/// <summary>
/// Variant of 4th step of normalizing(should be used if constraint system has more than(>=) and equal(=) constraints,
/// except less than constraints, which were changed on previous step)
/// </summary>
/// <param name="problem">Initial problem</param>
/// <returns>Changed problem(new object)</returns>
public LppForSimplexMethod ChangeBothTypesOfConstraints(LppForSimplexMethod problem)
{
var problemCopy = new LppForSimplexMethod(problem);
//1.
var maxIndex = EqualConstraintWithBiggestFreeCoefficient(problemCopy);
//2.
for (var i = 0; i < problemCopy.ConstraintCount; i++)
{
var currConstraint = problemCopy.GetConstraint(i);
if (problemCopy.LessThanConstraintsIndexes.Contains(i) || currConstraint.Sign != ">=")
continue;
var constraintWithMaxCoef = problemCopy.GetConstraint(maxIndex);
while (currConstraint.RightSide >= constraintWithMaxCoef.RightSide)
currConstraint.Divide(2);
currConstraint.Multiply(-1);
problemCopy.AddAdditionalVariable(i);
currConstraint.Add(constraintWithMaxCoef);
}
//3.
for (var i = 0; i < problemCopy.ConstraintCount; i++)
if (problemCopy.GetBasisVariableLabel(i) == null)
problemCopy.AddArtificialVariable(i);
return problemCopy;
}
/// <summary>
/// Returns index of constraint with biggest free coefficient
/// </summary>
private int EqualConstraintWithBiggestFreeCoefficient(LppForSimplexMethod problem)
{
var maxIndex = -1;
for (var i = 0; i < problem.ConstraintCount; i++)
{
var currConstraint = problem.GetConstraint(i);
if (currConstraint.Sign != "=" || problem.LessThanConstraintsIndexes.Contains(i)) continue;
if (maxIndex == -1)
{
maxIndex = i;
continue;
}
if (currConstraint.RightSide > problem.GetConstraint(maxIndex).RightSide)
maxIndex = i;
}
return maxIndex;
}
/// <summary>
/// Returns true if constraint system contains constraints with such sign
/// </summary>
private bool ContainsSuchConstraints(LppForSimplexMethod problem, string sign)
{
for (var i = 0; i < problem.ConstraintCount; i++)
{
if (problem.LessThanConstraintsIndexes.Contains(i)) continue;
if (problem.GetConstraint(i).Sign == sign)
return true;
}
return false;
}
/// <summary>
/// Variant of 4th step of normalizing(should be used if constraint system has only more than constraints,
/// except less than constraints, which were changed on previous step)
/// </summary>
/// <param name="problem">Initial problem</param>
/// <returns>Changed problem(new object)</returns>
public LppForSimplexMethod ChangeMoreThanConstraints(LppForSimplexMethod problem)
{
var problemCopy = new LppForSimplexMethod(problem);
//1.
for (var i = 0; i < problemCopy.ConstraintCount; i++)
if (!problemCopy.LessThanConstraintsIndexes.Contains(i))
problemCopy.AddAdditionalVariable(i);
//2.
var maxIndex = EqualConstraintWithBiggestFreeCoefficient(problemCopy);
//3.
for (var i = 0; i < problemCopy.ConstraintCount; i++)
{
if (problemCopy.LessThanConstraintsIndexes.Contains(i) || i == maxIndex) continue;
var first = problemCopy.GetConstraint(maxIndex);
var second = problemCopy.GetConstraint(i);
second.Multiply(-1);
second.Add(first);
}
//4.
if (problemCopy.GetBasisVariableLabel(maxIndex) == null)
problemCopy.AddArtificialVariable(maxIndex);
return problemCopy;
}
/// <summary>
/// 3rd step of normalizing
/// </summary>
/// <param name="problem">Initial problem</param>
/// <returns>Changed problem(new object)</returns>
public LppForSimplexMethod ChangeLessThanConstraints(LppForSimplexMethod problem)
{
var problemCopy = new LppForSimplexMethod(problem);
for (var i = 0; i < problemCopy.ConstraintCount; i++)
if (problemCopy.GetConstraint(i).Sign == "<=")
{
problemCopy.AddAdditionalVariable(i);
problemCopy.LessThanConstraintsIndexes.Add(i);
}
return problemCopy;
}
/// <summary>
/// Variant of 4th step of normalizing(should be used if constraint system has only equal constraints,
/// except less than constraints, which were changed on previous step)
/// </summary>
/// <param name="problem">Initial problem</param>
/// <returns>Changed problem(new object)</returns>
public LppForSimplexMethod ChangeEqualConstraints(LppForSimplexMethod problem)
{
var problemCopy = new LppForSimplexMethod(problem);
for (var i = 0; i < problemCopy.ConstraintCount; i++)
if (problemCopy.GetConstraint(i).Sign == "=" && problemCopy.GetBasisVariableLabel(i) == null)
problemCopy.AddArtificialVariable(i);
return problemCopy;
}
private void SetCoeffientsMatrix(LppForSimplexMethod problem)
{
_rows = new Dictionary<int, Fraction[]>();
_freeCoefficients = new Dictionary<int, Fraction>();
for (var rowIndex = 0; rowIndex < problem.ConstraintCount; rowIndex++)
{
var limitation = problem.GetConstraint(rowIndex);
var row = CreateRow(_allVariables.Count);
foreach (var var in limitation.LeftSide)
{
var cellIndex = IndexOf(var.Label);
row[cellIndex] = new Fraction(var.Coefficient);
}
_rows.Add(rowIndex, row);
_freeCoefficients.Add(rowIndex, limitation.RightSide);
}
}
