| 1 | """The fraction class. It converts ints and strings to fractions.""" |
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| 2 | |
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| 3 | # helper functions |
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| 4 | def gcd(a, b): |
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| 5 | if b == 0: |
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| 6 | return a |
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| 7 | |
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| 8 | return gcd(b, a % b) |
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| 9 | |
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| 10 | def lcm(a, b): |
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| 11 | return a * b / gcd(a, b) |
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| 12 | |
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| 13 | class Fraction: |
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| 14 | def __init__(self, val,denominator=None): |
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| 15 | import types |
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| 16 | |
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| 17 | if isinstance(val, self.__class__): |
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| 18 | self.num = val.num |
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| 19 | self.den = val.den |
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| 20 | |
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| 21 | #self.reduce() |
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| 22 | |
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| 23 | |
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| 24 | elif denominator: |
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| 25 | self.num = int(val) |
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| 26 | self.den = int(denominator) |
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| 27 | |
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| 28 | elif isinstance(val, types.StringType): |
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| 29 | if val.count('/') == 1: |
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| 30 | num, den = val.split('/') |
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| 31 | self.num, self.den = int(num), int(den) |
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| 32 | |
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| 33 | if self.den == 0: |
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| 34 | raise ZeroDenominatorError() |
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| 35 | |
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| 36 | if self.den < 0: # Move negative denominator to the numerator |
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| 37 | self.num, self.den = -self.num, -self.den |
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| 38 | |
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| 39 | else: |
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| 40 | self.num = int(val) |
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| 41 | self.den = 1 |
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| 42 | |
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| 43 | elif isinstance(val, types.IntType) or isinstance(val, types.LongType): |
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| 44 | self.num = val |
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| 45 | self.den = 1 |
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| 46 | |
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| 47 | elif isinstance(val, types.TupleType): |
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| 48 | self.num, self.den = val |
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| 49 | |
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| 50 | if not isinstance(self.num, types.IntType) or isinstance(self.num, types.LongType): |
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| 51 | raise Exception() |
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| 52 | |
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| 53 | if not isinstance(self.den, types.IntType) or isinstance(self.den, types.LongType): |
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| 54 | raise Exception() |
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| 55 | |
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| 56 | if self.den < 0: # Move negative denominator to the numberator |
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| 57 | self.num, self.den = -self.num, -self.den |
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| 58 | |
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| 59 | # TODO: optionally, float conversion? |
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| 60 | |
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| 61 | else: |
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| 62 | raise Exception('%s' % val) |
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| 63 | raise NotImplementedError() |
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| 64 | |
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| 65 | #self.reduce() |
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| 66 | |
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| 67 | def __add__(self, other): |
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| 68 | if not isinstance(other, Fraction): |
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| 69 | other = Fraction(other) |
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| 70 | |
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| 71 | new = Fraction((((self.num * other.den) + (other.num * self.den)), (self.den * other.den))) |
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| 72 | |
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| 73 | return new.reduce() |
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| 74 | |
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| 75 | |
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| 76 | def __sub__(self, other): |
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| 77 | copy = Fraction(other) |
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| 78 | copy.num = -copy.num |
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| 79 | |
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| 80 | return self + copy |
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| 81 | |
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| 82 | def __mul__(self, other): |
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| 83 | if not isinstance(other, Fraction): |
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| 84 | other = Fraction(other) |
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| 85 | |
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| 86 | new = Fraction(( (self.num * other.num), (self.den * other.den) )) |
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| 87 | |
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| 88 | return new.reduce() |
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| 89 | |
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| 90 | |
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| 91 | def __div__(self, other): |
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| 92 | if not isinstance(other, Fraction): |
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| 93 | other = Fraction(other) |
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| 94 | |
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| 95 | new = Fraction(( other.den, other.num )) # Inverse of other |
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| 96 | |
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| 97 | return self * new |
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| 98 | |
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| 99 | def reduce(self): |
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| 100 | """Reduce reduces a fraction to it's smallest numerator and denominator.""" |
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| 101 | |
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| 102 | if self.den == 0: |
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| 103 | raise ZeroDenominatorError() |
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| 104 | |
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| 105 | divisor = gcd(self.num, self.den) |
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| 106 | |
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| 107 | num = self.num / divisor |
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| 108 | den = self.den / divisor |
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| 109 | |
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| 110 | return Fraction(num,den) |
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| 111 | |
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| 112 | def __str__(self): |
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| 113 | if self.den != 1: |
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| 114 | return "%s/%s" % (self.num, self.den) |
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| 115 | else: |
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| 116 | return "%s" % (self.num) |
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| 117 | |
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| 118 | def __repr__(self): |
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| 119 | return "<Fraction: %s>" % str(self) |
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| 120 | |
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| 121 | def __eq__(self, other): |
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| 122 | if not isinstance(other, Fraction): |
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| 123 | other = Fraction(other) |
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| 124 | |
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| 125 | return self.num == other.num and self.den == other.den |
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| 126 | |
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| 127 | def __cmp__(self, other): |
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| 128 | import types |
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| 129 | if type(other) == types.FloatType: |
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| 130 | return cmp(self.float(),other) |
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| 131 | |
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| 132 | elif not isinstance(other, Fraction): |
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| 133 | other = Fraction(other) |
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| 134 | |
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| 135 | common = lcm(self.den, other.den) |
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| 136 | |
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| 137 | self_num = self.num * common / self.den |
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| 138 | other_num = other.num * common / other.den |
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| 139 | |
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| 140 | return self_num.__cmp__(other_num) |
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| 141 | |
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| 142 | def __gt__(self, other): |
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| 143 | return self.__cmp__(other) == 1 |
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| 144 | |
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| 145 | def __lt__(self, other): |
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| 146 | return self.__cmp__(other) == -1 |
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| 147 | |
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| 148 | def __ne__(self, other): |
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| 149 | return not self == other |
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| 150 | |
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| 151 | def __hash__(self): |
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| 152 | return str(self).__hash__() |
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| 153 | |
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| 154 | def float(self): |
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| 155 | return float(self.num)/float(self.den) |
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| 156 | |
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| 157 | class ZeroDenominatorError(Exception): |
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| 158 | """A fraction with a zero denominator cannot be computed.""" |
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