remove unnecessary comments

Fix Makefile and add optional rebuild shorcut function.
Fix outputs in simplex.cpp

.gitignore

@@ -1,3 +1,4 @@
+*.vscode
 # Prerequisites
 *.d
 CMakeLists.txt

Makefile

@@ -0,0 +1,67 @@
+GXX := g++ -std=c++20
+flags := -Wall -fsanitize=address
+TOOLS := tools
+BUILD := build
+
+build:
+	mkdir -p $(BUILD)
+	$(GXX) -c $(flags) $(TOOLS)/elimination.cpp -o $(BUILD)/elimination.obj
+	$(GXX) -c $(flags) $(TOOLS)/math.cpp -o $(BUILD)/math.obj
+	$(GXX) -c $(flags) $(TOOLS)/matrix.cpp -o $(BUILD)/matrix.obj
+	$(GXX) -c $(flags) simplex.cpp -o $(BUILD)/simplex.obj
+	$(GXX) -c $(flags) main.cpp -o $(BUILD)/main.obj
+
+	$(GXX) $(BUILD)/*.obj $(flags) -o simplex.out
+
+$(BUILD)/elimination.obj: $(TOOLS)/elimination.cpp
+	$(GXX) -c $(flags) $(TOOLS)/elimination.cpp -o $(BUILD)/elimination.obj
+
+$(BUILD)/math.obj: $(TOOLS)/math.cpp
+	$(GXX) -c $(flags) $(TOOLS)/math.cpp -o $(BUILD)/math.obj
+
+$(BUILD)/matrix.obj: $(TOOLS)/matrix.cpp
+	$(GXX) -c $(flags) $(TOOLS)/matrix.cpp -o $(BUILD)/matrix.obj
+
+$(BUILD)/simplex.obj: simplex.cpp
+	$(GXX) -c $(flags) simplex.cpp -o $(BUILD)/simplex.obj
+
+$(BUILD)/main.obj: main.cpp
+	$(GXX) -c $(flags) main.cpp -o $(BUILD)/main.obj
+
+simplex.out: $(BUILD)/elimination.obj $(BUILD)/math.obj $(BUILD)/matrix.obj $(BUILD)/simplex.obj $(BUILD)/main.obj
+	$(GXX) $(BUILD)/*.obj $(flags) -o simplex.out
+
+test: simplex.out
+	./simplex.out
+
+clean:
+	rm -rf $(BUILD)
+	rm -rf simplex.out
+
+rebuild:
+	rm -rf $(BUILD)
+	rm -rf simplex.out
+
+	mkdir -p $(BUILD)
+	$(GXX) -c $(flags) $(TOOLS)/elimination.cpp -o $(BUILD)/elimination.obj
+	$(GXX) -c $(flags) $(TOOLS)/math.cpp -o $(BUILD)/math.obj
+	$(GXX) -c $(flags) $(TOOLS)/matrix.cpp -o $(BUILD)/matrix.obj
+	$(GXX) -c $(flags) simplex.cpp -o $(BUILD)/simplex.obj
+	$(GXX) -c $(flags) main.cpp -o $(BUILD)/main.obj
+
+	$(GXX) $(BUILD)/*.obj $(flags) -o simplex.out
+
+	$(BUILD)/elimination.obj: $(TOOLS)/elimination.cpp
+	$(GXX) -c $(flags) $(TOOLS)/elimination.cpp -o $(BUILD)/elimination.obj
+
+	$(BUILD)/math.obj: $(TOOLS)/math.cpp
+	$(GXX) -c $(flags) $(TOOLS)/math.cpp -o $(BUILD)/math.obj
+
+	$(BUILD)/matrix.obj: $(TOOLS)/matrix.cpp
+	$(GXX) -c $(flags) $(TOOLS)/matrix.cpp -o $(BUILD)/matrix.obj
+
+	$(BUILD)/simplex.obj: simplex.cpp
+	$(GXX) -c $(flags) simplex.cpp -o $(BUILD)/simplex.obj
+
+	$(BUILD)/main.obj: main.cpp
+	$(GXX) -c $(flags) main.cpp -o $(BUILD)/main.obj

README.md

@@ -0,0 +1,7 @@
+<h1> Instructions for installing </h1>
+<h2>1. Clone the repository.</h2>
+  <code>git clone https://github.com/emil28092005/SimplexTASK/</code>
+<h2>2. Build the project (install Make if not present on your system): </h2>
+  <code>make build</code>
+<h2>3. Run tests via the following command: </h2>
+  <code>make test</code>

main.cpp

@@ -1,18 +1,410 @@
 #include <iostream>
+#include <functional>
 #include "tools/matrix.h"
+#include "tools/math.h"
+#include "simplex.h"
 
+void _printInitialInputs(Vector &C, Matrix &A, Vector &b, double eps, bool maximize)
+{
+    std::cout << "Running for the following inputs:" << std::endl
+              << std::endl;
+    std::cout << "epsilon: " << eps << std::endl;
+    if (maximize)
+    {
+        std::cout << "Maximize" << std::endl;
+    }
+    else
+    {
+        std::cout << "Minimize" << std::endl;
+    }
+    std::cout << "z = ";
+    bool previousIsZero = true;
+    bool lastNonZero = false;
+    for (int i = 0; i < C.size(); i++)
+    {
+        bool isNegative = false;
         
