/// <summary>
/// Разность
/// </summary>
public SimpleFractions Difference(SimpleFractions A, SimpleFractions B)
{
if (A.Numerator == 0)
{
return(Multiplication(Norm(B), new SimpleFractions(-1, 1)));
}
else if (B.Numerator == 0)
{
return(Norm(A));
}
SimpleFractions otv = new SimpleFractions();
SimpleFractions a = Norm(A), b = Norm(B);
if (a.Denominator == b.Denominator)
{
otv.Denominator = a.Denominator;
otv.Numerator = a.Numerator - b.Numerator;
}
else
{
int nok = NOK(Convert.ToInt32(a.Denominator), Convert.ToInt32(b.Denominator));
otv.Denominator = nok;
otv.Numerator = a.Numerator * (nok / a.Denominator) - b.Numerator * (nok / b.Denominator);
}
return(Norm(otv));
}
/// <summary>
/// Cокращение дроби
/// </summary>
public SimpleFractions Reduction(SimpleFractions simpleFractions)
{
SimpleFractions a = simpleFractions;
if ((simpleFractions.Denominator < 0 && simpleFractions.Numerator >= 0) || (simpleFractions.Numerator < 0 && simpleFractions.Denominator < 0))
{
simpleFractions.Numerator *= -1;
simpleFractions.Denominator *= -1;
}
var nod = NOD(new List <int> {
a.Numerator, a.Denominator
});
if (nod != 1)
{
a.Denominator /= nod;
a.Numerator /= nod;
}
//if (nod != 0)
//{
// a.Denominator /= nod;
// a.Numerator /= nod;
// nod = NOD(a.Numerator, a.Denominator);
//}
return(a);
}
/// <summary>
/// Вывод ответа
/// </summary>
private List <SimpleFractions> PrintAnswer(List <List <SimpleFractions> > table, List <int> basis, List <SimpleFractions> F)
{
List <SimpleFractions> answer = new List <SimpleFractions>();
string str = "";
for (int j = 1; j < table[0].Count; j++)
{
str += "x" + j + " = ";
var id = basis.FindIndex(a => a == j - 1);
if (id >= 0)
{
str += table[id][0].toString() + "\n";
answer.Add(table[id][0]);
}
else
{
str += "0\n";
answer.Add(new SimpleFractions(0, 1));
}
}
SimpleFractions fAnswer = new SimpleFractions(0, 1);
for (int i = 0; i < answer.Count; i++)
{
fAnswer = sFM.Sum(fAnswer, sFM.Multiplication(answer[i], F[i]));
}
fAnswer = sFM.Sum(fAnswer, F[F.Count - 1]);
answer.Add(fAnswer);
str += "Z = " + fAnswer.toString();
if (Notify != null)
{
Notify(str);
}
return(answer);
}
/// <summary>
/// Приведение дроби к нормальному виду (сокращение)
/// </summary>
public SimpleFractions Norm(SimpleFractions simpleFractions)
{
SimpleFractions fractions = simpleFractions;
if (fractions.Numerator == 0)
{
fractions.Denominator = 1; return(fractions);
}
fractions = Reduction(fractions);
if (NOD(new List <int> {
fractions.Numerator, fractions.Denominator
}) != 0)
{
int nod = NOD(new List <int> {
fractions.Numerator, fractions.Denominator
});
fractions.Numerator /= nod;
fractions.Denominator /= nod;
}
if (fractions.Denominator < 0)
{
fractions.Numerator *= -1;
fractions.Denominator *= -1;
}
return(fractions);
}
/// <summary>
/// Деление
/// </summary>
public SimpleFractions Division(SimpleFractions a, SimpleFractions b)
{
SimpleFractions otv = new SimpleFractions();
otv.Denominator = a.Denominator * b.Numerator;
