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bigm.cpp
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bigm.cpp
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// Big M method to solve linear equations
#include <bits/stdc++.h>
using namespace std;
int main()
{
int n; // number of variables
cout << "Enter number of Variables : ";
cin >> n;
double objective_function_coefficient[101]; // coefficient of objective function
cout << "Enter Coefficient of x in objective function :\n";
for (int i = 1; i <= n; i++)
{
cin >> objective_function_coefficient[i];
}
for (int i = n + 1; i <= 100; i++) // allocating 0 coefficient to slack and sulprus variables in objective function
objective_function_coefficient[i] = 0;
int flag; // Flag variable indicating we need to maximize objective function or minimize the objective function
cout << "\n'1' : to maximize\n'0' : to minimize\n Enter : ";
cin >> flag;
double sign = 1.0;
if (flag == 0)
sign = -1.00;
// minimizing objective function = maximizing -(objective function)
if (flag == 0)
{
for (int i = 1; i <= n; i++)
objective_function_coefficient[i] *= sign;
}
int m; // number of equations
cout << "Enter number of equations : ";
cin >> m;
int counter = n + m;
double coefficient[m + 1][101];
double b[m + 1];
double ma = 1000000.00;
double ans = 0.0;
int basis_index[m + 1];
for (int i = 1; i <= m; i++)
{
for (int j = 1; j <= n; j++)
{
cout << "ENTER COEFFICIENT OF x" << j << " IN " << i << "TH EQUATION:- ";
cin >> coefficient[i][j];
}
for (int j = n + 1; j <= 100; j++)
coefficient[i][j] = 0.0;
cout << "ENTER <= OR >= OR = SIGN IN " << i << "TH EQUATION:- ";
string s;
cin >> s;
if (s[0] == '>')
{
coefficient[i][n + i] = -1.0;
counter++;
coefficient[i][counter] = 1.0;
objective_function_coefficient[counter] = -ma;
basis_index[i] = counter;
}
else if (s[0] == '<')
{
coefficient[i][n + i] = 1.0;
basis_index[i] = n + i;
}
else if (s[0] == '=')
{
coefficient[i][n + i] = 0;
counter++;
coefficient[i][counter] = 1.0;
objective_function_coefficient[counter] = -ma;
basis_index[i] = counter;
}
cout << "ENTER CONSTANT TERM OF " << i << "th EQUATION ON RHS:- "
<< " ";
cin >> b[i];
ans += objective_function_coefficient[basis_index[i]] * b[i];
}
cout << "\n";
cout << fixed << setprecision(4);
// calculating zi for all the variables
double z[counter + 1];
int it = 1;
double basic_variables[101][m + 1][2]; // Stores information about basic variables and minimum ratio each iteration
double updated_ans[101];
double non_basic_variables[101][counter + 1 - m][2];
updated_ans[0] = ans;
double updated_z[101][counter + 1];
double updated_coefficient[101][m + 1][counter + 2];
int check = 1;
while (1)
{
for (int i = 1; i <= counter; i++)
{
z[i] = 0;
for (int j = 1; j <= m; j++)
z[i] += coefficient[j][i] * objective_function_coefficient[basis_index[j]];
// cout<<"z"<<i<<" - c"<<i<<" = "<<(z[i]-objective_function_coefficient[i])<<"\n";
}
vector<bool> vis(counter + 1, false);
for (int i = 1; i <= m; i++)
{
vis[basis_index[i]] = true;
basic_variables[it][i][0] = basis_index[i]; // Basic variable index
basic_variables[it][i][1] = b[i]; // Stores minimum ratio for that particular basic variable
}
int h = 1;
for (int i = 1; i <= counter; i++)
{
if (vis[i] == true)
continue;
non_basic_variables[it][h][0] = i; // Non-Basic variable index
non_basic_variables[it][h][1] = z[i] - objective_function_coefficient[i]; // Stores minimum ratio for that particular basic variable
