Polynomial Operation in C++, 다항식 연산 덧셈/뺄셈/곱셈

자료구조 수업을 들으면서 과제로 다항식 연산을 C++코드로 구현하라는 것이 나왔다.

C++ 자체가 처음이라 C++부터 공부를 했는데, 다행히도 내가 배운 C와 Java가 섞여있는 언어라

배우는데 그다지 오래 걸리지는 않았다.

다항식 연산에서 termArray를 static으로 쓰는 것이 포인트고,

매커니즘은 내가 그린 그림과 같다...(이렇게 그림 그려서 코드 작성하니 훨씬 쉬워지는 듯)

곱셈의 경우 추가적인 옵션 과제였는데,

나는 한번 곱셈해서 나온 다항식을 계속해서 더하는 방식으로

곱셈을 구현했다.

코드가 조금 길긴하지만 아래에 붙여넣도록 하겠다.

(다항식 곱셈에 관해서 조금더 효율적이 있는 방법이 있으신 분은 댓글로 같이 공유해봐요!)

#include <vector>
#include <algorithm>
#include <iostream>
 
#define RESET_COLOR "\033[0m"
#define GREEN  "\033[32m"
 
using namespace std;
 
class Term
{
    friend class Polynomial;
private:
    float coef;
    int exp;
};
 
class Polynomial {
public:
    Polynomial();
    Polynomial Add(Polynomial b);
    Polynomial Substraction(Polynomial b);
    Polynomial Multiplication(Polynomial b);
    void NewTerm(const float theCoeff, const int theExp);
    int Display();
    void GetData();
private:
    static Term *termArray;
    static int capacity;
    static int free;
    int terms;
    int start, finish;
    void ClearTerm(int startPos, int endPos);
};
 
Polynomial::Polynomial() {
    terms = 0;
}
 
int Polynomial::Display() {
    int aPos = start;
    for (; aPos <= finish; aPos++) {
        cout << termArray[aPos].coef << "x^" << termArray[aPos].exp;
        if (aPos != finish && termArray[aPos].coef > 0)
            cout << "+";
    }
    cout << "\n";
    return 0;
}
 
void Polynomial::GetData() {
    start = free;
 
    float theCoeff;
    int theExp;
    int pos = start;
    int answer;
 
    while (1) {
        cout << "Enter Coefficient of the term : ";
        cin >> theCoeff;
        cout << "Enter Exponent of the term : ";
        cin >> theExp;
 
        NewTerm(theCoeff, theExp);
 
        cout << "Do you want to input next term?\n[Yes = 1, No = 0] : ";
        cin >> answer;
        if (termArray[pos].exp == 0 || answer == 0) {
            break;
        }
        else {
            pos++;
        }
    }
    finish = pos;
}
 
void Polynomial::ClearTerm(int startPos, int endPos) {
    Term *temp = new Term[capacity];
    Term *resultTerm = new Term[free - endPos];
 
    copy(termArray + endPos + 1, termArray + free, resultTerm);
    copy(termArray, termArray + startPos, temp);
    copy(resultTerm, resultTerm + (free - endPos - 1), temp + startPos);
 
    delete[] termArray;
    delete[] resultTerm;
    termArray = temp;
 
    free = endPos;
    finish = free - 1;
}
 
void Polynomial::NewTerm(const float theCoeff, const int theExp)
{
    if (free == capacity)
    {
        capacity *= 2;
        Term *temp = new Term[capacity];
        copy(termArray, termArray + free, temp);
        delete[] termArray;
        termArray = temp;
    }
    termArray[free].coef = theCoeff;
    termArray[free++].exp = theExp;
 
    terms++;
}
 
Polynomial Polynomial::Add(Polynomial b)
{
    Polynomial c;
    int aPos = start;
    int bPos = b.start;
    int aTerms = start + terms;
    int bTerms = b.start + b.terms;
 
    c.start = free;
 
    while ((aPos < aTerms) && (bPos < bTerms))
        if ((termArray[aPos].exp == termArray[bPos].exp))
        {
            float t = termArray[aPos].coef + termArray[bPos].coef;
            if (t) c.NewTerm(t, termArray[aPos].exp);
            aPos++; bPos++;
        }
        else if ((termArray[aPos].exp < termArray[bPos].exp))
        {
            c.NewTerm(termArray[bPos].coef, termArray[bPos].exp);
            bPos++;
        }
        else
        {
            c.NewTerm(termArray[aPos].coef, termArray[aPos].exp);
            aPos++;
        }
 
    for (; aPos < aTerms; aPos++)
        c.NewTerm(termArray[aPos].coef, termArray[aPos].exp);
    for (; bPos < bTerms; bPos++)
        c.NewTerm(termArray[bPos].coef, termArray[bPos].exp);
    c.finish = free - 1;
    return c;
}
 