otv.Numerator = a.Numerator * b.Denominator;
return(Norm(otv));
}
/// <summary>
/// Произведение
/// </summary>
public SimpleFractions Multiplication(SimpleFractions a, SimpleFractions b)
{
SimpleFractions otv = new SimpleFractions();
otv.Denominator = a.Denominator * b.Denominator;
otv.Numerator = a.Numerator * b.Numerator;
return(otv);
}
/// <summary>
/// Если a < b, то true, иначе false
/// </summary>
public bool Comparisons(SimpleFractions a, SimpleFractions b)
{
var c = Difference(b, a);
if ((c.Numerator > 0 && c.Denominator > 0) || (c.Denominator < 0 && c.Numerator < 0))
{
return(true);
}
return(false);
}
/// <summary>
/// Модуль
/// </summary>
public SimpleFractions Mod(SimpleFractions fractions)
{
SimpleFractions f = new SimpleFractions();
if (fractions.Numerator < 0)
{
f.Numerator = fractions.Numerator * -1;
}
if (fractions.Denominator < 0)
{
f.Denominator = fractions.Denominator * -1;
}
return(f);
}
/// <summary>
/// Максимальный элемент (первый попавшийся)
/// </summary>
public SimpleFractions Max(SimpleFractions a, SimpleFractions b)
{
SimpleFractions a1 = Norm(a);
SimpleFractions b1 = Norm(b);
if (Difference(a1, b1).Numerator < 0)
{
return(b1);
}
else
{
return(a1);
}
}
/// <summary>
/// Модуль
/// </summary>
public SimpleFractions Abs(SimpleFractions fractions)
{
SimpleFractions simpleFractions = Norm(fractions);
if (simpleFractions.Denominator < 0)
{
simpleFractions.Denominator *= -1;
}
if (simpleFractions.Numerator < 0)
{
simpleFractions.Numerator *= -1;
}
return(simpleFractions);
}
public MatrixFractions(int[,] matrInt)
{
N = matrInt.GetLength(0);
M = matrInt.GetLength(1);
Matrix = new SimpleFractions[N, M];
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M; j++)
{
Matrix[i, j] = new SimpleFractions();
Matrix[i, j].Numerator = matrInt[i, j];
Matrix[i, j].Denominator = 1;
}
}
}
private bool ObmenStrok(MatrixFractions matrix, int a, int b)
{
if (a >= matrix.N || b >= matrix.N)
{
return(false);
}
SimpleFractions tmp = new SimpleFractions();
for (int i = 0; i < matrix.M; i++)
{
tmp = matrix.Matrix[a, i];
matrix.Matrix[a, i] = matrix.Matrix[b, i];
matrix.Matrix[b, i] = tmp;
}
return(true);
}
/// <summary>
/// Сумма
/// </summary>
public SimpleFractions Sum(SimpleFractions a, SimpleFractions b)
{
SimpleFractions otv = new SimpleFractions();
if (a.Denominator == b.Denominator)
{
otv.Denominator = a.Denominator;
otv.Numerator = a.Numerator + b.Numerator;
}
else
{
int nok = NOK(Convert.ToInt32(a.Denominator), Convert.ToInt32(b.Denominator));
otv.Denominator = nok;
otv.Numerator = a.Numerator * (nok / a.Denominator) + b.Numerator * (nok / b.Denominator);
}
return(Norm(otv));
}
/// <summary>
/// Сложение строк. True - удачно, False - невозможно
/// </summary>
/// <param name="num1">Строка, к которой прибалять и в которую записывается ответ</param>
/// <returns></returns>
public bool LineDifference(MatrixFractions matrix, int num1, int num2, SimpleFractions koeff)
{
MatrixFractions matrixFractions = matrix;
