Class operatorsClass operators

class class polynomialpolynomialclass polynomial{ protected: int n; double *a;

public: polynomial(){}; …..; // constructor ~polynomial(); // destructor

//member functions ... double f (const double) const; // polynomial value

// friend functions and operators friend polynomial operator+ (const polynomial, const polynomial); friend polynomial operator- (const polynomial, const polynomial); friend polynomial operator* (const double, const polynomial); }; // end of class definition

constructorsconstructors1. polynomial::polynomial(){}; // an empty polynomial

2. polynomial::polynomial(const int nn){ n = nn; a = new double[n+1];} // allocate space for coefficients, but don’t assign values.

3. polynomial::polynomial(const int nn, const double *c) { int j; n = nn; a = new double [n+1]; for (j=0; j<=n; j++) a[j] = c[j]; } // assign value for each coefficients.

4. polynomial::polynomial(const polynomial & p1) { int j; n = p1.n; a = new double [n+1]; for (j=0; j<=n; j++) a[j] = p1.a[j]; } // copy data from another polynomial

ConstructorConstructor

Allow multiple constructors, same principle as Allow multiple constructors, same principle as function overload.function overload.

Function name of constructor:Function name of constructor:

polynomial:: polynomial( arguments)polynomial:: polynomial( arguments)

{…; …; …; }{…; …; …; } No function type, no return variables.No function type, no return variables.

Dynamic allocation in c++Dynamic allocation in c++

In C: #include <stdlib.h> pointer variable = malloc(total_memory_size); or pointer varibale = calloc(dim, size_of_each_varible);

釋放記憶 : void free(void *ptr);

In C++: double pointer = new double [dimension];

釋放記憶 : delete [] pointer;

Copy constructorCopy constructor

polynomial::polynomial(const polynomial & p1) { int j;

this->n = p1.n; this->a = new double [n+1]; for (j=0; j<=n; j++) this->a[j] = p1.a[j]; } // copy data from another polynomial

Pass by referencePass by referencePass by value: double ssqq(double a) { a = 2.0 * a; return(a*a); }

Call: double aa = ssqq(a); // a 不變

Pass by address: double ssqq(double *a) { *a = 2.0 * (*a); return((*a)*(*a)); }

Call: double aa = ssqq(&ra); // ra 2(ra)

Pass by reference: double ssqq(double &a) { a = 2.0 * a; return(a*a); }

Call: double aa = ssqq(a); // a 2a

DeconstructorDeconstructor

class polynomialclass polynomial

{ protected: int n;{ protected: int n;

double *a;double *a;

public: …; …;public: …; …;

~polynomial{ delete [] this->a; }~polynomial{ delete [] this->a; }

};};

polynomial p1(5, acoef); // polynomial p1(5, acoef); // 宣告 宣告 5 5 階多項式階多項式 p1.~polynomial(); // p1.~polynomial(); // 釋放 釋放 p1.a[6] p1.a[6] 的記憶空間的記憶空間

Assignment operator=Assignment operator=Assignment operator is a member function:

p1 = p2; // syntax equivalent to p1.operator=(p2)

polynomial& polynomial::operator=(const polynomial & p1){ int i; if (this->n > 0) delete [] this->a; this->n = p1.n; this->a = new double[this->n + 1]; for (i=0; i<=n; i++) this->a[i] = p1.a[i]; return(*this);}

operatorsoperatorspolynomial operator* (const double rr, const polynomial p1){ int i; polynomial p2(p1); for (i=0; i<=p1.n; i++) p2.a[i] *= rr; return(p2);}

Operators: +, -, *, /, % >, <, >=, <=, >>, << [], ++, --, +=, -= *=, %=

operatorsoperators

Operator is a friend function.Operator is a friend function. polynomial p1(5, acoef), p2(4, bceof);polynomial p1(5, acoef), p2(4, bceof); polynomial p3 = p1 + p2;polynomial p3 = p1 + p2; 可以寫成 可以寫成 p3 = operator+ (p1, p2)p3 = operator+ (p1, p2) Function overlaod Function overlaod 的原則可以運用到 的原則可以運用到 operator operator 的的

定義定義 .. example double * polynomial;example double * polynomial; polynomial * double;polynomial * double; polynomial * polynomial;polynomial * polynomial;