-int main() {
-    int n, m;
-    ColumnVector C(n);
-    Matrix A(n, m);
-    ColumnVector b(n);
-    double eps;
-    double eps_default;
+        for (int k = i; k < C.size(); k++)
+        {
+            if (C[k] == 0)
+            {
+                lastNonZero = true;
+            } else{
+                lastNonZero = false;
+                break;
+            }
+                
+        }
+
+        if (!previousIsZero && !lastNonZero){
+            std::cout << " + ";
+        }
+
+        if (C[i] != 0){
+            if (C[i] != 1) {
+                if (C[i] < 0){
+                    isNegative = true;
+                    std::cout << "(";
+                }
+                std::cout << C[i] << " * ";
+            }
+            std::cout << "x" << i + 1;
+            if (isNegative){
+                std::cout << ")";
+            }
+            previousIsZero = false;
+        }else {
+            previousIsZero = true;
+        }
+
+    }
+    std::cout << std::endl
+              << "subject to the constrains:" << std::endl;
+    std::cout << std::endl;
+    for (int i = 0; i < b.size(); i++)
+    {
+        bool previousIsZero = true;
+        bool lastNonZero = false;
+
+        for (int j = 0; j < A.getColumns(); j++)
+        {
+            bool isNegative = false;
+
+            for (int k = j; k < A[i].size(); k++)
+            {
+                if (A[i][k] == 0)
+                {
+                    lastNonZero = true;
+                } else{
+                    lastNonZero = false;
+                    break;
+                }
+                
+            }
+
+            if (!previousIsZero && !lastNonZero){
+                std::cout << " + ";
+            }
+
+            if (A[i][j] != 0) { 
+                if (A[i][j] != 1) {
+                    if (A[i][j] < 0) {
+                        isNegative = true;
+                        std::cout << "(";
+                    }
+                    std::cout << A[i][j] << " * ";
+                }
+                std::cout << "x" << j + 1;
+                if (isNegative) {
+                    std::cout << ")";
+                }
+                previousIsZero = false;
+                
+            }else {
+                previousIsZero = true;
+            }
+        }
+        std::cout << " <= " << b[i] << std::endl;
+    }
+}
+
+int printResult(Result result)
+{
+    if (result.state == unsolvable)
+    {
+        std::cout << "The method is not applicable!" << std::endl;
+    }else if (result.state == unbounded ) {
+        std::cout << "Unbounded problem!" << std::endl;
+    }
+    else
+    {
+        std::cout << "SOLVED!" << std::endl;
+        std::cout << "Decision variables: [";
+
+        for (int i = 0; i < result.solution.size(); i++)
+        {
+            std::cout << result.solution[i];
+            if (i != result.solution.size() - 1)
+            {
+                std::cout << ", ";
+            }
+        }
+        std::cout << "]";
+        std::cout << std::endl;
+        if (result.maximize)
+        {
+            std::cout << "Maximum ";
+        }
+        else
+        {
+            std::cout << "Minimum ";
+        }
+        std::cout << "objective function value: " << result.objective_function_value << std::endl;
+    }
+    return 0;
+}
+
+bool check_eq(double a, double b, double relativeEpsilon = 0.0001)
+{
+    double diff = std::abs(a - b);
+    a = std::abs(a);
+    b = std::abs(b);
+    double largest = (b > a) ? b : a;
+    
+    return diff <= largest * relativeEpsilon;
+}
+
+int TEST_GENERAL_CASE()
+{
+    std::cout << "----------------------------RUNNING_TEST_GENERAL_CASE----------------------------" << std::endl;
+    Vector C = {5, 4};
+    Matrix A = {
+        {6, 4},
+        {1, 2},
+        {-1, 1},
+        {0, 1}};
+    Vector b = {24, 6, 1, 2};
+    _printInitialInputs(C, A, b, 0.01, true);
+    auto result = simplex(C, A, b);
+
+    if (!(result.state == bounded))
+    {
+        std::string state_name;
+        switch (result.state)
+        {
+        case unsolvable:
+            state_name = "unsolvable";
+            break;
+        case unbounded:
+            state_name = "unbounded";
+            break;
+        default:
+            state_name = "bounded";
+            break;
+        }
+        std::cout << "Incorrect state type. Expected bounded. Got " << state_name << std::endl;
+        return 0;
+    }
+
+    if (!check_eq(result.objective_function_value, 21))
+    {
+        std::cout << "Incorrect objective function value. Expected 21. Got "
+                  << result.objective_function_value << std::endl;
+        return 0;
+    }
+
+    if (!(check_eq(result.solution[0], 3) && check_eq(result.solution[1], 1.5)))
+    {
+        std::cout << "Incorrect desire variables. Expected 3 and 1.5. Got "
+                  << result.solution;
+        return 0;
+    }
+
+    printResult(result);
+    return 1;
+}
+
+int TEST_MINIMIZE_CASE()
+{
+    std::cout << "----------------------------RUNNING_TEST_MINIMIZE_CASE----------------------------" << std::endl;
+    Vector C = {-2, 2, -6};
+    Matrix A = {
+        {2, 1, -2},
+        {1, 2, 4},
+        {1, -1, 2}};
+    Vector b = {24, 23, 10};
+    _printInitialInputs(C, A, b, 0.01, false);
+    auto result = simplex(C, A, b, 0.01, false);
+
+    if (!(result.state == bounded))
+    {
+        std::string state_name;
+        switch (result.state)
+        {
+        case unsolvable:
+            state_name = "unsolvable";
+            break;
+        case unbounded:
+            state_name = "unbounded";
+            break;
+        default:
+            state_name = "bounded";
+            break;
+        }
+        std::cout << "Incorrect state type. Expected bounded. Got " << state_name << std::endl;
+        return 0;
+    }
+
+    if (!check_eq(result.objective_function_value, -30.75))
+    {
+        std::cout << "Incorrect objective function value. Expected -30.75. Got "
+                  << result.objective_function_value << std::endl;
+        return 0;
+    }
+
+    if (!(check_eq(result.solution[0], 0) && check_eq(result.solution[1], 0.75) && check_eq(result.solution[2], 5.375)))
+    {
+        std::cout << "Incorrect desire variables. Expected 3 and 1.5. Got "
+                  << result.solution;
+        return 0;
+    }
+
+    printResult(result);
+
+    return 1;
+}
+
+int TEST_WITH_SLACK_CASE()
+{
+    std::cout << "----------------------------RUNNING_TEST_WITH_SLACK_CASE----------------------------" << std::endl;
+
+    Vector C = {2, -1, 0, -1};
+    Matrix A = {
+        {1, -2, 1, 0},
+        {-2, -1, 0, -2},
+        {3, 2, 0, 1}};
+    Vector b = {10, 18, 36};
+
+    _printInitialInputs(C, A, b, 0.01, true);
+
+    auto result = simplex(C, A, b);
+
+    if (!(result.state == bounded))
+    {
+        std::string state_name;
+        switch (result.state)
+        {
+        case unsolvable:
+            state_name = "unsolvable";
+            break;
+        case unbounded:
+            state_name = "unbounded";
+            break;
+        default:
+            state_name = "bounded";
+            break;
+        }
+        std::cout << "Incorrect state type. Expected bounded. Got " << state_name << std::endl;
+        return 0;
+    }
+
+    if (result.objective_function_value != 22.25)
+    {
+        std::cout << "Incorrect objective function value. Expected 22.25. Got "
+                  << result.objective_function_value << std::endl;
+        return 0;
+    }
+
+    if (!((result.solution[0] == 11.5) || (result.solution[1] == 0.75) ||
+          (result.solution[2] == 0) || (result.solution[3] == 0)))
+    {
+        std::cout << "Incorrect desire variables. Expected 11.5, 0.75, 0, and 0. Got "
+                  << result.solution;
+        return 0;
+    }
+
+    printResult(result);
+
+    return 1;
+}
+
+int TEST_UNBOUNDED_CASE()
+{
+    std::cout << "----------------------------RUNNING_TEST_UNBOUNDED_CASE----------------------------" << std::endl;
+
+    Vector C = {2, 1};
+    Matrix A = {
+        {1, -1},
+        {2, 0}};
+    Vector b = {10, 40};
+
+    _printInitialInputs(C, A, b, 0.01, true);
+
+    auto result = simplex(C, A, b);
+
+    if (!(result.state == unbounded))
+    {
+        std::string state_name;
+        switch (result.state)
+        {
+        case unsolvable:
+            state_name = "unsolvable";
+            break;
+        case unbounded:
+            state_name = "unbounded";
+            break;
+        default:
+            state_name = "bounded";
+            break;
+        }
+        std::cout << "Incorrect state type. Expected unbounded. Got " << state_name << std::endl;
+        return 0;
+    }
+
+    printResult(result);
+
+    return 1;
+}
+
+int TEST_UNSOLVABLE_CASE()
+{
+    std::cout << "----------------------------RUNNING_TEST_UNSOLVABLE_CASE----------------------------" << std::endl;
+
+    Vector C = {5, 4, 0, -5, 13};
+    Matrix A = {
+        {6, 4, 1, 3, 4},
+        {1, 2, 0, 0, 2},
+        {-1, 0, 0, 10, 0},
+        {0, 1, 1, -5, 1}};
+    Vector b = {-24, 6, 1, 2};
+
+    _printInitialInputs(C, A, b, 0.01, true);
+
+    auto result = simplex(C, A, b);
+
+    if (!(result.state == unsolvable))
+    {
+        std::string state_name;
+        switch (result.state)
+        {
+        case unsolvable:
+            state_name = "unsolvable";
+            break;
+        case unbounded:
+            state_name = "unbounded";
+            break;
+        default:
+            state_name = "bounded";
+            break;
+        }
+        std::cout << "Incorrect state type. Expected unsolvable. Got " << state_name << std::endl;
+        return 0;
+    }
+
+    printResult(result);
+
+    return 1;
+}
+
+int main()
+{
+    std::vector<std::function<int(void)>> tests = {
+        TEST_GENERAL_CASE,
+        TEST_MINIMIZE_CASE,
+        TEST_WITH_SLACK_CASE,
+        TEST_UNBOUNDED_CASE,
+        TEST_UNSOLVABLE_CASE};
+
+    int counter = 0;
+
+    for (auto &test : tests)
+    {
+        counter += test();
+    }
+
+    std::cout << "----------------------------RESULTS----------------------------" << std::endl;
+    std::cout << "Total number of tests: " << tests.size() << std::endl;
+    std::cout << "Total number of passed tests: " << counter << std::endl;
 