if (num1 > matrixFractions.N || num2 > matrixFractions.N || num1 < 0 || num2 < 0)
{
return(false);
}
SimpleFractionsMeneger sFM = new SimpleFractionsMeneger();
for (int j = 0; j < matrixFractions.M; j++)
{
matrixFractions.Matrix[num1, j] = sFM.Sum(matrixFractions.Matrix[num1, j],
sFM.Multiplication(koeff, matrixFractions.Matrix[num2, j]));
}
matrix = matrixFractions;
return(true);
}
public bool RectangleMetod(MatrixFractions matrix)
{
List <int> banIndexStrList = new List <int>();
if (matrix.M < matrix.N)
{
if (Notify != null)
{
Notify($"Строк больше столбцов! Невозможно решить! (Код 1.0)\n");
}
return(false);
}
for (int nowStr = 0, nowCol = 0; nowStr < matrix.N || nowCol < matrix.N; nowStr++, nowCol++)
{
if (_mFM.Norm(matrix))
{
if (Notify != null)
{
Notify("Сокращение:\n" + matrix.toString() + "\n");
}
}
//блок проверки
var check = CheckExceptions(matrix);
if (check == null)
{
if (Notify != null)
{
Notify($"Ошибка! \n");
}
return(false);
}
if (check.SingleOrDefault() == -1)
{
if (Notify != null)
{
Notify($"Противоречие! \n");
}
return(false);
}
if (check.Count > 0)
{
foreach (var ch in check)
{
banIndexStrList.Add(ch);
}
}
if (Notify != null)
{
Notify($"Пока что все идет по плану... наверное! \n");
}
//проверка банлиста
int strNullCount = CheckBanlist(check, nowStr, matrix.N);
if (strNullCount > 0)
{
nowStr += strNullCount - 1;
if (nowStr >= matrix.N)
{
if (Notify != null)
{
Notify("Зануленная строка!\n" + matrix.toString() + "\n");
}
}
}
if (nowStr >= matrix.N)
{
return(true);
}
//проверка на 0-вой элемент
if (matrix.Matrix[nowStr, nowCol].Numerator == 0)
{
int Str = nowStr;
Str++;
if (Str >= matrix.N)
{
if (Notify != null)
{
Notify($"Ведущий элемент 0, а строки закончились. Упс... \n");
}
return(true);
}
while (matrix.Matrix[Str, nowCol].Numerator == 0)
{
Str++;
if (Str >= matrix.N)
{
if (Notify != null)
{
Notify($"Ведущий элемент 0, а строки закончились. Упс... \n");
}
return(true);
}
}
ObmenStrok(matrix, Str, nowStr);
if (Notify != null)
{
Notify($"Обмен: ({nowStr} и {Str})\n"); Notify(matrix.toString() + "\n");
}
}
//приводим к 1
if (matrix.Matrix[nowStr, nowCol].Numerator != matrix.Matrix[nowStr, nowCol].Denominator)
{
SimpleFractions kof = matrix.Matrix[nowStr, nowCol];
for (int j1 = 0; j1 < matrix.M; j1++)
{
matrix.Matrix[nowStr, j1] = _sFM.Division(matrix.Matrix[nowStr, j1], kof);
}
if (Notify != null)
{
Notify($"Приведение: ({nowStr + 1}) : {kof.toString()} \n"); Notify(matrix.toString() + "\n");
}
}
//прямоугольники
for (int j1 = nowStr + 1; j1 < matrix.M; j1++)
{
for (int i1 = 0; i1 < matrix.N; i1++)
{
if (i1 != nowCol)
{
matrix.Matrix[i1, j1] =
_sFM.Difference(matrix.Matrix[i1, j1],
_sFM.Multiplication(matrix.Matrix[nowStr, j1], matrix.Matrix[i1, nowCol]));
}
}
}
for (int i = 0; i < matrix.N; i++)
{
if (i != nowStr)
{
matrix.Matrix[i, nowCol].Denominator = 1;
matrix.Matrix[i, nowCol].Numerator = 0;
}
}
if (Notify != null)
{
Notify("После прямоугольников: \n" + matrix.toString() + "\n");
}
}
return(true);
}
