feat: OT Lab - 5 (Implement Simplex algorithm for linear programming problem)

Author: Samya-S

OT Lab - 5 (23-08-24)/5.cpp

@@ -0,0 +1,169 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+class Simplex {
+    private:
+    int n, m;
+    vector<vector<double>> A;
+    vector<double> c;
+    vector<double> b;
+    vector<double> CB;
+    vector<double> B;
+    vector<double> delta;
+
+    public:
+    Simplex(int variables, int constraints) : n(variables), m(constraints), A(constraints, vector<double> (variables + constraints)), c(variables + constraints), b(constraints), CB(constraints), B(constraints), delta(variables + constraints) {}
+
+    void readInput() {
+        // cout << "Enter the coefficients of the objective function: ";
+        for (int i = 0; i < n; i++) {
+            cin >> c[i];
+        }
+
+        // cout << "Enter the coefficients of the constraints:" << endl;
+        for (int i = 0; i < m; i++) {
+            for (int j = 0; j < n; j++) {
+                cin >> A[i][j];
+            }
+        }
+
+        // cout << "Enter the right-hand side of the constraints: ";
+        for (int i = 0; i < m; i++) {
+        cin >> b[i];
+        }
+
+        for (int i = 0; i < m; i++) {
+            A[i][n + i] = 1.0;
+            c[n + i] = 0.0;
+            B[i] = n + i;
+            CB[i] = 0.0;
+        }
+    }
+
+    void computeDelta() {
+        for (int j = 0; j < n + m; j++) {
+            double sum = 0.0;
+            for (int i = 0; i < m; i++) {
+                sum += CB[i] * A[i][j];
+            }
+            delta[j] = sum - c[j];
+        }
+    }
+
+    int findEnteringVariable() {
+        int entering = -1;
+        for (int j = 0; j < n + m; j++) {
+            if (delta[j] < 0) {
+                if (entering == -1 || delta[j] < delta[entering]) {
+                    entering = j;
+                }
+            }
+        }
+        return entering;
+    }
+
+    int findLeavingVariable(int entering) {
+        int leaving = -1;
+        double minRatio = 1e18;
+        for (int i = 0; i < m; i++) {
+            if (A[i][entering] > 0) {
+            double ratio = b[i] / A[i][entering];
+            if (ratio < minRatio) {
+                minRatio = ratio;
+                leaving = i;
+                }
+            }
+        }
+        return leaving;
+    }
+
+    void pivot(int entering, int leaving) {
+        double pivotElement = A[leaving][entering];
+
+        for (int j = 0; j < n + m; j++) {
+            A[leaving][j] /= pivotElement;
+        }
+        b[leaving] /= pivotElement;
+
+        for (int i = 0; i < m; i++) {
+            if (i != leaving) {
+                double factor = A[i][entering];
+                for (int j = 0; j < n + m; j++) {
+                    A[i][j] -= factor * A[leaving][j];
+                }
+                b[i] -= factor * b[leaving];
+            }
+        }
+
+        B[leaving] = entering;
+        CB[leaving] = c[entering];
+    }
+
+    void printTable() {
+        cout << "Simplex Table:" << endl;
+        cout << "\tXB" << "\tCB";
+        for (int j = 0; j < n + m; j++) {
+            cout << "\tX" << j + 1;
+        }
+        cout << "\tb" << endl;
+
+        for (int i = 0; i < m; i++) {
+            cout << "\tX" << B[i] + 1 << "\t" << CB[i];
+            for (int j = 0; j < n + m; j++) {
+                cout << "\t" << A[i][j];
+            }
+            cout << "\t" << b[i] << endl;
+        }
+
+        cout << "Δj:\t\t";
+        for (int j = 0; j < n + m; j++) {
+            cout << "\t" << delta[j];
+        }
+        cout << endl << endl;
+    }
+
+    void solve() {
+        while (true) {
+        computeDelta();
+        printTable();
+
+        int entering = findEnteringVariable();
+        if (entering == -1) {
+            cout << "Optimal solution found." << endl;
+            break;
+        }
+
+        int leaving = findLeavingVariable(entering);
+        if (leaving == -1) {
+            cout << "Problem is unbounded." << endl;
+            break;
+        }
+
+        pivot(entering, leaving);
+        }
+
+        cout << "Final Solution:" << endl;
+        for (int i = 0; i < m; i++) {
+            cout << "X" << B[i] + 1 << " = " << b[i] << endl;
+        }
+        double optimalValue = 0;
+        for (int i = 0; i < m; i++) {
+            optimalValue += CB[i] * b[i];
+        }
+        cout << "Optimal value of the objective function: " << optimalValue << endl;
+    }
+};
+
+int main() {
+    int n,m;
+    // cout << "Enter the number of variables: ";
+    cin >> n;
+    // cout << "Enter the number of constraints: ";
+    cin >> m;
+
+    Simplex simplex(n, m);
+    simplex.readInput();
+    simplex.solve();
+
+    return 0;
+}