Because we can't know that 10 / 3 will eventually result in a precise integer answer until after the * 6 we have to defer it until then with a promise:
public sealed class Precise
{
private interface IOperation
{
int Calculate(int value);
IOperation Combine(IOperation next);
}
private sealed class NoOp : IOperation
{
public static NoOp Instance = new NoOp();
public int Calculate(int value)
{
return value;
}
public IOperation Combine(IOperation next)
{
return next;
}
}
private sealed class Combo : IOperation
{
private readonly IOperation _first;
private readonly IOperation _second;
public Combo(IOperation first, IOperation second)
{
_first = first;
_second = second;
}
public int Calculate(int value)
{
return _second.Calculate(_first.Calculate(value));
}
public IOperation Combine(IOperation next)
{
return new Combo(_first, _second.Combine(next));
}
}
private sealed class Mult : IOperation
{
private readonly int _multiplicand;
public Mult(int multiplicand)
{
_multiplicand = multiplicand;
}
public int Calculate(int value)
{
return value * _multiplicand;
}
public int Multiplicand
{
get { return _multiplicand; }
}
public IOperation Combine(IOperation next)
{
var nextMult = next as Mult;
if(nextMult != null)
return new Mult(_multiplicand * nextMult._multiplicand);
var nextDiv = next as Div;
if(nextDiv != null)
{
int divisor = nextDiv.Divisor;
if(divisor == _multiplicand)
return NoOp.Instance;//multiplcation by 1
if(divisor > _multiplicand)
{
if(divisor % _multiplicand == 0)
return new Div(divisor / _multiplicand);
}
if(_multiplicand % divisor == 0)
return new Mult(_multiplicand / divisor);
}
return new Combo(this, next);
}
}
private sealed class Div : IOperation
{
private readonly int _divisor;
public Div(int divisor)
{
_divisor = divisor;
}
public int Divisor
{
get { return _divisor; }
}
public int Calculate(int value)
{
int ret = value / _divisor;
if(value != ret * _divisor)
throw new InvalidOperationException("Imprecise division");
return ret;
}
public IOperation Combine(IOperation next)
{
var nextDiv = next as Div;
if(nextDiv != null)
return new Div(_divisor * nextDiv._divisor);
var nextMult = next as Mult;
if(nextMult != null)
{
var multiplicand = nextMult.Multiplicand;
if(multiplicand == _divisor)
return NoOp.Instance;
if(multiplicand > _divisor)
{
if(multiplicand % _divisor == 0)
return new Mult(multiplicand / _divisor);
}
else if(_divisor % multiplicand == 0)
return new Div(multiplicand / _divisor);
}
return new Combo(this, next);
}
}
private sealed class Plus : IOperation
{
private readonly int _addend;
public Plus(int addend)
{
_addend = addend;
}
public int Calculate(int value)
{
return value + _addend;
}
public IOperation Combine(IOperation next)
{
var nextPlus = next as Plus;
if(nextPlus != null)
{
int newAdd = _addend + nextPlus._addend;
return newAdd == 0 ? (IOperation)NoOp.Instance : new Plus(newAdd);
}
return new Combo(this, next);
}
}
private readonly int _value;
private readonly IOperation _operation;
public static readonly Precise Zero = new Precise(0);
private Precise(int value, IOperation operation)
{
_value = value;
_operation = operation;
}
public Precise(int value)
: this(value, NoOp.Instance)
{
}
public int GetNumber()
{
return _operation.Calculate(_value);
}
public static explicit operator int(Precise value)
{
return value.GetNumber();
}
public static implicit operator Precise(int value)
{
return new Precise(value);
}
public override string ToString()
{
return GetNumber().ToString();
}
public Precise Multiply(int multiplicand)
{
if(multiplicand == 0)
return Zero;
return new Precise(_value, _operation.Combine(new Mult(multiplicand)));
}
public static Precise operator * (Precise precise, int value)
{
return precise.Multiply(value);
}
public Precise Divide(int divisor)
{
return new Precise(_value, _operation.Combine(new Div(divisor)));
}
public static Precise operator / (Precise precise, int value)
{
return precise.Divide(value);
}
public Precise Add(int addend)
{
return new Precise(_value, _operation.Combine(new Plus(addend)));
}
public Precise Subtract(int minuend)
{
return Add(-minuend);
}
public static Precise operator + (Precise precise, int value)
{
return precise.Add(value);
}
public static Precise operator - (Precise precise, int value)
{
return precise.Subtract(value);
}
}
Here each Precise has both an integer value and an operation that will be performed on it. Further operations produce a new Precise (doing this sort of thing as a mutable is crazy) with a new operation but when possible those operations are combined into a single simpler operation. Hence "divide by three then multiply by six" becomes "multiply by two".
We can test this thus:
public static void Main(string[] args)
{
Precise A = 10;
A /= 3;
try
{
var test = (int)A;
}
catch(InvalidOperationException)
{
Console.Error.WriteLine("Invalid operation attempted");
}
A *= 6;
int result = (int)A;
Console.WriteLine(result);
// Let's do 10 / 5 * 2 = 4 because it works but can't be pre-combined:
Console.WriteLine(new Precise(10) / 5 * 2);
// Let's do 10 / 5 * 2 - 6 + 4 == 2 to mix in addition and subtraction:
Console.WriteLine(new Precise(10) / 5 * 2 - 6 + 4);
Console.Read();
}
A good solution would also deal well with operations done where the LHS was an integer and the RHS a Precise and where both where a Precise; left as an exercise for the reader ;)
Sadly we have to get much more complicated to handle (10 / 3 + 1) * 3, with the improvement having to be made in the Combine implementations.
Edit: Musing a bit further on the issues of doing the above well enough to catch at least most of the edge cases, I think it should start with only dealing with operations between two Precise objects, because going int -> Precise is trivial and can easily be put on top, but going Precise -> int requires a call to the calculation, perhaps too early. I'd also make the operations the key thing acted upon (have the operation store one or two objects which in turn contain an operation or a value). Then if you started with a representation of the sum (10 / 3) + 5 and multiplied it by 6 it's easier to turn that into (10 * (6 / 3)) + (5 * 6) which upon final calculation can give the precise result 50 rather than fail because it hits the imprecise 10 / 3.
