Arithmetic/Rational: Difference between revisions
New post without using external libraries, in addition to an existing post which uses the external library "Boost".
(New post without using external libraries, in addition to an existing post which uses the external library "Boost".) |
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return 0;
}</syntaxhighlight>
===Without external libraries===
=={{header|C++}}==
<syntaxhighlight lang="c++">
#include <cmath>
#include <cstdint>
#include <iostream>
#include <numeric>
#include <stdexcept>
class Rational {
public:
/// Constructors ///
Rational() : numer(0), denom(1) {}
Rational(const int64_t number) : numer(number), denom(1) {}
Rational(const int64_t& numerator, const int64_t& denominator) : numer(numerator), denom(denominator) {
if ( numer == 0 ) {
denom = 1;
} else if ( denom == 0 ) {
throw std::invalid_argument("Denominator cannot be zero: " + denom);
} else if ( denom < 0 ) {
numer = -numer;
denom = -denom;
}
int64_t divisor = std::gcd(numerator, denom);
numer = numer / divisor;
denom = denom / divisor;
}
Rational(const Rational& other) : numer(other.numer), denom(other.denom) {}
/// Operators ///
Rational& operator=(const Rational& other) {
if ( *this != other ) { numer = other.numer; denom = other.denom; }
return *this;
}
bool operator!=(const Rational& other) const { return ! ( *this == other ); }
bool operator==(const Rational& other) const {
if ( numer == other.numer && denom == other.denom ) { return true; }
return false;
}
Rational& operator+=(const Rational& other) {
*this = Rational(numer* other.denom + other.numer * denom, denom * other.denom);
return *this;
}
Rational operator+(const Rational& other) const { return Rational(*this) += other; }
Rational& operator-=(const Rational& other) {
Rational temp(other);
temp.numer = -temp.numer;
return *this += temp;
}
Rational operator-(const Rational& other) const { return Rational(*this) -= other; }
Rational& operator*=(const Rational& other) {
*this = Rational(numer * other.numer, denom * other.denom);
return *this;
}
Rational operator*(const Rational& other) const { return Rational(*this) *= other; };
Rational& operator/=(const Rational other) {
Rational temp(other.denom, other.numer);
*this *= temp;
return *this;
}
Rational operator/(const Rational& other) const { return Rational(*this) /= other; };
bool operator<(const Rational& other) const { return numer * other.denom < denom * other.numer; }
bool operator<=(const Rational& other) const { return ! ( other < *this ); }
bool operator>(const Rational& other) const { return other < *this; }
bool operator>=(const Rational& other) const { return ! ( *this < other ); }
Rational operator-() const { return Rational(-numer, denom); }
Rational& operator++() { numer += denom; return *this; }
Rational operator++(int) { Rational temp = *this; ++*this; return temp; }
Rational& operator--() { numer -= denom; return *this; }
Rational operator--(int) { Rational temp = *this; --*this; return temp; }
friend std::ostream& operator<<(std::ostream& outStream, const Rational& other) {
outStream << other.numer << "/" << other.denom;
return outStream;
}
/// Methods ///
Rational reciprocal() const { return Rational(denom, numer); }
Rational positive() const { return Rational(abs(numer), denom); }
int64_t to_integer() const { return numer / denom; }
double to_double() const { return (double) numer / denom; }
int64_t hash() const { return std::hash<int64_t>{}(numer) ^ std::hash<int64_t>{}(denom); }
private:
int64_t numer;
int64_t denom;
};
int main() {
std::cout << "Perfect numbers less than 2^19:" << std::endl;
const int32_t limit = 1 << 19;
for ( int32_t candidate = 2; candidate < limit; ++candidate ) {
Rational sum = Rational(1, candidate);
int32_t square_root = (int32_t) sqrt(candidate);
for ( int32_t factor = 2; factor <= square_root; ++factor ) {
if ( candidate % factor == 0 ) {
sum += Rational(1, factor);
sum += Rational(1, candidate / factor);
}
}
if ( sum == Rational(1) ) {
std::cout << candidate << std::endl;
}
}
}
</syntaxhighlight>
{{ out }}
<pre>
Perfect numbers less than 2^19:
6
28
496
8128
</pre>
=={{header|Clojure}}==
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