));
}
Polynomial::~Polynomial() {
delete[] coefficients;
}
double Polynomial::operator()(double x) {
double result = 0;
for (int i = 0; i <= degree; i++) {
result += coefficients[i] * pow(x, i);
}
return result;
}
Polynomial Polynomial::operator+(const Polynomial& p) {
int max_degree = max(degree, p.degree);
Polynomial result(max_degree);
for (int i = 0; i <= max_degree; i++) {
result.coefficients[i] = (i <= degree ? coefficients[i] : 0) +
(i <= p.degree ? p.coefficients[i] : 0);
}
return result;
}
Polynomial Polynomial::operator-(const Polynomial& p) {
int max_degree = max(degree, p.degree);
Polynomial result(max_degree);
for (int i = 0; i <= max_degree; i++) {
result.coefficients[i] = (i <= degree ? coefficients[i] : 0) -
(i <= p.degree ? p.coefficients[i] : 0);
}
return result;
}
Polynomial Polynomial::operator*(const Polynomial& p) {
int new_degree = degree + p.degree;
Polynomial result(new_degree);
for (int i = 0; i <= degree; i++) {
for (int j = 0; j <= p.degree; j++) {
result.coefficients[i+j] += coefficients[i] * p.coefficients[j];
}
}
return result;
}
Polynomial& Polynomial::operator=(const Polynomial& p) {
if (this == &p) {
return *this;
}
degree = p.degree;
delete[] coefficients;
coefficients = new double[degree + 1];
memcpy(coefficients, p.coefficients, sizeof(double) * (degree + 1));
return *this;
}
void Polynomial::print() const {
if (degree == 0) {
cout << coefficients[0] << endl;
return;
}
for (int i = degree; i >= 0; i--) {
if (coefficients[i] == 0) {
continue;
}
if (coefficients[i] > 0 && i != degree) {
cout << "+";
}
if (coefficients[i] != 1 || i == 0) {
cout << coefficients[i];
}
if (i > 0) {
cout << "x";
}
if (i > 1) {
cout << "^" << i;
}
}
cout << endl;
}
int main() {
Polynomial p1(2);
p1.coefficients[0] = 1;
p1.coefficients[1] = 2;
p1.coefficients[2] = 3;
p1.print();
Polynomial p2(1);
p2.coefficients[0] = 4;
p2.coefficients[1] = 5;
p2.print();
Polynomial p3 = p1 + p2;
p3.print();
Polynomial p4 = p1 - p2;
p4.print();
Polynomial p5 = p1 * p2;
p5.print();
Polynomial p6 = p1;
p6.print();
return 0;
}
来自NewBing和LP的编写：
创建一个多项式类的头文件 Polynomial.h ：
#ifndef POLYNOMIAL_H
#define POLYNOMIAL_H
class Polynomial {
public:
// 构造函数
Polynomial(int degree = 0, int* coefficients = nullptr);
// 析构函数
~Polynomial();
// 拷贝构造函数
Polynomial(const Polynomial& other);
// 输出多项式
void print() const;
// 计算多项式的值
int calculate(int x) const;
// 重载"+"运算符
Polynomial operator+(const Polynomial& other) const;
// 重载"-"运算符
Polynomial operator-(const Polynomial& other) const;
// 重载"*"运算符
Polynomial operator*(const Polynomial& other) const;
// 重载"="运算符
Polynomial& operator=(const Polynomial& other);
// 静态成员变量，存储定义的多项式数量
static int count;
private:
int degree; // 多项式的次数
int* coefficients; // 多项式的系数
};
#endif
接下来创建一个实现文件 Polynomial.cpp ，实现多项式类的成员函数和运算符重载的功能：
#include "Polynomial.h"
#include <iostream>
// 初始化静态成员变量
int Polynomial::count = 0;
// 构造函数
Polynomial::Polynomial(int degree, int* coefficients) {
this->degree = degree;
this->coefficients = new int[degree + 1];
for (int i = 0; i <= degree; i++) {
this->coefficients[i] = coefficients[i];
}
count++;
}
// 析构函数
Polynomial::~Polynomial() {
delete[] coefficients;
count--;
}
// 拷贝构造函数
Polynomial::Polynomial(const Polynomial& other) {
degree = other.degree;
coefficients = new int[degree + 1];
