private static FractionedNumber[,] VogelFirstPart(FractionedNumber[,] costs, FractionedNumber[] demand, FractionedNumber[] supply)
{
verifyVogel(demand, supply, costs);
Functions.result += "Matriz de custos de entrada:\n";
Functions.result += printMatrix(costs);
Functions.result += "Supply de entrada:\n";
for(int i = 0;i < supply.Length;i++) {
Functions.result += supply[i] + (i+1<supply.Length?", ":"");
}
Functions.result += "\nDemand de entrada:\n";
for(int i = 0;i < demand.Length;i++) {
Functions.result += demand[i] + (i + 1 < demand.Length ? ", " : "");
}
Functions.result += "\n----------------------------\n";
FractionedNumber[] demandRemaining = new FractionedNumber[demand.Length];
FractionedNumber[] supplyRemaining = new FractionedNumber[supply.Length];
FractionedNumber[,] result = new FractionedNumber[costs.GetLength(0), costs.GetLength(1)];
List<VogelPos> taxaDegeneracao = new List<VogelPos>();
Array.Copy(demand, demandRemaining, demand.Length);
Array.Copy(supply, supplyRemaining, supply.Length);
List<VogelPos> temp = new List<VogelPos>();
for (int l = 0; l < costs.GetLength(0); l++) {
temp.Clear();
for (int c = 0; c < costs.GetLength(1); c++) {
temp.Add(new VogelPos(l,c, costs[l, c],true));
}
var n = temp.OrderBy(x => x.number);
if(costs[n.ElementAt(0).x, n.ElementAt(0).y] < costs[n.ElementAt(1).x, n.ElementAt(1).y]) {
taxaDegeneracao.Add(new VogelPos(n.ElementAt(0).x, n.ElementAt(0).y, n.ElementAt(1).number - n.ElementAt(0).number,true));
} else {
taxaDegeneracao.Add(new VogelPos(n.ElementAt(1).x, n.ElementAt(1).y, n.ElementAt(0).number - n.ElementAt(1).number,true));
}
}
for(int c = 0;c < costs.GetLength(1);c++) {
temp.Clear();
for(int l = 0;l < costs.GetLength(0);l++) {
temp.Add(new VogelPos(l, c, costs[l, c],false));
}
temp = temp.OrderBy(x => x.number).ToList();
if(costs[temp.ElementAt(0).x, temp.ElementAt(0).y] < costs[temp.ElementAt(1).x, temp.ElementAt(1).y]) {
taxaDegeneracao.Add(new VogelPos(temp.ElementAt(0).x, temp.ElementAt(0).y, temp.ElementAt(1).number - temp.ElementAt(0).number,false));
} else {
taxaDegeneracao.Add(new VogelPos(temp.ElementAt(1).x, temp.ElementAt(1).y, temp.ElementAt(0).number - temp.ElementAt(1).number,false));
}
}
Functions.result += "Taxa de degeneração: \n";
for(int i = 0;i < taxaDegeneracao.Count;i++) {
Functions.result += taxaDegeneracao[i].number + " @ " + (taxaDegeneracao[i].x + 1) + "," + (taxaDegeneracao[i].y + 1) + (taxaDegeneracao[i].line?" linha ":" coluna ") + "\n";
}
Functions.result += "---------- \n";
taxaDegeneracao = taxaDegeneracao.OrderBy(x => 0-x.number).ThenBy(x=>costs[x.x,x.y]).ToList();
Functions.result += "Taxa de degeneração ordenada: \n";
for(int i = 0;i < taxaDegeneracao.Count;i++) {
Functions.result += taxaDegeneracao[i].number + " @ " + (taxaDegeneracao[i].x + 1) + "," + (taxaDegeneracao[i].y + 1) + (taxaDegeneracao[i].line ? " linha " : " coluna ") + "\n";
}
Functions.result += "---------- \n";
//Respeita a ordem da taxa de degeneracao
for(int i = 0;i < taxaDegeneracao.Count;i++) {
int l = taxaDegeneracao[i].x;
int c = taxaDegeneracao[i].y;
FractionedNumber min = long.MaxValue;
FractionedNumber minSupplyDemand;
if(taxaDegeneracao[i].line) {
for(int j = 0;j < costs.GetLength(1);j++) {
if(costs[l, j] < min) {
if(supply[l] > 0 && demand[j] > 0) {
min = costs[l, j];
c = j;
}
}
}
} else {
for(int j = 0;j < costs.GetLength(0);j++) {
if(costs[j, c] < min) {
if(supply[j] > 0 && demand[c] > 0) {
min = costs[j, c];
l = j;
}
}
}
}
if(supply[l] == 0 || demand[c] == 0)
continue;
minSupplyDemand = FractionedNumber.Min(supply[l], demand[c]);
