public void DoesNotSolveUnsolvableSystem()
{
var coefficients = new List <long[]>
{
new[] { true, false, false }.ToLongs()
};
var solution = GaussianEliminationHelpers.Solve(coefficients, 3).ToList();
if (solution.Count > 0)
{
Assert.True(solution[solution.Count].Operation != Operation.Complete);
}
}
public void DoesNotSolveUnsolvableSystem()
{
var coefficients = new List <Packed>
{
Packed.Create(new[] { true, false, false })
};
var solution = GaussianEliminationHelpers.Solve(coefficients, 3).ToList();
if (solution.Count > 0)
{
Assert.IsTrue(solution[solution.Count].Operation != Operation.Complete);
}
}
public void SolvesAlreadySolvedSystem()
{
var coefficients = new List <long[]>
{
new[] { true, false, false }.ToLongs(),
new[] { false, true, false }.ToLongs(),
new[] { false, false, true }.ToLongs()
};
var steps = GaussianEliminationHelpers.Solve(coefficients, 3).ToList();
Assert.True(steps.Count > 0);
Assert.Equal(Operation.Complete, steps[steps.Count - 1].Operation);
AssertIsSolved(coefficients, 3);
}
public void SolvesComplicatedSystem()
{
var coefficients = new List <Packed>
{
Packed.Create(new[] { true, false, true }),
Packed.Create(new[] { true, true, true }),
Packed.Create(new[] { false, false, true })
};
var steps = GaussianEliminationHelpers.Solve(coefficients, 3).ToList();
Assert.IsTrue(steps.Count > 0);
Assert.AreEqual(Operation.Complete, steps[steps.Count - 1].Operation);
AssertIsSolved(coefficients, 3);
}
public void ProducesStepsWhichResultInIdenticalChangesAndASolution()
{
var coefficients = new List <long[]>
{
new [] { true, true, true }.ToLongs(),
new [] { false, true, true }.ToLongs(),
new [] { false, true, false }.ToLongs()
};
var copy = coefficients.Select(x => x.Clone() as long[]).ToList();
var steps = GaussianEliminationHelpers.Solve(coefficients, 3).ToList();
// Assert that it has been solved
Assert.True(steps.Count > 0);
Assert.Equal(Operation.Complete, steps[steps.Count - 1].Operation);
AssertIsSolved(coefficients, 3);
// Perform the steps on the copy
var mappedOperations = new Dictionary <Operation, Action <int, int, IList <long[]> > >
{
{
Operation.Swap,
(from, to, list) =>
{
var temp = list[to];
list[to] = list[from];
list[from] = temp;
}
},
{
Operation.Xor,
(from, to, list) => list[to].Xor(list[from])
}
};
foreach (var step in steps)
{
if (!mappedOperations.TryGetValue(step.Operation, out var operation))
{
continue;
}
operation.Invoke(step.From, step.To, copy);
}
// Assert that the copy has been solved
AssertIsSolved(copy, 3);
}
/// <summary>
/// Tries to decode the original data from all <see cref="Slice"/>s previously given to
/// <see cref="Remember"/>.
/// </summary>
/// <remarks>
/// Decoding the original data is akin to solving a set of linear equations. Each <see cref="Slice"/>
/// represents one more equation. So enough <see cref="Slice"/>s have to be given to <see cref="Remember"/>
/// in order to be able to solve them.
/// </remarks>
public bool TrySolve(out byte[] solution)
{
var solved = false;
foreach (var step in GaussianEliminationHelpers.Solve(
_coefficientsList,
_numCoefficients))
{
switch (step.Operation)
{
case Operation.Complete:
solved = true;
break;
case Operation.Swap:
Swap(
step.From,
step.To,
_solutionsList);
break;
case Operation.Xor:
Xor(
step.From,
step.To,
_solutionsList);
break;
default:
throw new NotImplementedException();
}
}
solution =
solved
? _solutionsList
.SelectMany(x => x.GetBytes(_sliceSize))
.Take(_totalLength)
.ToArray()
: null;
return(solved);
}
/// <summary>
/// Tries to decode the original data from all <see cref="Slice"/>s previously given to
/// <see cref="RememberAsync"/>.
/// </summary>
/// <remarks>
/// Decoding the original data is akin to solving a set of linear equations. Each <see cref="Slice"/>
/// represents one more equation. So enough <see cref="Slice"/>s have to be given to <see cref="RememberAsync"/>
/// in order to be able to solve them.
/// </remarks>
public async Task <byte[]> TrySolveAsync()
{
using (await _guard.LockAsync())
{
var solved = false;
foreach (var step in GaussianEliminationHelpers.Solve(_coefficientsList))
{
switch (step.Operation)
{
case Operation.Complete:
solved = true;
break;
case Operation.Swap:
Swap(step.From, step.To, _solutionsList);
break;
case Operation.Xor:
Xor(step.From, step.To, _solutionsList);
break;
default:
throw new NotImplementedException();
}
}
if (!solved)
{
return(null);
}
return
(_solutionsList
.SelectMany(x => x.GetBytes().Take(_sliceSize))
.Take(_totalLength)
.ToArray());
}
}
public void CanBeCalledWithoutEquations()
{
// ReSharper disable once ReturnValueOfPureMethodIsNotUsed
GaussianEliminationHelpers.Solve(new List <long[]>(), 1).ToList();
}