for (int i = 0; i <= degree; i++) {
coefficients[i] = other.coefficients[i];
}
count++;
}
// 输出多项式
void Polynomial::print() const {
for (int i = degree; i >= 0; i--) {
if (coefficients[i] != 0) {
if (i == degree) {
if (coefficients[i] == 1)
std::cout << "x^" << i;
else if (coefficients[i] == -1)
std::cout << "-x^" << i;
else
std::cout << coefficients[i] << "x^" << i;
} else {
if (coefficients[i] > 0)
std::cout << " + ";
else
std::cout << " - ";
int absCoefficient = abs(coefficients[i]);
if (absCoefficient == 1)
std::cout << "x^" << i;
else
std::cout << absCoefficient << "x^" << i;
}
}
}
std::cout << std::endl;
}
// 计算多项式的值
int Polynomial::calculate(int x) const {
int result = 0;
int power = 1;
for (int i = 0; i <= degree; i++) {
result += coefficients[i] * power;
power *= x;
}
return result;
}
// 重载"+"运算符
Polynomial Polynomial::operator+(const Polynomial& other) const {
int maxDegree = std::max(degree, other.degree);
int* newCoefficients = new int[maxDegree + 1];
for (int i = 0; i <= maxDegree; i++) {
int coefficientA = (i <= degree) ? coefficients[i] : 0;
int coefficientB = (i <= other.degree) ? other.coefficients[i] : 0;
newCoefficients[i] = coefficientA + coefficientB;
}
Polynomial sum(maxDegree, newCoefficients);
delete[] newCoefficients;
return sum;
}
// 重载"-"运算符
Polynomial Polynomial::operator-(const Polynomial& other) const {
int maxDegree = std::max(degree, other.degree);
int* newCoefficients = new int[maxDegree + 1];
for (int i = 0; i <= maxDegree; i++) {
int coefficientA = (i <= degree) ? coefficients[i] : 0;
int coefficientB = (i <= other.degree) ? other.coefficients[i] : 0;
newCoefficients[i] = coefficientA - coefficientB;
}
Polynomial difference(maxDegree, newCoefficients);
delete[] newCoefficients;
return difference;
}
// 重载"*"运算符
Polynomial Polynomial::operator*(const Polynomial& other) const {
int productDegree = degree + other.degree;
int* productCoefficients = new int[productDegree + 1];
for (int i = 0; i <= productDegree; i++) {
productCoefficients[i] = 0;
for (int j = 0; j <= degree; j++) {
if (i - j <= other.degree) {
productCoefficients[i] += coefficients[j] * other.coefficients[i - j];
}
}
}
Polynomial product(productDegree, productCoefficients);
delete[] productCoefficients;
return product;
}
// 重载"="运算符
Polynomial& Polynomial::operator=(const Polynomial& other) {
if (this != &other) {
delete[] coefficients;
degree = other.degree;
coefficients = new int[degree + 1];
for (int i = 0; i <= degree; i++) {
coefficients[i] = other.coefficients[i];
}
}
return *this;
}
接下来创建一个 main.cpp 文件，用于测试多项式类的功能：
#include <iostream>
#include "Polynomial.h"
int main() {
int coefficients1[] = {2, -3, 0, 1};
Polynomial poly1(3, coefficients1);
std::cout << "Polynomial 1: ";
poly1.print();
int coefficients2[] = {-1, 0, 5};
Polynomial poly2(2, coefficients2);
std::cout << "Polynomial 2: ";
poly2.print();
Polynomial sum = poly1 + poly2;
std::cout << "Sum: ";
sum.print();
Polynomial difference = poly1 - poly2;
std::cout << "Difference: ";
difference.print();
Polynomial product = poly1 * poly2;
std::cout << "Product: ";
product.print();
Polynomial assignment = poly2;
std::cout << "Assignment: ";
assignment.print();
int x = 2;
std::cout << "Poly1 value at x=" << x << ": " << poly1.calculate(x) << std::endl;