supply.SetValue(supply.ElementAt(l) - minSupplyDemand, l);
demand.SetValue(demand.ElementAt(c) - minSupplyDemand, c);
result[l, c] = minSupplyDemand;
}
temp.Clear();
for(int l = 0;l < costs.GetLength(0);l++) {
for(int c = 0;c < costs.GetLength(1);c++) {
temp.Add(new VogelPos(l, c, costs[l, c],false));
}
}
temp = temp.OrderBy(x => x.number).ToList();
for(int i = 0;i < temp.Count;i++) {
if(supply[temp[i].x] > 0) {
if(demand[temp[i].y] > 0){
FractionedNumber min = FractionedNumber.Min(supply[temp[i].x], demand[temp[i].y]);
result[temp[i].x, temp[i].y] = min;
supply[temp[i].x] -= min;
demand[temp[i].y] -= min;
}
}
}
Functions.result += "Matriz antes de fazer a segunda parte:\n";
Functions.result += printMatrix(result);
Functions.result += "-------------------------------\n";
return result;
}
private static FractionedNumber[,] VogelSecondPart(FractionedNumber[,] costs, FractionedNumber[] demand, FractionedNumber[] supply, FractionedNumber[,] matrix)
{
VogelPos min;
int count = 1;
do {
min = new VogelPos(-1, -1, long.MaxValue, false);
FractionedNumber[,] res = new FractionedNumber[matrix.GetLength(0), matrix.GetLength(1)];
bool[,] usedMatrix = GetMatrixInsideVogel(matrix);
bool[,] usedMatrix2 = new bool[usedMatrix.GetLength(0), usedMatrix.GetLength(1)];
System.Array.Copy(usedMatrix, usedMatrix2, usedMatrix.Length);
FractionedNumber[,] tempMatrix = new FractionedNumber[matrix.GetLength(0), matrix.GetLength(1)];
Functions.result += "=============================\n";
Functions.result += "Iteração "+count+"\n";
Functions.result += "=============================\n";
FractionedNumber[] lines = new FractionedNumber[matrix.GetLength(0)];
FractionedNumber[] colums = new FractionedNumber[matrix.GetLength(1)];
goLine(-1, -1, 0, tempMatrix, costs, usedMatrix2, lines, colums);
bool erroL = false;
bool erroC = false;
for(int i = 0;i < lines.Length;i++) {
if(lines[i] == null)
erroL = true;
}
for(int i = 0;i < colums.Length;i++) {
if(colums[i] == null)
erroC = true;
}
if(erroL || erroC) {
min.number = -1;
Functions.result += "=============================\n";
Functions.result += "Não foi possível colocar valores em todas as linhas e colunas.\n";
Functions.result += "Deve-se criar uma variável artificial.\n";
int posX = -1;
int posY = -1;
if(erroL){
for(int i = 0;i < lines.Length;i++) {
if(lines[i] == null) {
for(int j = 0;j < matrix.GetLength(1);j++) {
if(matrix[i, j] == null) {
posX = i;
posY = j;
break;
}
}
break;
}
}
} else {
for(int i = 0;i < colums.Length;i++) {
if(colums[i] == null) {
for(int j = 0;j < matrix.GetLength(0);j++) {
if(matrix[j, i] == null) {
posX = i;
posY = j;
break;
}
}
break;
}
}
}
matrix[posX, posY] = 0;
Functions.result += "Ela foi colocada em: L"+(posX+1)+", C"+(posY+1)+"\n";
Functions.result += "=============================\n";
continue;
}
for(int i = 0;i < lines.Length;i++) {
Functions.result += "L" + (i + 1) + ":" + lines[i] + ", \t";
}
Functions.result += "\n";
for(int i = 0;i < colums.Length;i++) {
Functions.result += "C" + (i + 1) + ":" + colums[i] + ", \t"; ;
}
Functions.result += "\n\n";
Functions.result += "Matriz dentro:\n";
Functions.result += printMatrix(tempMatrix);
Functions.result += "-------------------------\n";
sumOut(lines, colums, usedMatrix, costs, tempMatrix);
Functions.result += "Matriz fora:\n";
Functions.result += printMatrix(tempMatrix);
Functions.result += "-------------------------\n";
for(int l = 0;l < tempMatrix.GetLength(0);l++) {
for(int c = 0;c < tempMatrix.GetLength(1);c++) {
if(tempMatrix[l, c] != null) {
if(tempMatrix[l, c] < min.number) {
