math/math_007_fraction.cpp

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• Last update: 2019-11-22 21:50:52+09:00

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// fraction library (use C++11)
struct fraction{
    // init (nume / deno)
    int numerator, denominator;
    fraction(int i) : numerator(i), denominator(1) {}
    fraction(int i, int j) : numerator(i), denominator(j) {}
    fraction(string s) {
        int i = s.find('/');
        if(i != string::npos) {
            numerator = atoi(s.substr(0,i).c_str());
            denominator = atoi(s.substr(i+1).c_str());
        }
        else {
            numerator = atoi(s.c_str());
            denominator = 1;
        }
    }

    fraction fixshape(fraction A) {
        int p = A.denominator, q = A.numerator;
        if(p < 0) {p *= -1; q *= -1;}
        int k = gcd(abs(p), abs(q));
        p /= k, q /= k;
        A.denominator = p, A.numerator = q;
        return A;
    }
};

// print fraction
string printfrac(fraction A, int n) {
    if(!n) return to_string(A.numerator) + "/" + to_string(A.denominator);
    else {
        if(A.denominator == 1) return to_string(A.numerator);
        else return printfrac(A, 0);
    }
}

string printfrac(fraction A) {
    if(A.denominator == 1) return to_string(A.numerator);
    else return printfrac(A, 0);
}

void simplify(fraction &A, fraction &B) {
    int k = lcm(A.denominator, B.denominator);
    A.numerator *= (k / A.denominator);
    B.numerator *= (k / B.denominator);
    A.denominator = k; B.denominator = k;
}

// overloading the arithmetic operators
fraction operator+(const fraction &A, const fraction &B) {
    int q = lcm(A.denominator, B.denominator);
    int p = A.numerator * (q / A.denominator) + B.numerator * (q / B.denominator);
    fraction ret = ret.fixshape(fraction(p, q));
    return ret;
}

fraction operator-(const fraction &A, const fraction &B) {
    int q = lcm(A.denominator, B.denominator);
    int p = A.numerator * (q / A.denominator) - B.numerator * (q / B.denominator);
    fraction ret = ret.fixshape(fraction(p, q));
    return ret;
}

fraction operator*(const fraction &A, const fraction &B) {
    int p = A.numerator * B.numerator;
    int q = A.denominator * B.denominator;
    int k = gcd(abs(p), abs(q));
    p /= k, q /= k;
    fraction ret = ret.fixshape(fraction(p, q));
    return ret;
}

fraction operator/(const fraction &A, const fraction &B) {
    fraction C = C.fixshape(fraction(B.denominator, B.numerator));
    fraction ret = ret.fixshape(A*C);
    return ret;
}

bool operator<(const fraction &A, const fraction &B) {
    fraction C = A, D = B;
    simplify(C, D);
    return C.numerator < D.numerator;
}

bool operator>(const fraction &A, const fraction &B) {
    fraction C = A, D = B;
    simplify(C, D);
    return C.numerator > D.numerator;
}
// fraction library end

#line 1 "math/math_007_fraction.cpp"
// fraction library (use C++11)
struct fraction{
    // init (nume / deno)
    int numerator, denominator;
    fraction(int i) : numerator(i), denominator(1) {}
    fraction(int i, int j) : numerator(i), denominator(j) {}
    fraction(string s) {
        int i = s.find('/');
        if(i != string::npos) {
            numerator = atoi(s.substr(0,i).c_str());
            denominator = atoi(s.substr(i+1).c_str());
        }
        else {
            numerator = atoi(s.c_str());
            denominator = 1;
        }
    }

    fraction fixshape(fraction A) {
        int p = A.denominator, q = A.numerator;
        if(p < 0) {p *= -1; q *= -1;}
        int k = gcd(abs(p), abs(q));
        p /= k, q /= k;
        A.denominator = p, A.numerator = q;
        return A;
    }
};

// print fraction
string printfrac(fraction A, int n) {
    if(!n) return to_string(A.numerator) + "/" + to_string(A.denominator);
    else {
        if(A.denominator == 1) return to_string(A.numerator);
        else return printfrac(A, 0);
    }
}

string printfrac(fraction A) {
    if(A.denominator == 1) return to_string(A.numerator);
    else return printfrac(A, 0);
}

void simplify(fraction &A, fraction &B) {
    int k = lcm(A.denominator, B.denominator);
    A.numerator *= (k / A.denominator);
    B.numerator *= (k / B.denominator);
    A.denominator = k; B.denominator = k;
}

// overloading the arithmetic operators
fraction operator+(const fraction &A, const fraction &B) {
    int q = lcm(A.denominator, B.denominator);
    int p = A.numerator * (q / A.denominator) + B.numerator * (q / B.denominator);
    fraction ret = ret.fixshape(fraction(p, q));
    return ret;
}

fraction operator-(const fraction &A, const fraction &B) {
    int q = lcm(A.denominator, B.denominator);
    int p = A.numerator * (q / A.denominator) - B.numerator * (q / B.denominator);
    fraction ret = ret.fixshape(fraction(p, q));
    return ret;
}

fraction operator*(const fraction &A, const fraction &B) {
    int p = A.numerator * B.numerator;
    int q = A.denominator * B.denominator;
    int k = gcd(abs(p), abs(q));
    p /= k, q /= k;
    fraction ret = ret.fixshape(fraction(p, q));
    return ret;
}

fraction operator/(const fraction &A, const fraction &B) {
    fraction C = C.fixshape(fraction(B.denominator, B.numerator));
    fraction ret = ret.fixshape(A*C);
    return ret;
}

bool operator<(const fraction &A, const fraction &B) {
    fraction C = A, D = B;
    simplify(C, D);
    return C.numerator < D.numerator;
}

bool operator>(const fraction &A, const fraction &B) {
    fraction C = A, D = B;
    simplify(C, D);
    return C.numerator > D.numerator;
}
// fraction library end

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