Created
March 31, 2013 20:49
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Fraction class, can turn any ordinary fraction into decimal
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public class Fraction | |
{ | |
private int[] _decimalDigits; | |
private int _cycleStart; | |
private static int GCD(int a, int b) | |
{ | |
if (a % b == 0) | |
{ | |
return b; | |
} | |
bool aIsEven = (a & 1) == 0; | |
bool bIsEven = (b & 1) == 0; | |
if (aIsEven && bIsEven) | |
{ | |
return 2 * GCD(a >> 1, b >> 1); | |
} else if (aIsEven) { | |
return GCD(a >> 1, b); | |
} else if (bIsEven) { | |
return GCD(a, b >> 1); | |
} else if (a > b) { | |
return GCD((a - b) >> 1, b); | |
} else { | |
return GCD((b - a) >> 1, a); | |
} | |
} | |
public int IntegerPart { get; private set; } | |
public int Numerator { get; private set; } | |
public int Denominator { get; private set; } | |
public int CycleLength | |
{ | |
get | |
{ | |
return _decimalDigits.Length - _cycleStart; | |
} | |
} | |
public Fraction(int numerator, int denominator) | |
{ | |
int gcd = GCD(denominator, numerator); | |
IntegerPart = numerator / denominator; | |
Numerator = (numerator - (denominator * IntegerPart)) / gcd; | |
Denominator = denominator / gcd; | |
ComputeDecimalForm(); | |
} | |
private void ComputeDecimalForm() | |
{ | |
HashSet<int> numerators = new HashSet<int>(); | |
List<int> decimalDigits = new List<int>(); | |
int numerator = Numerator; | |
int denominator = Denominator; | |
int countOfZeroes = 0; | |
while (numerator < denominator && numerator > 0) | |
{ | |
numerator *= 10; | |
countOfZeroes++; | |
} | |
while (numerator % denominator != 0) | |
{ | |
while (numerator < denominator) | |
{ | |
numerator *= 10; | |
} | |
if (!numerators.Add(numerator)) | |
{ | |
int cycleStart = 0; | |
foreach (var item in numerators) | |
{ | |
if (numerator == item) | |
{ | |
break; | |
} | |
cycleStart++; | |
} | |
_cycleStart = cycleStart + countOfZeroes; | |
_decimalDigits = new int[countOfZeroes + decimalDigits.Count]; | |
Array.Copy(decimalDigits.ToArray(), 0, _decimalDigits, countOfZeroes, decimalDigits.Count); | |
return; | |
} | |
decimalDigits.Add(numerator / denominator); | |
numerator = numerator % denominator; | |
} | |
decimalDigits.Add(numerator / denominator); | |
_decimalDigits = new int[countOfZeroes + decimalDigits.Count]; | |
Array.Copy(decimalDigits.ToArray(), 0, _decimalDigits, countOfZeroes, decimalDigits.Count); | |
_cycleStart = _decimalDigits.Length; | |
} | |
public override string ToString() | |
{ | |
var sb = new System.Text.StringBuilder(_decimalDigits.Length + 4); | |
sb.AppendFormat("{0}.", IntegerPart); | |
for (int i = 1; i < _cycleStart; i++) | |
{ | |
sb.Append(_decimalDigits[i]); | |
} | |
if (_cycleStart < _decimalDigits.Length) | |
{ | |
sb.Append("("); | |
for (int i = _cycleStart; i < _decimalDigits.Length; i++) | |
{ | |
sb.Append(_decimalDigits[i]); | |
} | |
sb.Append(")"); | |
} | |
return String.Format("{0}/{1} == {2}", Numerator + IntegerPart * Denominator, Denominator, sb); | |
} | |
} |
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