make x column

.gitignore

@@ -1,6 +1,7 @@
 # Prerequisites
 *.d
-
+CMakeLists.txt
+.idea
 # Compiled Object files
 *.slo
 *.lo

main.cpp

@@ -1,6 +1,18 @@
 #include <iostream>
+#include "tools/matrix.h"
+
 
 int main() {
-    std::cout << "Hello World!\n";
+    int n, m;
+    ColumnVector C(n);
+    Matrix A(n, m);
+    ColumnVector b(n);
+    double eps;
+    double eps_default;
+
+    std::cin >> C;
+    std::cin >> A;
+    std::cin >> b;
+    std::cin >> eps;
     return 0;
 }

simplex.cpp

@@ -1 +1,85 @@
-// implementation of simplex task
+#include <algorithm>
+#include <iostream>
+#include "tools/matrix.h"
+
+enum solver_state {
+	unbounded,
+	bounded
+};
+
+struct Result {
+	solver_state state;
+	ColumnVector *solution;
+	double objective_fucntion_value;
+};
+
+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;
+
+	for (int i = 1; i < basicVars.size(); i++) {
+		basicVars[i] = static_cast<int>(basicVars.size()) + i;
+	}
+
+	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;
+		}
+	}
+
+	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;
+		}
+		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];
+	}
+}
+
+/*
+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
+*/