-    std::cin >> C;
-    std::cin >> A;
-    std::cin >> b;
-    std::cin >> eps;
     return 0;
 }

simplex.cpp

@@ -1,85 +1,144 @@
 #include <algorithm>
 #include <iostream>
 #include "tools/matrix.h"
+#include "tools/math.h"
+#include "tools/elimination.h"
 
-enum solver_state {
+enum solver_state
+{
 	unbounded,
-	bounded
+	bounded,
+	unsolvable
 };
 
-struct Result {
+struct Result
+{
 	solver_state state;
-	ColumnVector *solution;
-	double objective_fucntion_value;
+	Vector solution;
+	double objective_function_value;
+	bool maximize;
 };
 
-Result Simplex(ColumnVector C, Matrix A, ColumnVector b, double eps = 0.01, bool maximize) {
-	Result result;
-	std::vector<int> basicVars(A.getColumns() - A.getRows());
-	basicVars[0] = -1;
+void _stopIterating(Matrix &generalMatrix, Vector &C, std::vector<int> &basicVars, solver_state state, Result &result)
+{
+	DestroyMatrix destroyedGeneralMatrix = disassembleGeneralMatrix(generalMatrix);
+	Matrix _A = destroyedGeneralMatrix.A;
+	Vector _C = destroyedGeneralMatrix.C;
+	Vector _b = destroyedGeneralMatrix.b;
 