Polynomial operator +Polynomial operator +

polynomial operator+(polynomial p1, polynomial p2) { int i; if (p1.n > p2.n) { polynomial pp(p1); for (i=0; i<=p2.n; i++) pp.a[i] += p2.a[i]; return(pp); } else { polynomial pp(p2); for (i=0; i<=p1.n; i++) pp.a[i] += p1.a[i]; return(pp); }

}

polynomial operator -polynomial operator -

if (p1.n > p2.n) { polynomial pp(p1); for (i=0; i<=p2.n; i++) pp.a[i] -= p2.a[i]; return(pp); } else { polynomial pp(p2); pp = (-1.0) * pp; for (i=0; i<=p1.n; i++) pp.a[i] += p1.a[i]; return(pp); }

Polynomial operator*Polynomial operator*

polynomial operator* (const polynomial p1, const polynomial p2){ int i, j, n3=p1.n+p2.n; double sum; polynomial p3(n3); for (i=0; i<=n3; i++) { sum = 0.0; for (j=0; j<=i; j++) if ((j<=p1.n) && (i-j)<= p2.n) sum += (p1.a[j]*p2.a[i-j]); p3.a[i] = sum; } return(p3); }

Polynomial operator/Polynomial operator/

n3 = p1.n – p2.n;if (n3 < 0) { n3 = 0; polynomial p3(n3); p3.a[0] = 0.0; return(p3); } else { polynomial p3(n3); polynomial pp(p1); for (i=n3; i>=0; i--) { ncur = pp.n - n3 + i; att = pp.a[ncur] / p2.a[p2.n]; p3.a[i] = att; for (j=0; j<=p2.n; j++) pp.a[pp.n-n3+i-p2.n+j] -= att*p2.a[j]; } return(p3); }

Polynomial operator %Polynomial operator % poynomial p1 % polynomial p2

留下餘數 p3, 階數小於 p2.

程式與上頁相同 , 但回傳是留下來的餘 多項式 .

n3 = p2.n – 1;

但要留意 p3.a 的高次項係數為零時 , 要將階數下降

n3 = p2.n – 1;

while ((fabs(pp.a[n3]) < 1.0e-7) && (n3>0) ) { n3 --; }

practicepractice

Write a polynomial class with constructors, Write a polynomial class with constructors, member functions and operators for the c++ member functions and operators for the c++ programs.programs. The class require the following The class require the following minimal features:minimal features:

1.1. Copy constructor.Copy constructor.

2.2. Operators: +, -, *, /, %. Operators: +, -, *, /, %.

Class MatrixClass Matrix

class Matrix{ protected: int nrow, ncol; double *xpt; public: constructors; member_functions; friend_operators;};

nrow: number of rows ncol: number of columns xpt : pointer for memory reallocation for matrix elements

Example

Plan for construction of Matrix classPlan for construction of Matrix class

General matirx (n x m)

Template with double and complex

Square matrix Column vector Row vector

Base class

Derivedclass

注意要點注意要點

1. 每一個 class 編輯器都會自動設兩個 member functions: 一個 desrtuctor, ~class(). 另一個是 class::operator=(class). Destructor

釋放 member 中的 array. 而等號運算是 copy 另一個 class 再 把 members 的值轉過去 .

2. 但是目前 Matrix 的結構中 , xpt[n*m] 的 array 並非是 class member.因此編輯器預設的 destrcutor 不會消滅 array xpt[]. 而等號算符會將兩個 Matrix 的 xpt 指標 , 指向同一記憶位址 , 產生錯誤運算 .

3. 因此 , 等號算符和 destructor 都必須再重新 overload.

Destructor

~Matrix(){ delete [] this->xpt; this->ncol = this->nrow = 0;}

Matrix & Matrix::operator=(Matrix b){ if (this->dim() > 0) delete [] this->xpt; // 去除舊陣列 this->ncol = b.ncol; this->nrow = b.nrow; if (this->dim() > 0 ) { this->xpt = new double [this->dim()]; // 建新陣列 if (this->xpt != NULL) for (i=0; i<this->dim(); i++) this->xpt[i] = b.xpt[i]; //copy b 矩陣值 else this->ncol = this->nrow = 0; } return *this;}