[英]C++ Polynomial addition
我试图在C ++中添加两个多项式,但我什至不知道从哪里开始。 因此,用户可以输入多项式的值,而不必按顺序输入或输入任何值。
例如,可以是:多边形1:2x ^ 5 + 5x ^ 2-2x + 9多边形2:x ^ 2 + 0
我将系数和指数存储在类(对象)专用字段中。 那么,我会看看Poly 1中的第一个指数吗,首先在Poly 2中搜索相同的指数,如果找到,则添加它们? 然后继续第二学期?
要求的代码:(注意:目前的实现是错误的,我需要有关如何解决此问题的帮助。)
#include <cmath>
#include <iostream>
using namespace std;
class polynomial
{
public:
polynomial();
polynomial(int);
polynomial(int exponent[], int coefficient[], int);
~polynomial();
polynomial &operator = (const polynomial &obj);
int evaluate(double uservalue);
polynomial operator+(const polynomial &obj) const;
void operator-(const polynomial &obj) const;
void operator*(const polynomial &obj) const;
friend istream & operator>> (istream & in, polynomial &obj);
friend ostream & operator<< (ostream & out, const polynomial &obj);
friend void growone(polynomial &obj);
private:
int *coefficient;
int *exponent;
int size;
};
并执行
polynomial polynomial::operator+(const polynomial &obj) const
{
bool matchFound = false;
polynomial tmp;
if (size >= obj.size) {
for (int i = 0; i < size; i++) {
if (i >= tmp.size) {
growone(tmp);
}
for(int y = 0; i < obj.size; i++) {
if (exponent[i] == obj.exponent[y]) {
tmp.coefficient[i] = (coefficient[i]+obj.coefficient[y]);
tmp.exponent[i] = exponent[i];
tmp.size++;
matchFound = true;
}
}
if (matchFound == false) {
tmp.coefficient[i] = coefficient[i];
tmp.exponent[i] = exponent[i];
tmp.size++;
}
matchFound = false;
}
} else {
}
return tmp;
}
您并没有真正充分利用C ++的功能。 一个好的规则是,如果对任何东西都使用非智能指针,则应该退后一步,重新思考一下。
大量有关堆栈溢出C的问题与指针问题无关:-)并非偶然
我要补充的另一点是,实际上值得浪费少量的内存来大大简化代码。 这样,我的意思是不要尝试创建稀疏数组来保存您的项(系数-指数对)。 取而代之的是,让每个表达式最多保留每一项,并将未使用的项的系数简单地设置为零。 除非您有类似4x 99999999999999 + 3
的表达式,否则占用的额外内存量可能是值得的。
为此,我建议仅对从零指数开始的系数使用std::vector
。 指数实际上是由向量中的位置决定的。 所以表达式4x 9 - 17x 3 + 3
将被存储为矢量:
{3, 0, 0, -17, 0, 0, 0, 0, 0, 4}
0 <------- exponent -------> 9
实际上,由于系数都很好地排列在一起,因此使多项式相加和相减的任务非常容易。
因此,考虑到这一点,让我们介绍一个简化的类以显示其完成方式:
#include <iostream>
#include <vector>
using std::cout;
using std::vector;
using std::ostream;
class Polynomial {
public:
Polynomial();
Polynomial(size_t expon[], int coeff[], size_t sz);
~Polynomial();
Polynomial &operator=(const Polynomial &poly);
Polynomial operator+(const Polynomial &poly) const;
friend ostream &operator<<(ostream &os, const Polynomial &poly);
private:
std::vector<int> m_coeff;
};
默认的构造函数(和析构函数)非常简单,我们只需确保初始化的多项式始终具有至少一项:
Polynomial::Polynomial() { m_coeff.push_back(0); }
Polynomial::~Polynomial() {}
数组构造函数稍微复杂一点,因为我们希望尽早将用户的“一切”格式转换为易于使用的格式:
Polynomial::Polynomial(size_t expon[], int coeff[], size_t sz) {
// Work out largest exponent and size vector accordingly.
auto maxExpon = 0;
for (size_t i = 0; i < sz; ++i) {
if (expon[i] > maxExpon) {
maxExpon = expon[i];
}
}
m_coeff.resize(maxExpon + 1, 0);
// Fill in coefficients.
for (size_t i = 0; i < sz; ++i) {
m_coeff[expon[i]] = coeff[i];
}
}
现在,您将了解为什么我们决定不使用稀疏数组,并将零指数放在向量的开头。 operator=
和operator+
都很简单,因为它们已经知道所有术语在哪里:
Polynomial &Polynomial::operator=(const Polynomial &poly) {
if (this != &poly) {
m_coeff.clear();
for (int coeff: poly.m_coeff) {
m_coeff.push_back(coeff);
}
}
return *this;
}
Polynomial Polynomial::operator+(const Polynomial &poly) const {
// Create sum with required size.
size_t thisSize = this->m_coeff.size();
size_t polySize = poly.m_coeff.size();
Polynomial sum;
if (thisSize > polySize) {
sum.m_coeff.resize(thisSize, 0);
} else {
sum.m_coeff.resize(polySize, 0);
}
// Do the actual sum (ignoring terms beyond each limit).
for (size_t idx = 0; idx < sum.m_coeff.size(); ++idx) {
if (idx < thisSize) sum.m_coeff[idx] += this->m_coeff[idx];
if (idx < polySize) sum.m_coeff[idx] += poly.m_coeff[idx];
}
return sum;
}
现在,我们只需要使用输出功能和一条小的测试主线来完成此操作:
ostream &operator<< (ostream &os, const Polynomial &poly) {
bool firstTerm = true;
if (poly.m_coeff.size() == 1 && poly.m_coeff[0] == 0) {
os << "0";
return os;
}
for (size_t idx = poly.m_coeff.size(); idx > 0; --idx) {
if (poly.m_coeff[idx - 1] != 0) {
if (firstTerm) {
os << poly.m_coeff[idx - 1];
} else if (poly.m_coeff[idx - 1] == 1) {
os << " + ";
if (idx == 1) {
os << poly.m_coeff[idx - 1];
}
} else if (poly.m_coeff[idx - 1] == -1) {
os << " - ";
} else if (poly.m_coeff[idx - 1] < 0) {
os << " - " << -poly.m_coeff[idx - 1];
} else {
os << " + " << poly.m_coeff[idx - 1];
}
if (idx > 1) {
os << "x";
if (idx > 2) {
os << "^" << idx - 1;
}
}
firstTerm = false;
}
}
return os;
}
int main() {
int c1[] = {1, 2, 3, 4, 5};
size_t e1[] = {3, 1, 4, 0, 9};
Polynomial p1(e1, c1, (size_t)5);
cout << "Polynomial 1 is " << p1 << " (p1)\n";
int c2[] = {6, 7, 8};
size_t e2[] = {3, 7, 9};
Polynomial p2(e2, c2, (size_t)3);
cout << "Polynomial 2 is " << p2 << " (p2)\n";
Polynomial p3 = p1 + p2;
cout << "Polynomial 3 is " << p3 << " (p3 = p1 = p2);
}
我对输出进行了稍微重新格式化以显示类似的术语,并将其显示为实际操作:
Polynomial 1 is 5x^9 + 3x^4 + x^3 + 2x + 4
Polynomial 2 is 8x^9 + 7x^7 + 6x^3
===================================
Polynomial 3 is 13x^9 + 7x^7 + 3x^4 + 7x^3 + 2x + 4
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