-	for (int i = 1; i < basicVars.size(); i++) {
-		basicVars[i] = static_cast<int>(basicVars.size()) + i;
+	result.state = state;
+	if (state == bounded)
+	{
+		result.solution = Vector(C.size());
+		for (int i = 0; i < C.size(); i++)
+		{
+			result.solution[i] = 0;
 		}
-
-	int kc = 0;
-	double temp = A[0][0];
-	for (int j = 0; j< A.getColumns(); j++) {
-		if (A[0][j] < temp) {
-			temp = A[0][j];
-			kc = j;
+		for (size_t i = 1; i < basicVars.size(); i++)
+		{
+			if (basicVars[i] < C.size())
+			{
+				result.solution[basicVars[i]] = _b[i];
 			}
 		}
 
-	if (A[0][kc] >= 0) {
-		result.state = unbounded;
-		result.solution = new ColumnVector(C.getRows());
-		for (int i = 0; i < C.getRows(); i++) {
-			result.solution->operator[](i) = 0;
+		result.objective_function_value = _b[0];
 	}
-		for (int i = 1; i < basicVars.size(); i++) {
-			if (basicVars[i] <= C.getRows()) {
-				(*result.solution)[basicVars[i]] = b.getRows() - 1;
-			}
-		}
-		result.objective_fucntion_value = b[0];
+	else
+	{
+		result.solution = Vector({0});
+		result.objective_function_value = 0;
 	}
 }
 
 /*
-Function_name(C, A, b, eps = eps_default)
-
-Input:
-- C: A vector of coefficients of the objective function
-- A: A matrix of coefficients of the constraint functions
-- b: A vector of right-hand side values
-- eps: Approximation accuracy (optional, default = eps_default)
-
-Steps:
-1. Print the optimization problem:
-   - max (or min) z = C[0] * x1 + C[1] * x2 + ... + C[n] * xn
-   - subject to the constraints:
-     - A[0] * x <= b[0]
-     - A[1] * x <= b[1]
-     - ...
-     - A[m] * x <= b[m]
-
-2. Initialize:
-   - Form the initial tableau by introducing slack variables to convert inequalities into equalities.
-
-3. Iteratively apply the Simplex method:
-   - Step 1: Identify the entering variable (most negative coefficient in the objective row).
-   - Step 2: Identify the leaving variable (smallest positive ratio of RHS to pivot column).
-   - Step 3: Perform pivot operations to update the tableau.
-
-4. Check for optimality or unboundedness:
-   - If all coefficients in the objective function row are non-negative, the solution is optimal.
-   - If no leaving variable exists, the problem is unbounded.
-
-5. Return:
-   - solver_state: {solved, unbounded}
-   - x*: Optimal vector of decision variables (if solved)
-   - z: Maximum (or minimum) value of the objective function (if solved)
-
-End Function
+	Implementation of the Simplex method.
 */
+Result simplex(Vector &C, Matrix &A, Vector &b, double eps = 0.01, bool maximize = true)
+{
+
+	if (maximize == true)
+	{
+		for (int i = 0; i < C.size(); i++)
+		{
+			C[i] = -C[i];
+		}
+	}
+	Result result{};
+	result.maximize = maximize;
+
+	Matrix generalMatrix = createGeneralMatrix(A, C, b);
+	std::cout << generalMatrix;
+	std::vector<int> basicVars(generalMatrix.getRows());
+	basicVars[0] = -1;
+
+	for (int i = 0; i < b.size(); ++i)
+	{
+		if (b[i] < 0)
+		{
+			_stopIterating(generalMatrix, C, basicVars, unsolvable, result);
+			return result;
+		}
+	}
+
+	for (size_t i = 1; i < basicVars.size(); i++)
+	{
+		basicVars[i] = static_cast<int>(basicVars.size()) + i;
+	}
+	int iterationCount = 0;
+	while (true)
+	{
+		// 3
+		iterationCount++;
+		int pivot_column_index = 0;
+
+		pivot_column_index = min_index(generalMatrix[0]);
+
+		if (generalMatrix[0][pivot_column_index] >= 0)
+		{
+			_stopIterating(generalMatrix, C, basicVars, bounded, result);
+			if (!maximize)
+			{
+				result.objective_function_value = -result.objective_function_value;
+			}
+			return result;
+		}
+
+		// 4
+		Vector ratio_vector(generalMatrix.getRows());
+		for (int i = 1; i < generalMatrix.getRows(); i++)
+		{
+			if (generalMatrix[i][pivot_column_index] != 0)
+			{
+				ratio_vector[i] = generalMatrix[i][generalMatrix.getColumns() - 1] / generalMatrix[i][pivot_column_index];
+				if (std::abs(ratio_vector[i]) < eps)
+				{
+					ratio_vector[i] = 0;
+				}
+			}
+			else
+			{
+				ratio_vector[i] = 0;
+			}
+		}
+		ratio_vector[0] = 0;
+
+		int pivot_row_index = min_index_positive(ratio_vector);
+
+		// No leaving variable exists
+		if (pivot_row_index == -1)
+		{
+			_stopIterating(generalMatrix, C, basicVars, unbounded, result);
+			return result;
+		}
+
+		basicVars[pivot_row_index] = pivot_column_index;
+
+		// 5
+		elimination(generalMatrix, pivot_row_index, pivot_column_index);
+		std::cout << "Iteration " << iterationCount << " " << std::endl;
+		;
+		std::cout << generalMatrix;
+	}
+	return result;
+}

simplex.h

@@ -0,0 +1,26 @@
+#ifndef SIMPLEX_H
+#define SIMPLEX_H
+
+#include <vector>
+#include "tools/matrix.h"
+
+enum solver_state
+{
+  unbounded,
+  bounded,
+  unsolvable
+};
+
+struct Result
+{
+  solver_state state;
+  Vector solution;
+  double objective_function_value;
+  bool maximize;
+};
+
+void _printInitialInputs(Vector &C, Matrix &A, Vector &b);
+void _stopIterating(Matrix &generalMatrix, std::vector<int> &basicVars, Result &result);
+Result simplex(Vector &C, Matrix &A, Vector &b, double eps = 0.01, bool maximize = true);
+
+#endif // SIMPLEX_H