Polynomial Polynomial::Substraction(Polynomial b)
{
    Polynomial c;
    int aPos = start;
    int bPos = b.start;
    int aTerms = start + terms;
    int bTerms = b.start + b.terms;
    c.start = free;
 
    while ((aPos < aTerms) && (bPos < bTerms))
        if ((termArray[aPos].exp == termArray[bPos].exp))
        {
            float t = termArray[aPos].coef - termArray[bPos].coef;
            if (t) c.NewTerm(t, termArray[aPos].exp);
            aPos++; bPos++;
        }
        else if ((termArray[aPos].exp < termArray[bPos].exp))
        {
            c.NewTerm(-termArray[bPos].coef, termArray[bPos].exp);
            bPos++;
        }
        else
        {
            c.NewTerm(-termArray[aPos].coef, termArray[aPos].exp);
            aPos++;
        }
 
    for (; aPos < aTerms; aPos++)
        c.NewTerm(-termArray[aPos].coef, termArray[aPos].exp);
    for (; bPos < bTerms; bPos++)
        c.NewTerm(-termArray[bPos].coef, termArray[bPos].exp);
    c.finish = free - 1;
    return c;
}
 
Polynomial Polynomial::Multiplication(Polynomial b)
{
    Polynomial c;
    int aPos = start;
    int aTerms = start + terms;
    int bTerms = b.start + b.terms;
    c.start = free++;
 
    for (; aPos < aTerms; aPos++) {
        Polynomial k, r;
        r = c;
        k.start = c.terms ? c.start + c.terms : (c.start + c.terms + 1);
 
        for (int bPos = b.start; bPos < bTerms; bPos++) {
            float multCoef = termArray[aPos].coef * termArray[bPos].coef;
            int multExp = termArray[aPos].exp + termArray[bPos].exp;
            k.NewTerm(multCoef, multExp);
            k.finish = free - 1;
        }
        r = r.Add(k);
        c.finish = k.start - 1;
        c.terms = r.terms;
        c.ClearTerm(c.start, k.finish);
    }
    return c;
}
 
int Polynomial::capacity = 1;
Term *Polynomial::termArray = new Term[capacity];
int Polynomial::free = 0;
 
int main() {
    int choice;
 
    Polynomial P1, P2, P3;
    cout << "Instruction:- \nExample:-\nP(x)=5x^3+3x^1\nEnter the Polynomial like\nP(x)=5x^3+0x^2+3x^1+0x^0\n";
    cout << "Enter Polynomial1:-" << endl;
    P1.GetData();
    cout << "Enter Polynomial2:-" << endl;
    P2.GetData();
 
    while (1) {
        cout << "\n****** Menu Selection ******" << endl;
        cout << "1: Addition\n2: Substraction\n3: Multiplication\n0: Exit" << endl;
        cout << "Enter ypur choice:";
        cin >> choice;
        switch (choice) {
        case 1:
            cout << "\n--------------- Addition ---------------\n";
            cout << "Polynomial1:";
            P1.Display();
            cout << "Polynomial2:";
            P2.Display();
            P3 = P1.Add(P2);
            cout << "Result :";
            P3.Display();
            cout << "----------------------------------------\n";
            break;
        case 2:
 
            cout << "\n------------- Substraction -------------\n";
            cout << "Polynomial1:";
            P1.Display();
            cout << "Polynomial2:";
            P2.Display();
            P3 = P1.Substraction(P2);
            cout << "Result :";
            P3.Display();
            cout << "----------------------------------------\n";
            break;
        case 3:
            cout << "\n----------- Multiplication -------------\n";
            cout << "Polynomial1:";
            P1.Display();
            cout << "Polynomial2:";
            P2.Display();
            P3 = P1.Multiplication(P2);
            cout << "Result :";
            P3.Display();
            cout << "----------------------------------------\n";
            break;
        case 0:
            cout << "Good Bye...!!!" << endl;
            exit(0);
        }
    }
    return 0;
}