min.y = c;
min.x = l;
min.number = tempMatrix[l, c];
}
}
}
}
Functions.result += "Valor mínimo: "+min.number+" na linha "+(min.x+1)+" e coluna "+(min.y+1)+"\n";
if(min.number < 0) {
List<VogelPos> list = VogelFindWay(min, usedMatrix, matrix);
if(list == null)
break;
FractionedNumber min2 = FractionedNumber.Min(list[0].number, list[list.Count - 1].number);
Functions.result += "Minimo: " + min2 + "\n";
bool soma = false;
for(int i = 0;i < list.Count;i++) {
if(matrix[list[i].x, list[i].y] == null)
matrix[list[i].x, list[i].y] = 0;
if(soma) {
matrix[list[i].x, list[i].y] += min2;
} else {
matrix[list[i].x, list[i].y] -= min2;
}
if(matrix[list[i].x, list[i].y] == 0)
matrix[list[i].x, list[i].y] = null;
soma = !soma;
}
matrix[min.x, min.y] += min2;
Functions.result += "Fez a troca\n";
}
Functions.result += "-------------------------\n";
Functions.result += "Matriz: \n";
Functions.result += "-------------------------\n";
Functions.result += printMatrix(matrix);
Functions.result += "-------------------------\n";
count++;
} while(min.number<0 && count <= 25);
if(count > 20) {
Functions.result += "***********************\n";
Functions.result += "Houve muitas iterações, algo está errado!\n";
Functions.result += "***********************\n";
}
bool tirouArt = false;
for(int l = 0;l < matrix.GetLength(0);l++) {
for(int c = 0;c < matrix.GetLength(1);c++) {
if(matrix[l, c] == 0) {
matrix[l, c] = null;
tirouArt = true;
}
}
}
if(tirouArt) {
Functions.result += "Foram tiradas as variáveis artificiais, ficando assim:\n";
Functions.result += printMatrix(matrix);
Functions.result += "-------------------------\n";
}
return matrix;
}
private static void verifyVogel(FractionedNumber[] demand, FractionedNumber[] supply, FractionedNumber[,] matrix)
{
if(matrix.GetLength(1) != demand.Length || matrix.GetLength(0) != supply.Length) {
string msg = "The demand and supply array doesn't have the same size of the matix\n";
msg += "demand["+demand.Length+"], supply["+supply.Length+"], costs["+matrix.GetLength(0)+","+matrix.GetLength(1)+"]";
throw new Exception(msg);
}
FractionedNumber sumSupply = SumNumbers(supply);
FractionedNumber sumDemand = SumNumbers(demand);
if(sumSupply != sumDemand) {
string msg = "The sums of the supply and demand are differents!\n";
msg += "Supply sum: " + sumSupply + ", Demand sum: " + sumDemand+"\n";
msg += "You need to insert a new ";
if(sumSupply > sumDemand)
msg += "demand (row bellow)";
else
msg += "supply (colum on right)";
msg += " with the value " + (FractionedNumber.Max(sumDemand, sumSupply) - FractionedNumber.Min(sumDemand, sumSupply));
throw new Exception(msg);
}
}
private static FractionedNumber VogelCalculateTotalCost(FractionedNumber[,] matrix, FractionedNumber[,] costs)
{
result += "Total cost: ";
FractionedNumber sum = 0;
for(int l = 0;l < matrix.GetLength(0);l++) {
for(int c = 0;c < matrix.GetLength(1);c++) {
sum += matrix[l, c] * costs[l, c];
}
}
result += sum;
result += "\n";
return sum;
}
private static string printMatrix(FractionedNumber[,] m)
{
string s = "";
for(int l = 0;l < m.GetLength(0);l++) {
for(int c = 0;c < m.GetLength(1);c++) {
s += (m[l, c] + "\t|");
}
s += "\n";
}
return s;
}
private static void sumOut(FractionedNumber[] lines, FractionedNumber[] colums, bool[,] usedMatrix, FractionedNumber[,] costs, FractionedNumber[,] tempMatrix)
{
for(int l = 0;l < tempMatrix.GetLength(0);l++) {
for(int c = 0;c < tempMatrix.GetLength(1);c++) {
if(!usedMatrix[l, c]) {
tempMatrix[l, c] = costs[l, c] - lines[l] - colums[c];
} else {
tempMatrix[l, c] = null;
}
}
}
}