tools/elimination.cpp

@@ -0,0 +1,118 @@
+#include "elimination.h"
+#include "math.h"
+
+FracturedMatrix::FracturedMatrix(const FracturedMatrix &other) : A(other.A), C(other.C), b(other.b), pivot_column_index(other.pivot_column_index), pivot_row_index(other.pivot_row_index) {}
+FracturedMatrix::FracturedMatrix(Matrix A, Vector C, Vector b, int pivot_column_index, int pivot_row_index) : A(A), C(C), b(b), pivot_column_index(pivot_column_index), pivot_row_index(pivot_row_index) {}
+FracturedMatrix &FracturedMatrix::operator=(const FracturedMatrix &other)
+{
+    A = other.A;
+    C = other.C;
+    b = other.b;
+    pivot_column_index = other.pivot_column_index;
+    pivot_row_index = other.pivot_row_index;
+    return *this;
+}
+
+DestroyMatrix disassembleGeneralMatrix(Matrix &generalMatrix)
+{
+    int rows = generalMatrix.getRows();
+    int cols = generalMatrix.getColumns();
+
+    Matrix A(rows - 1, cols - 1);
+    Vector C(cols - 1);
+    Vector b(rows);
+
+    for (int j = 0; j < cols - 1; ++j)
+    {
+        C[j] = generalMatrix[0][j];
+    }
+
+    for (int i = 0; i < rows; ++i)
+    {
+        b[i] = generalMatrix[i][cols - 1];
+    }
+
+    for (int i = 1; i < rows; ++i)
+    {
+        for (int j = 0; j < cols - 1; ++j)
+        {
+            A[i - 1][j] = generalMatrix[i][j];
+        }
+    }
+
+    return {A, C, b};
+}
+
+Matrix createGeneralMatrix(Matrix &A, Vector &C, Vector &b)
+{
+
+    int m = A.getRows() + 1;
+    int n = A.getColumns() + A.getRows() + 1;
+    Matrix generalMatrix(m, n);
+
+    for (int i = 0; i < n; i++)
+    {
+        if (i < C.size())
+        {
+            generalMatrix[0][i] = C[i];
+        }
+        else
+        {
+            generalMatrix[0][i] = 0;
+        }
+    }
+
+    // For objective function (j=0) the value is set to zero one step before
+    for (int j = 1; j < m; j++)
+    {
+        generalMatrix[j][n - 1] = b[j - 1];
+    }
+
+    int k = 0;
+    for (int i = 0; i < m - 1; i++)
+    {
+        for (int j = 0; j < n - 1; j++)
+        {
+            if (j < A.getColumns())
+            {
+                generalMatrix[i + 1][j] = A[i][j];
+            }
+            else
+            {
+                generalMatrix[i + 1][j] = 0;
+            }
+        }
+
+        generalMatrix[i + 1][A.getColumns() + k] = 1;
+        ++k;
+    }
+
+    return generalMatrix;
+}
+
+void elimination(Matrix &generalMatrix, int pivot_row_index, int pivot_column_index)
+{
+
+    int rows = generalMatrix.getRows();
+    int cols = generalMatrix.getColumns();
+
+    double pivotElement = generalMatrix[pivot_row_index][pivot_column_index];
+
+    for (int j = 0; j < cols; ++j)
+    {
+        generalMatrix[pivot_row_index][j] /= pivotElement;
+    }
+
+    for (int i = 0; i < rows; ++i)
+    {
+        if (i == pivot_row_index)
+            continue;
+
+        double pivotColumnCoefficient = generalMatrix[i][pivot_column_index];
+
+        for (int j = 0; j < cols; ++j)
+        {
+            generalMatrix[i][j] -= pivotColumnCoefficient * generalMatrix[pivot_row_index][j];
+        }
+    }
+}

tools/elimination.h

@@ -0,0 +1,30 @@
+#ifndef ELIMINATION_H
+#define ELIMINATION_H
+
+#include "matrix.h"
+
+struct FracturedMatrix
+{
+	Matrix A;
+	Vector C;
+	Vector b;
+	int pivot_column_index;
+	int pivot_row_index;
+	FracturedMatrix() = default;
+	FracturedMatrix(const FracturedMatrix &other);
+	FracturedMatrix(Matrix A, Vector C, Vector b, int pivot_column_index, int pivot_row_index);
+	FracturedMatrix &operator=(const FracturedMatrix &other);
+};
+
+struct DestroyMatrix
+{
+	Matrix A;
+	Vector C;
+	Vector b;
+};
+
+DestroyMatrix disassembleGeneralMatrix(Matrix &generalMatrix);
+void elimination(Matrix &, int pivot_row_index, int pivot_column_index);
+Matrix createGeneralMatrix(Matrix &A, Vector &C, Vector &b);
+
+#endif // ELIMINATION_H