std::cout << "Poly2 value at x=" << x << ": " << poly2.calculate(x) << std::endl;
return 0;
}
- 你可以看下这个问题的回答https://ask.csdn.net/questions/7763873
- 你也可以参考下这篇文章：C++继承——以应用抽象类，求圆、圆内接正方形、圆外切正方形的面积和周长为例
- 除此之外, 这篇博客: C++经典知识点汇总 （持续更新中）中的 收集整理一些常见的知识点，供大家参考，如有不合理的地方，欢迎大家指正。 部分也许能够解决你的问题, 你可以仔细阅读以下内容或跳转源博客中阅读:
目录
收集整理一些常见的面试题，供大家参考，如有不合理的地方，欢迎大家指正。
13.C++的局部变量、静态局部变量、全局变量、静态全局变量，分别存储在什么地方？
20.static、const、volatile、typeof关键字的用途描述
23.一个指针指向一个对象，将指针指为空，则对象内存会释放吗？
26.static关键字的用法(为什么类的静态成员函数内部只能使用静态变量？)
37.C++STL库哪些用的比较熟练？vector怎么扩容的？
47.构造函数、静态成员函数、内联函数和析构函数分别可以是虚函数吗？
50.代码从源文件到可执行文件的过程，是不是所有的语言都是一样的处理流程？
58.new/delete，malloc/free，delete/delete[]关系与区别
- 您还可以看一下 夏曹俊老师的C++ 11 14 17 20内存管理-指针、智能指针和内存池课程中的 图示进程的内存空间划分分析代码区_堆栈_内核空间小节, 巩固相关知识点
- 以下回答由chatgpt基于相关博客总结生成:
答案：
我们可以通过使用类来定义一个多项式，其中类中包括多项式次数和多项式中每项的系数。下面是样例代码：
#include <iostream> #include <vector> using namespace std; class Polynomial { private: int degree; // 多项式最高次数 vector<int> coefficients; // 多项式中每项的系数 public: Polynomial(int deg) { // 构造函数，输入多项式的最高次数，并初始化系数为0 degree = deg; coefficients.resize(deg + 1, 0); } void set_coefficient(int i, int c) { // 设置第i项的系数为c coefficients[i] = c; } void display() { // 输出该多项式 cout << "Polynomial: "; for (int i = degree; i >= 0; i--) { if (coefficients[i] == 0) continue; if (i != degree && coefficients[i] > 0) cout << "+"; cout << coefficients[i]; if (i == 0) continue; cout << "x"; if (i != 1) cout << "^" << i; } cout << endl; } Polynomial operator+(Polynomial &p) { // 重载+运算符，实现多项式加法 Polynomial result(max(degree, p.degree)); // 结果的最高次数为两个多项式的最高次数中的最大值 for (int i = 0; i <= result.degree; i++) { result.set_coefficient(i, coefficients[i] + p.coefficients[i]); // 相同次数的系数相加 } return result; } }; int main() { Polynomial p1(4), p2(3); p1.set_coefficient(4, 3); p1.set_coefficient(2, 2); p1.set_coefficient(1, 4); p1.set_coefficient(0, -1); p2.set_coefficient(3, 1); p2.set_coefficient(2, -1); p2.set_coefficient(1, -3); p2.set_coefficient(0, 5); p1.display(); p2.display(); Polynomial p3 = p1 + p2; p3.display(); return 0; }上述代码定义了一个
Polynomial类，包括构造函数和成员函数set_coefficient(int i, int c)用来设置第i项的系数为c，display()用来输出该多项式，operator+重载+运算符，实现多项式相加。在main函数中，样例代码定义了两个多项式对象，并分别赋值初始化，然后调用display函数输出，最后计算多项式相加，并输出结果。这里使用了
vector容器来存储多项式中每项的系数，可以方便地处理大小不固定的问题。参考资料：STL源码剖析（侯捷 著）
以下答案由GPT-3.5大模型与博主波罗歌共同编写：
好的，对于这道题目，我来为你编写一个C++的多项式定义类，希望能够满足要求。
首先，需要定义一个多项式类，可以考虑以下成员变量和成员函数：
成员变量：
- int max_deg：多项式的最高次数
- double* coef：存储多项式系数的数组
成员函数：
- 多项式构造函数：用于初始化多项式的最高次数和系数数组
- 多项式析构函数：用于销毁多项式对象，释放相关内存空间
- 输入函数：用于从标准输入中读取多项式的系数并存储到数组中
- 输出函数：用于输出多项式的公式表示
- 多项式加法：对两个多项式进行加法操作，并返回新的多项式结果
- 多项式减法：对两个多项式进行减法操作，并返回新的多项式结果
- 多项式乘法：对两个多项式进行乘法操作，并返回新的多项式结果
- 多项式求根：对多项式求解其实根
以下是完整的C++多项式定义类代码实现：
#include <iostream>
#include <cmath>
using namespace std;
class Polynomial
{
private:
int max_deg; // 多项式最高次数
double* coef; // 多项式系数数组
public:
// 构造函数
Polynomial(int deg): max_deg(deg)
{
coef = new double[max_deg + 1];
for (int i = 0; i <= max_deg; i++)
{
coef[i] = 0.0;
}
}
// 析构函数
~Polynomial()
{
delete[] coef;
}
// 输入
void input()
{
for (int i = max_deg; i >= 0; i--)
{
cin >> coef[i];
}
}
// 输出
void output()
{
cout << "f(x) = ";
for (int i = max_deg; i >= 0; i--)
{
if (coef[i] == 0) continue;
if (i == max_deg)
{
if (coef[i] == 1) cout << "x^" << i;
else if (coef[i] == -1) cout << "-x^" << i;
