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tphase algo done

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This commit is contained in:
Zastian Pretorius
2022-08-01 00:34:14 +01:00
parent bbdc97752e
commit 8847d71936
8 changed files with 290 additions and 19 deletions
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2
Program.cs
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@@ -7,6 +7,8 @@ class lpr381
//simplex.simplexAlgo();
twoPhaseSimplex twoPhaseSimplex = new twoPhaseSimplex();
twoPhaseSimplex.twoPhaseSimplexAlgo();
//chesssolver chesssolver = new chesssolver();
//chesssolver.chessAlgo();
}
}

8
chess.cs
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@@ -3,8 +3,7 @@ using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace Backtracking
{
class chesssolver
{
static int N;
@@ -51,9 +50,9 @@ namespace Backtracking
}
return false;
}
static void Main(string[] args)
public void chessAlgo()
{
Console.WriteLine("state size of chess table exp '4' if you wish to make blocks out do exp 4[1][2]");
Console.WriteLine("state size of chess table example: 4");
N = Convert.ToInt32(Console.ReadLine());
int[,] board = new int[N, N];
if (!theBoardSolver(board, 0))
@@ -64,4 +63,3 @@ namespace Backtracking
Console.ReadLine();
}
}
}

12
input.txt
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@@ -1,4 +1,8 @@
max +60 +30 +20
+8 +6 +1 <= 48
+4 +2 +1.5 >= 20
+2 +1.5 +0.5 = 8
max +1 +1
+8 +4 <= 160
+4 +4 <= 100
+1 +0 <= 17
+1 +0 >= 5
+0 +1 >= 2
+1 -1 >= 0
+1 -4 <= 0

2
obj/Debug/net6.0/lpr381.csproj.CoreCompileInputs.cache
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@@ -1 +1 @@
2378da97a7cf4743291d214cf9ba5b9a5bd52a98
42cc27e0497d325b5a06d599f420fe32fe1e67ba