tools/math.cpp

@@ -0,0 +1,139 @@
+#include "math.h"
+
+double min(Vector vector)
+{
+    double temp = vector[0];
+    for (int j = 0; j < vector.size(); j++)
+    {
+        if (vector[j] < temp)
+        {
+            temp = vector[j];
+        }
+    }
+    return temp;
+}
+
+double max(Vector vector)
+{
+    double temp = vector[0];
+    for (int j = 0; j < vector.size(); j++)
+    {
+        if (vector[j] > temp)
+        {
+            temp = vector[j];
+        }
+    }
+    return temp;
+}
+
+int min_index_positive(Vector vector)
+{
+    int i = 0;
+    while (i < vector.size() && vector[i] <= 0)
+    {
+        ++i;
+    }
+    if (i >= vector.size())
+    {
+        // No positive value found -> iterations stop
+        return -1;
+    }
+    int temp_index = i;
+    double temp = vector[i];
+
+    for (int j = i + 1; j < vector.size(); j++)
+    {
+        if (vector[j] < temp && vector[j] > 0)
+        {
+            temp_index = j;
+            temp = vector[j];
+        }
+    }
+    return temp_index;
+}
+
+int min_index(Vector vector)
+{
+    int temp_index = 0;
+    double temp = vector[0];
+    for (int j = 0; j < vector.size(); j++)
+    {
+        if (vector[j] < temp)
+        {
+            temp_index = j;
+            temp = vector[j];
+        }
+    }
+    return temp_index;
+}
+
+int max_index(Vector vector)
+{
+    int temp_index = 0;
+    double temp = vector[0];
+    for (int j = 0; j < vector.size(); j++)
+    {
+        if (vector[j] > temp)
+        {
+            temp_index = j;
+            temp = vector[j];
+        }
+    }
+    return temp_index;
+}
+
+double min(std::vector<double> array)
+{
+    double temp = array[0];
+    for (size_t i = 1; i < array.size(); i++)
+    {
+        if (array[i] < temp)
+        {
+            temp = array[i];
+        }
+    }
+    return temp;
+}
+
+double max(std::vector<double> array)
+{
+    double temp = array[0];
+    for (size_t i = 1; i < array.size(); i++)
+    {
+        if (array[i] > temp)
+        {
+            temp = array[i];
+        }
+    }
+    return temp;
+}
+
+int min_index(std::vector<double> array)
+{
+    int temp_index = 0;
+    double temp = array[0];
+    for (size_t i = 1; i < array.size(); i++)
+    {
+        if (array[i] < temp)
+        {
+            temp_index = i;
+            temp = array[i];
+        }
+    }
+    return temp_index;
+}
+
+int max_index(std::vector<double> array)
+{
+    int temp_index = 0;
+    double temp = array[0];
+    for (size_t i = 1; i < array.size(); i++)
+    {
+        if (array[i] > temp)
+        {
+            temp_index = i;
+            temp = array[i];
+        }
+    }
+    return temp_index;
+}

tools/math.h

@@ -0,0 +1,17 @@
+#ifndef MATH_H
+#define MATH_H
+
+#include <vector>
+#include "matrix.h"
+
+double min(Vector vector);
+double max(Vector vector);
+int min_index(Vector vector);
+int min_index_positive(Vector vector);
+int max_index(Vector vector);
+double min(std::vector<double> array);
+double max(std::vector<double> array);
+int min_index(std::vector<double> array);
+int max_index(std::vector<double> array);
+
+#endif // MATH_H

tools/matrix.cpp

@@ -1,120 +1,175 @@
 #include "matrix.h"
 
-ColumnVector::ColumnVector(int n) {
+Vector::Vector(int n)
+{
   rows = n;
   columns = 1;
-  columnVector.resize(n);
+  vector.resize(n);
 }
 
-ColumnVector::ColumnVector(const ColumnVector& other) {
+Vector::Vector(const Vector &other)
+{
   rows = other.rows;
   columns = other.columns;
-  columnVector = other.columnVector;
+  vector = other.vector;
 }
 
-int ColumnVector::getRows() const {
+Vector::Vector(std::initializer_list<double> init)
+{
+  rows = init.size();
+  columns = 1;
+  vector = std::vector<double>(rows);
+
+  auto it = init.begin();
+
+  for (size_t i = 0; i < init.size(); ++i)
+  {
+    vector[i] = *it++;
+  }
+}
+
+int Vector::size() const
+{
   return rows;
 }
 
-int ColumnVector::getColumns() const {
-  return columns;
+double &Vector::operator[](int row)
+{
+  return vector[row];
 }
 
-double& ColumnVector::operator[](int row) {
-  return columnVector[row];
-}
-
-ColumnVector& ColumnVector::operator=(const ColumnVector& other) {
+Vector &Vector::operator=(const Vector &other)
+{
   rows = other.rows;
   columns = other.columns;
-  columnVector = other.columnVector;
+  vector = other.vector;
   return *this;
 }
 
-ColumnVector ColumnVector::operator+(ColumnVector& other) {
-  if (rows != other.rows) {
+Vector Vector::operator+(Vector &other)
+{
+  if (rows != other.rows)
+  {
     throw std::runtime_error("Error: the dimensional problem occurred");
   }
-  ColumnVector result(rows);
-  for (int i = 0; i < rows; ++i) {
-    result[i] = columnVector[i] + other[i];
+  Vector result(rows);
+  for (int i = 0; i < rows; ++i)
+  {
+    result[i] = vector[i] + other[i];
   }
 
   return result;
 }
 
-ColumnVector ColumnVector::operator-(ColumnVector& other) {
-  if (rows != other.rows) {
+Vector Vector::operator-(Vector &other)
+{
+  if (rows != other.rows)
+  {
     throw std::runtime_error("Error: the dimensional problem occurred");
   }
-  ColumnVector result(rows);
-  for (int i = 0; i < rows; ++i) {
-    result[i] = columnVector[i] - other[i];
+  Vector result(rows);
+  for (int i = 0; i < rows; ++i)
+  {
+    result[i] = vector[i] - other[i];
   }
 
   return result;
 }
 
-std::istream& operator>>(std::istream& cin, ColumnVector& vectorObj) {
-  for (int i = 0; i < vectorObj.rows; ++i) {
+std::istream &operator>>(std::istream &cin, Vector &vectorObj)
+{
+  for (int i = 0; i < vectorObj.rows; ++i)
+  {
     cin >> vectorObj[i];
   }
   return cin;
 }
 