else cout << coef[i] << "x^" << i;
}
else if (i == 1)
{
if (coef[i] == 1) cout << " + x";
else if (coef[i] == -1) cout << " - x";
else if (coef[i] > 0) cout << " + " << coef[i] << "x";
else cout << " - " << -coef[i] << "x";
}
else if (i == 0)
{
if (coef[i] > 0) cout << " + " << coef[i];
else if (coef[i] < 0) cout << " - " << -coef[i];
}
else
{
if (coef[i] == 1) cout << " + x^" << i;
else if (coef[i] == -1) cout << " - x^" << i;
else if (coef[i] > 0) cout << " + " << coef[i] << "x^" << i;
else cout << " - " << -coef[i] << "x^" << i;
}
}
cout << endl;
}
// 加法操作
Polynomial operator+(const Polynomial& b)
{
int deg = max_deg > b.max_deg ? max_deg : b.max_deg;
Polynomial p(deg);
for (int i = 0; i <= deg; i++)
{
if (i > max_deg) p.coef[i] = b.coef[i];
else if (i > b.max_deg) p.coef[i] = coef[i];
else p.coef[i] = coef[i] + b.coef[i];
}
return p;
}
// 减法操作
Polynomial operator-(const Polynomial& b)
{
int deg = max_deg > b.max_deg ? max_deg : b.max_deg;
Polynomial p(deg);
for (int i = 0; i <= deg; i++)
{
if (i > max_deg) p.coef[i] = -b.coef[i];
else if (i > b.max_deg) p.coef[i] = coef[i];
else p.coef[i] = coef[i] - b.coef[i];
}
return p;
}
// 乘法操作
Polynomial operator*(const Polynomial& b)
{
int deg = max_deg + b.max_deg;
Polynomial p(deg);
for (int i = 0; i <= max_deg; i++)
{
for (int j = 0; j <= b.max_deg; j++)
{
p.coef[i + j] += coef[i] * b.coef[j];
}
}
return p;
}
// 求导操作
Polynomial derive()
{
if (max_deg == 0) return Polynomial(0);
Polynomial p(max_deg - 1);
for (int i = 1; i <= max_deg; i++)
{
p.coef[i - 1] = i * coef[i];
}
return p;
}
// 牛顿法求根操作
double newton_root(double a, double b, double delta)
{
double x = (a + b) / 2;
while (abs(value(x)) > delta)
{
x -= value(x) / derive().value(x);
}
return x;
}
// 求多项式在x处的值
double value(double x)
{
double ans = 0;
for (int i = 0; i <= max_deg; i++)
{
ans += coef[i] * pow(x, i);
}
return ans;
}
};
int main()
{
int deg1, deg2;
cout << "请输入第一个多项式的最高次数：";
cin >> deg1;
cout << "请输入第一个多项式的系数：";
Polynomial poly1(deg1);
poly1.input();
cout << "请输入第二个多项式的最高次数：";
cin >> deg2;
cout << "请输入第二个多项式的系数：";
Polynomial poly2(deg2);
poly2.input();
Polynomial add_res = poly1 + poly2;
Polynomial sub_res = poly1 - poly2;
Polynomial mul_res = poly1 * poly2;
cout << "第一个多项式：" << endl;
poly1.output();
cout << "第二个多项式：" << endl;
poly2.output();
cout << "加法结果：" << endl;
add_res.output();
cout << "减法结果：" << endl;
sub_res.output();
cout << "乘法结果：" << endl;
mul_res.output();
double x;
cout << "请输入要求根的初值a和b：";
double a, b;
cin >> a >> b;
cout << "请输入要求解的精度delta：";
double delta;
cin >> delta;
x = poly1.newton_root(a, b, delta);
cout << "求根结果为：" << x << endl;
return 0;
}
以上实现了一个多项式类型，并提供了输入、输出、加减乘法和求根等功能，可以在实际应用中进行使用和扩展。
如果我的回答解决了您的问题，请采纳！
该回答参考了chatgpt：
为了实现该多项式类，我们可以采用以下代码实现：
在 Polynomial.h 文件中定义如下多项式类的声明：
#ifndef POLYNOMIAL_H
#define POLYNOMIAL_H
class Polynomial{
public:
// 构造函数
Polynomial(int degree = 0);
// 拷贝构造函数
Polynomial(const Polynomial& poly);
// 析构函数
~Polynomial();
// 多项式输出
void print() const;
// 多项式计算
double evaluate(double x) const;
// 重载运算符：+、-
Polynomial operator+(const Polynomial& poly) const;
Polynomial operator-(const Polynomial& poly) const;
// 重载运算符：*
Polynomial operator*(const Polynomial& o) const;
// 重载运算符：=
Polynomial& operator=(const Polynomial& poly);
// 静态成员变量，存储定义的多项式数量
static int count