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obj/Debug/net6.0/lpr381.dll
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obj/Debug/net6.0/lpr381.pdb
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obj/Debug/net6.0/ref/lpr381.dll
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285
twoPhaseSimplex.cs
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@@ -41,12 +41,42 @@ class twoPhaseSimplex
table = prepareTable(newTable, constraintsList);
// print table
printTable(table, varCount);
printTablePhaseOne(table, varCount);
flipZ(table);
printTablePhaseOne(table, varCount);
bool isOptimal = isOptimalPhaseOne(table);
while (!isOptimal)
{
int pivotCol = findPivotCol(table);
List<float> ratio = ratioTest(table, pivotCol);
int pivotRow = findPivotRow(ratio);
table = pivotTable(table, pivotRow, pivotCol);
printTablePhaseOne(table, varCount);
isOptimal = isOptimalPhaseOne(table);
}
table = dropCol(table, varCount);
isOptimal = isOptimalPhaseTwo(table);
printTablePhaseTwo(table, varCount);
while (!isOptimal)
{
int pivotCol = findPivotCol(table);
List<float> ratio = ratioTest(table, pivotCol);
int pivotRow = findPivotRow(ratio);
table = pivotTable(table, pivotRow, pivotCol);
printTablePhaseTwo(table, varCount);
isOptimal = isOptimalPhaseTwo(table);
}
}
void printTable(List<List<float>> table, int varCount)
void printTablePhaseOne(List<List<float>> table, int varCount)
{
int count = 1;
string[] headers = new string[table[0].Count];
for (int i = 0; i < table[0].Count; i++)
{
@@ -56,10 +86,48 @@ class twoPhaseSimplex
}
else if (i < table[0].Count - 1)
{
headers[i] = "e" + (i - varCount + 1);
headers[i+1] = "a" + (i - varCount + 1);
headers[i+2] = "s" + (i - varCount + 1);
headers[i] = "e" + (count);
headers[i+1] = "a" + (count);
headers[i+2] = "s" + (count);
i = i + 2;
count++;
}
else
{
headers[i] = "rhs";
}
}
var conTable = new ConsoleTable(headers);
foreach (List<float> row in table)
{
// convert row to object array
object[] rowArray = new object[row.Count];
for (int i = 0; i < row.Count; i++)
{
rowArray[i] = row[i];
}
conTable.AddRow(rowArray);
}
conTable.Write(Format.Alternative);
}
void printTablePhaseTwo(List<List<float>> table, int varCount)
{
int count = 1;
string[] headers = new string[table[0].Count];
for (int i = 0; i < table[0].Count; i++)
{
if (i < varCount)
{
headers[i] = "x" + (i + 1);
}
else if (i < table[0].Count - 1)
{
headers[i] = "e" + (count);
headers[i+1] = "s" + (count);
i = i + 1;
count++;
}
else
{
@@ -94,21 +162,32 @@ class twoPhaseSimplex
}
newTable.Add(newRow);
}
List<int> rowsWithW = new List<int>();
List<string> signs = new List<string>();
foreach (Constraints constraint in constraints)
{
signs.Add(constraint.sign);
}
// ammount of values in newTable startring from newTable[1])
int varCount = 0;
for (int i = 1; i < newTable.Count; i++)
{
varCount = varCount + newTable[i].Count;
}
for (int i = 0; i < signs.Count ; i++)
{
table[0].Add(0);
table[0].Add(0);
table[0].Add(0);
int temp = (newTable[i+1].Count-1) * signs.Count;
// add 3 0s to each row for every column in table
for (int j = 0; j < newTable[i+1].Count-1; j++)
for (int j = 0; j < signs.Count ; j++)
{
if (signs[i] == ">=")
{
// make s = 1
if (i == j)
{
table[i+1].Add(0);
@@ -124,11 +203,13 @@ class twoPhaseSimplex
}
else if (signs[i] == "<=")
{
//make e and a = 1
if (i == j)
{
table[i+1].Add(1);
table[i+1].Add(-1);
table[i+1].Add(1);
table[i+1].Add(0);
rowsWithW.Add(i+1);
}
else
{
@@ -139,11 +220,13 @@ class twoPhaseSimplex
}
else if (signs[i] == "=")
{
// make a = 1
if (i == j)
{
table[i+1].Add(0);
table[i+1].Add(1);
table[i+1].Add(0);
rowsWithW.Add(i+1);
}
else
{
@@ -155,14 +238,198 @@ class twoPhaseSimplex
}
}
table[0].Add(0);
// create list of floats called wRow size table[0].Count - 1
List<float> wRow = new List<float>();
for (int i = 0; i < table[0].Count; i++)
{
wRow.Add(0);
}
for (int i = 0; i < table[0].Count; i++)
{
// if i is in rowsWithW
if (rowsWithW.Contains(i))
{
for (int j = 0; j < wRow.Count; j++)
{
wRow[j] = wRow[j] + (-table[i][j]);
}
}
}
//add wRow to the start of table
table.Insert(1, wRow);
// remove intex newTable.Count-1 from table and place it in the back of table
for (int i = 1; i < table.Count; i++)
for (int i = 2; i < table.Count; i++)
{
table[i].RemoveAt(newTable.Count-1);
table[i].Add(newTable[i][newTable.Count-1]);
table[i].Add(newTable[i-1][newTable[i-1].Count-1]);
}
// remove the value of newTable.Count-1 from table[1] and place it in the back of table[1]
float lastValue = table[1][newTable.Count-1];
table[1].RemoveAt(newTable.Count-1);
table[1].Add(lastValue);
return table;
}
static List<List<float>> flipZ(List<List<float>> table)
{
for (int i = 0; i < table[0].Count; i++)
{
if (table[0][i] > 0)
{
table[0][i] = -table[0][i];
}
}
return table;
}
static int findPivotCol(List<List<float>> table)
{
float largest = 0;
int largestIndex = 0;
for (int i = 0; i < table[0].Count; i++)
{
if (table[0][i] < largest)
{
largest = table[0][i];
largestIndex = i;
}
}
return largestIndex;
}
static List<float> ratioTest(List<List<float>> table, int testCol)
{
List<float> ratios = new List<float>();
for (int i = 1; i < table.Count; i++)
{
if (table[i][testCol] != 0)
{
ratios.Add(table[i][table[i].Count - 1] / table[i][testCol]);
}
else
{
ratios.Add(float.MaxValue);
}
}
return ratios;
}
static int findPivotRow(List<float> ratios)
{
float smallest = float.MaxValue;
int smallestIndex = 0;
for (int i = 0; i < ratios.Count; i++)
{
if (ratios[i] < smallest && ratios[i] > 0.0)
{
smallest = ratios[i];
smallestIndex = i;
}
}
return smallestIndex;
}
static List<List<float>> pivotTable(List<List<float>> table, int pivotRow, int pivotCol)
{
//clone table in to newTable
List<List<float>> newTable = new List<List<float>>();
foreach (List<float> row in table)
{
List<float> newRow = new List<float>();
for (int i = 0; i < row.Count; i++)
{
newRow.Add(row[i]);
}
newTable.Add(newRow);
}
var pivotPoint = newTable[pivotRow + 1][pivotCol];
// divide pivot row by pivot point
for (int i = 0; i < newTable[pivotRow + 1].Count; i++)
{
newTable[pivotRow + 1][i] = newTable[pivotRow + 1][i] / pivotPoint;
}
// current possition-(pivot_row*new_table pivot_point)
for (int i = 0; i < newTable.Count; i++)
{
if (i != pivotRow + 1)
{
var currentPossition = newTable[i][pivotCol];
for (int j = 0; j < newTable[i].Count; j++)
{
newTable[i][j] = newTable[i][j] - (currentPossition * newTable[pivotRow + 1][j]);
}
}
}
return newTable;
}
//check if the table is optimal first phase
// table is optimal if all values in table[1] are positive
static bool isOptimalPhaseOne(List<List<float>> table)
{
int wIndex = 0;
for (int i = 0; i < table[1].Count; i++)
{
if (table[1][i] < 0)
{
wIndex = i;
}
}
if (wIndex == 0)
{
return true;
}
else
{
return false;
}
}
static bool isOptimalPhaseTwo(List<List<float>> table)
{
int wIndex = 0;
for (int i = 0; i < table[0].Count; i++)
{
if (table[0][i] < 0)
{
wIndex = i;
}
}
if (wIndex == 0)
{
return true;
}
else
{
return false;
}
}
//drop all a coloumn from the table and drop w row from the table
static List<List<float>> dropCol(List<List<float>> table, int varCount)
{
table.RemoveAt(1);
// for each row in table drop the varCount-1th element
for (int i = 0; i < table.Count; i++)
{
for (int j = varCount + 1; j < table[i].Count - 1; j+=3)
{
table[i].RemoveAt(j);
j = j - 1;
}
}
return table;
}
}