-std::ostream& operator<<(std::ostream& cout, ColumnVector& vectorObj) {
-  for (int i = 0; i < vectorObj.rows; ++i) {
-    if (i == vectorObj.rows - 1) {
+std::ostream &operator<<(std::ostream &cout, Vector &vectorObj)
+{
+  for (int i = 0; i < vectorObj.rows; ++i)
+  {
+    if (i == vectorObj.rows - 1)
+    {
       cout << vectorObj[i] << std::endl;
     }
-    else {
+    else
+    {
       cout << vectorObj[i] << ' ';
     }
   }
   return cout;
 }
 
-Matrix::Matrix(int n, int m) {
+Matrix::Matrix(int n, int m)
+{
   rows = n;
   columns = m;
-  matrix.resize(n);
-  for (auto& row : matrix) {
-    row = ColumnVector(m);
+  matrix.resize(n, Vector(m));
+  for (auto &row : matrix)
+  {
+    row = Vector(m);
   }
 }
 
-Matrix::Matrix(const Matrix& other) {
+Matrix::Matrix(const Matrix &other)
+{
   rows = other.rows;
   columns = other.columns;
   matrix = other.matrix;
 }
 
-int Matrix::getRows() const {
+Matrix::Matrix(std::initializer_list<std::vector<double>> init)
+{
+  rows = init.size();
+  auto it = init.begin();
+  columns = it->size();
+  matrix = std::vector<Vector>(rows, Vector(columns));
+
+  for (int i = 0; i < rows; ++i)
+  {
+    for (int j = 0; j < columns; ++j)
+    {
+      matrix[i][j] = it->operator[](j);
+    }
+    ++it;
+  }
+}
+
+int Matrix::getRows() const
+{
   return rows;
 }
 
-int Matrix::getColumns() const {
+int Matrix::getColumns() const
+{
   return columns;
 }
 
-ColumnVector& Matrix::operator[](int row) {
+Vector &Matrix::operator[](int row)
+{
   return matrix[row];
 }
 
-Matrix& Matrix::operator=(const Matrix& other) {
+Matrix &Matrix::operator=(const Matrix &other)
+{
   rows = other.rows;
   columns = other.columns;
   matrix = other.matrix;
   return *this;
 }
 
-Matrix Matrix::operator+(Matrix& other) const {
-  if (rows != other.rows || columns != other.columns) {
+Matrix Matrix::operator+(Matrix &other) const
+{
+  if (rows != other.rows || columns != other.columns)
+  {
     throw std::runtime_error("Error: the dimensional problem occurred");
   }
   Matrix result(rows, columns);
-  for (int i = 0; i < rows; ++i) {
-    for (int j = 0; j < columns; ++j) {
+  for (int i = 0; i < rows; ++i)
+  {
+    for (int j = 0; j < columns; ++j)
+    {
       auto x = matrix[i];
       auto y = other[i];
       result[i][j] = x[j] + y[j];
@@ -124,13 +179,17 @@ Matrix Matrix::operator+(Matrix& other) const {
   return result;
 }
 
-Matrix Matrix::operator-(Matrix& other) const {
-  if (rows != other.rows || columns != other.columns) {
+Matrix Matrix::operator-(Matrix &other) const
+{
+  if (rows != other.rows || columns != other.columns)
+  {
     throw std::runtime_error("Error: the dimensional problem occurred");
   }
   Matrix result(rows, columns);
-  for (int i = 0; i < rows; ++i) {
-    for (int j = 0; j < columns; ++j) {
+  for (int i = 0; i < rows; ++i)
+  {
+    for (int j = 0; j < columns; ++j)
+    {
       auto x = matrix[i];
       auto y = other[i];
       result[i][j] = x[j] - y[j];
@@ -140,16 +199,21 @@ Matrix Matrix::operator-(Matrix& other) const {
   return result;
 }
 
-Matrix Matrix::operator*(Matrix& other) const {
-  if (columns != other.rows) {
+Matrix Matrix::operator*(Matrix &other) const
+{
+  if (columns != other.rows)
+  {
     throw std::runtime_error("Error: the dimensional problem occurred");
   }
 
   Matrix result(rows, other.columns);
-  for (int i = 0; i < rows; ++i) {
-    for (int j = 0; j < other.columns; ++j) {
+  for (int i = 0; i < rows; ++i)
+  {
+    for (int j = 0; j < other.columns; ++j)
+    {
       result[i][j] = 0;
-      for (int k = 0; k < columns; ++k) {
+      for (int k = 0; k < columns; ++k)
+      {
         auto x = matrix[i];
         auto y = other[k];
         result[i][j] += x[k] * y[j];
@@ -160,15 +224,19 @@ Matrix Matrix::operator*(Matrix& other) const {
   return result;
 }
 
-ColumnVector Matrix::operator*(ColumnVector other) const {
-  if (columns != other.getRows()) {
+Vector Matrix::operator*(Vector other) const
+{
+  if (columns != other.size())
+  {
     throw std::runtime_error("Error: the dimensional problem occurred");
   }
 
-  ColumnVector result(rows);
-  for (int i = 0; i < rows; ++i) {
+  Vector result(rows);
+  for (int i = 0; i < rows; ++i)
+  {
     result[i] = 0;
-    for (int k = 0; k < columns; ++k) {
+    for (int k = 0; k < columns; ++k)
+    {
       auto x = matrix[i];
       result[i] += x[k] * other[k];
     }
@@ -177,10 +245,13 @@ ColumnVector Matrix::operator*(ColumnVector other) const {
   return result;
 }
 