private static FractionedNumber[,] NorthWestFirstPart(FractionedNumber[,] costs, FractionedNumber[] demand, FractionedNumber[] supply)
{
verifyVogel(demand, supply, costs);
Functions.result += "Matriz de custos de entrada:\n";
Functions.result += printMatrix(costs);
Functions.result += "Supply de entrada:\n";
for(int i = 0;i < supply.Length;i++) {
Functions.result += supply[i] + (i + 1 < supply.Length ? ", " : "");
}
Functions.result += "\nDemand de entrada:\n";
for(int i = 0;i < demand.Length;i++) {
Functions.result += demand[i] + (i + 1 < demand.Length ? ", " : "");
}
Functions.result += "\n----------------------------\n";
FractionedNumber[] demandRemaining = new FractionedNumber[demand.Length];
FractionedNumber[] supplyRemaining = new FractionedNumber[supply.Length];
FractionedNumber[,] result = new FractionedNumber[costs.GetLength(0), costs.GetLength(1)];
Array.Copy(demand, demandRemaining, demand.Length);
Array.Copy(supply, supplyRemaining, supply.Length);
int posL = 0;
int posC = 0;
while(demandRemaining[posC]!=0 && supplyRemaining[posL]!=0) {
FractionedNumber min = FractionedNumber.Min(demandRemaining[posC], supplyRemaining[posL]);
result[posL, posC] = min;
demandRemaining[posC] -= min;
supplyRemaining[posL] -= min;
if(supplyRemaining[posL] == 0) {
if(supplyRemaining.Length!=posL+1)
posL++;
}
if(demandRemaining[posC] == 0) {
if(demandRemaining.Length != posC + 1)
posC++;
}
}
Functions.result += "Matriz antes de fazer a segunda parte:\n";
Functions.result += printMatrix(result);
Functions.result += "-------------------------------\n";
return result;
}
private static void goLine(int x, int y, FractionedNumber v, FractionedNumber[,] m, FractionedNumber[,] costs, bool[,] usedMatrix, FractionedNumber[] lines, FractionedNumber[] colums)
{
if(x == -1 && y == -1) {
lines[0] = 0;
}
for(int i = 0;i < m.GetLength(1);i++) {
if(i == y)
continue;
if((x == -1 && y == -1) || usedMatrix[x,i]) {
if(x == -1 && y == -1) {
if(usedMatrix[0, i]) {
m[0, i] = 0 - v + costs[0, i];
if(colums[i] == null)
colums[i] = m[0, i];
usedMatrix[0, i] = false;
goColum(0, i, m[0, i], m, costs, usedMatrix, lines, colums);
}
} else {
m[x, i] = 0 - v + costs[x, i];
if(colums[i] == null)
colums[i] = m[x, i];
usedMatrix[x, i] = false;
goColum(x, i, m[x, i], m, costs, usedMatrix, lines, colums);
}
}
}
}
private static void goColum(int x, int y, FractionedNumber v, FractionedNumber[,] m, FractionedNumber[,] costs, bool[,] usedMatrix, FractionedNumber[] lines, FractionedNumber[] colums)
{
for(int i = 0;i < m.GetLength(0);i++) {
if(i == x)
continue;
if(usedMatrix[i,y]) {
m[i,y] = 0 - v + costs[i,y];
if(lines[i] == null)
lines[i] = m[i, y];
usedMatrix[i,y] = false;
goLine(i,y, m[i,y], m, costs, usedMatrix, lines, colums);
}
}
}
private static bool[,] GetMatrixInsideVogel(FractionedNumber[,] matrix)
{
bool[,] res = new bool[matrix.GetLength(0), matrix.GetLength(1)];
for (int l = 0; l < matrix.GetLength(0); l++) {
for (int c = 0; c < matrix.GetLength(1); c++) {
if (matrix[l, c] != null)
res[l, c] = true;
else
res[l, c] = false;
}
}
return res;
}
public static FractionedNumber[,] VogelInverseMatrix(FractionedNumber[,] matrix)
{
FractionedNumber max = long.MinValue;
FractionedNumber[,] newMatrix = new FractionedNumber[matrix.GetLength(0), matrix.GetLength(1)];
for(int l = 0;l < matrix.GetLength(0);l++) {
for(int c = 0;c < matrix.GetLength(1);c++) {
max = FractionedNumber.Max(max, matrix[l, c]);
}
}
for(int l = 0;l < matrix.GetLength(0);l++) {
for(int c = 0;c < matrix.GetLength(1);c++) {
newMatrix[l, c] = max - matrix[l, c];
}
}
return newMatrix;
}