-Matrix Matrix::transpose() const {
+Matrix Matrix::transpose() const
+{
   Matrix result(columns, rows);
-  for (int i = 0; i < rows; ++i) {
-    for (int j = 0; j < columns; ++j) {
+  for (int i = 0; i < rows; ++i)
+  {
+    for (int j = 0; j < columns; ++j)
+    {
       auto x = matrix[i];
       result[j][i] = x[j];
     }
@@ -189,25 +260,69 @@ Matrix Matrix::transpose() const {
   return result;
 }
 
-std::istream& operator>>(std::istream& cin, Matrix& matrixObj) {
-  for (int i = 0; i < matrixObj.rows; ++i) {
-    for (int j = 0; j < matrixObj.columns; ++j) {
+std::istream &operator>>(std::istream &cin, Matrix &matrixObj)
+{
+  for (int i = 0; i < matrixObj.rows; ++i)
+  {
+    for (int j = 0; j < matrixObj.columns; ++j)
+    {
       cin >> matrixObj[i][j];
     }
   }
   return cin;
 }
 
-std::ostream& operator<<(std::ostream& cout, Matrix& matrixObj) {
-  for (int i = 0; i < matrixObj.rows; ++i) {
-    for (int j = 0; j < matrixObj.columns; ++j) {
-      if (j == matrixObj.columns - 1) {
-        cout << matrixObj[i][j] << std::endl;
-      }
-      else {
-        cout << matrixObj[i][j] << ' ';
+std::ostream &operator<<(std::ostream &cout, Matrix &matrixObj)
+{
+  size_t maxNumberLength = 1;
+  for (int y = 0; y < matrixObj.getRows(); y++)
+  {
+    for (int x = 0; x < matrixObj.getColumns(); x++)
+    {
+      if (std::to_string(matrixObj[y][x]).length() > maxNumberLength)
+      {
+        maxNumberLength = std::to_string(matrixObj[y][x]).length();
       }
     }
   }
+  // std::cout << maxNumberLength << std::endl;
+  std::cout << std::endl;
+  for (int y = 0; y < matrixObj.getRows(); y++)
+  {
+    std::string row = "";
+    for (int x = 0; x < matrixObj.getColumns(); x++)
+    {
+      std::string strNumber = std::to_string(matrixObj[y][x]);
+      bool spaceRight = true;
+      while (strNumber.length() < maxNumberLength)
+      {
+        if (spaceRight)
+        {
+          strNumber += " ";
+        }
+        else
+        {
+          strNumber = " " + strNumber;
+        }
+        spaceRight = !spaceRight;
+        strNumber = "" + strNumber;
+      }
+      if (matrixObj[y][x] == 0)
+      {
+        row += "[\033[0m" + strNumber + "\033[0m] ";
+      }
+      else if (matrixObj[y][x] > 0)
+      {
+        row += "[\033[32m" + strNumber + "\033[0m] ";
+      }
+      else
+      {
+        row += "[\033[31m" + strNumber + "\033[0m] ";
+      }
+    }
+    std::cout << row << std::endl;
+  }
+  std::cout << std::endl;
+
   return cout;
 }

tools/matrix.h

@@ -6,43 +6,45 @@
 #include <vector>
 
 /**
-* ColumnVector is a class to represent
+ * Vector is a class to represent
  * a column vector with n rows.
  */
-class ColumnVector {
+
+class Vector
+{
 protected:
 	// Number of rows in vector
 	int rows;
 	// Number of columns in vector
 	int columns;
 	// Matrix representation as vector of vectors of integers
-	std::vector<double> columnVector;
-public:
-	ColumnVector(int n);
+	std::vector<double> vector;
 
-	ColumnVector(const ColumnVector& other);
+public:
+	Vector(int n);
+
+	Vector(const Vector &other);
+
+	Vector(std::initializer_list<double>);
 
 	/* Getter for the number of rows */
-	int getRows() const;
-
-	/* Getter for the number of columns */
-	int getColumns() const;
+	int size() const;
 
 	double &operator[](int row);
 
-	ColumnVector& operator=(const ColumnVector& other);
+	Vector &operator=(const Vector &other);
 
-	ColumnVector operator+(ColumnVector& other);
+	Vector operator+(Vector &other);
 
-	ColumnVector operator-(ColumnVector& other);
+	Vector operator-(Vector &other);
 
 	/* Input operator reads element of vector */
-	friend std::istream& operator>>(std::istream& cin, ColumnVector& vectorObj);
+	friend std::istream &operator>>(std::istream &cin, Vector &vectorObj);
 
 	/* Output operator prints elements of the vector
 	 * in a row separated with a space (no space at the end of the line)
 	 */
-	friend std::ostream& operator<<(std::ostream& cout, ColumnVector& vectorObj);
+	friend std::ostream &operator<<(std::ostream &cout, Vector &vectorObj);
 };
 
 /**
@@ -50,26 +52,30 @@ public:
  * a matrix of size n x m
  * of type integer.
  */
-class Matrix {
+class Matrix
+{
 protected:
 	// Number of rows in matrix
 	int rows;
 	// Number of columns in matrix
 	int columns;
 	// Matrix representation as vector of vectors of integers
-	std::vector<ColumnVector> matrix;
+	std::vector<Vector> matrix;
+
 public:
 	Matrix(int n, int m);
 
 	Matrix(const Matrix &other);
 
+	Matrix(std::initializer_list<std::vector<double>>);
+
 	/* Getter for the number of rows */
 	int getRows() const;
 
 	/* Getter for the number of columns */
 	int getColumns() const;
 
-	ColumnVector& operator[](int row);
+	Vector &operator[](int row);
 
 	Matrix &operator=(const Matrix &other);
 
@@ -80,7 +86,7 @@ public:
 	Matrix operator*(Matrix &other) const;
 
 	/* Matrix-Vector multiplication */
-	ColumnVector operator*(ColumnVector other) const;
+	Vector operator*(Vector other) const;
 
 	/* Produces transposed version of the matrix */
 	Matrix transpose() const;