h++;
}
for (int i = 1; i <= m; i++)
{
for (int j = 1; j <= counter; j++)
{
updated_coefficient[it][i][j] = coefficient[i][j];
}
updated_coefficient[it][i][counter + 1] = b[i];
}
int position = 1;
for (int i = 1; i <= counter; i++)
{
// cout<<"z"<<i<<" - c"<<i<<" = "<<(z[i]-objective_function_coefficient[i])<<"\n";
updated_z[it][i] = z[i] - objective_function_coefficient[i];
if (z[i] - objective_function_coefficient[i] < z[position] - objective_function_coefficient[position])
position = i;
}
if (z[position] - objective_function_coefficient[position] >= -0.001)
{
break;
}
else
{
int pos1 = 0;
for (int i = 1; i <= m; i++)
{
if (coefficient[i][position] != 0)
{
if (pos1 == 0 && b[i] / coefficient[i][position] >= 0.0)
{
pos1 = i;
}
else if (b[i] / coefficient[i][position] < b[pos1] / coefficient[pos1][position] && b[i] / coefficient[i][position] >= 0.0)
{
pos1 = i;
}
}
}
if (pos1 == 0)
{
check = 0;
break;
}
basis_index[pos1] = position;
double val = coefficient[pos1][position];
for (int i = 1; i <= counter; i++)
{ // Making coeff of xpos 1 in pos1 th equation
coefficient[pos1][i] /= val;
}
b[pos1] /= val;
for (int i = 1; i <= m; i++)
{ // Making coeff of xpos 0 in all other equation
val = coefficient[i][position];
for (int j = 1; j <= counter && i != pos1; j++)
{
coefficient[i][j] -= val * coefficient[pos1][j];
}
if (i != pos1)
b[i] -= val * b[pos1];
}
val = 0;
for (int i = 1; i <= m; i++)
{
val += objective_function_coefficient[basis_index[i]] * b[i];
}
ans = max(ans, val);
updated_ans[it] = val;
it++;
}
}
cout << "NUMBER OF ITERATIONS FOR THE PROCESS IS:- " << it << "\n\n";
for (int it1 = 1; it1 <= it; it1++)
{
cout << "SIMPLEX TABLEAU FOR ITERATION " << it1 << " IS AS FOLLOWS:-\n\n";
cout << "\t\tCoefficient in Z\t";
for (int i = 1; i <= counter; i++)
{
if (objective_function_coefficient[i] >= 0.0)
cout << " ";
cout << objective_function_coefficient[i] << "\t\t";
}
cout << "\n";
cout << "\t Cb\t\t Basis\t\t";
for (int i = 1; i <= counter; i++)
cout << " x" << i << "\t\t";
cout << " RHS\n";
for (int j = 1; j <= m; j++)
{
cout << "\t";
if (objective_function_coefficient[(int)basic_variables[it1][j][0]] >= 0.0 && objective_function_coefficient[(int)basic_variables[it1][j][0]] < 10.0)
cout << " ";
cout << objective_function_coefficient[(int)basic_variables[it1][j][0]] << "\t\t"
<< "x" << (int)basic_variables[it1][j][0] << "\t\t";
for (int i = 1; i <= counter + 1; i++)
{
if (updated_coefficient[it1][j][i] >= 0.0)
cout << " ";
cout << updated_coefficient[it1][j][i] << "\t\t";
}
cout << "\n";
}
cout << "\t\t\tzj-cj\t\t";
for (int i = 1; i <= counter; i++)
{
if (updated_z[it1][i] >= 0.0)
cout << " ";
cout << updated_z[it1][i] << "\t\t";
}
cout << updated_ans[it1 - 1] << "\n";
cout << "\n";
}
for (int j = 1; j <= m; j++)
{
int position = basic_variables[it][j][0];
if (position > n + m && basic_variables[it][j][1] != 0.0000)
check = -1;
}
if (check == 1)
{
cout << "OPTIMAL VALUE OCCURS AT:- \n";
double solution[n + 1];
for (int j = 1; j <= n; j++)
solution[j] = 0.0;
for (int j = 1; j <= m; j++)
{
int pos = basic_variables[it][j][0];
if (pos <= n)
solution[pos] = basic_variables[it][j][1];
}
for (int i = 1; i <= n; i++)
{
cout << "x" << i << " = " << solution[i];
if (i < n)
cout << " , ";
}
cout << "\n\n";
cout << "OPTIMAL VALUE IS = " << (ans * sign) << '\n';
}
else if (check == 0)
{
cout << "OPTIMAL VALUE IS UNBOUNDED!!\n";
cout << "\n";
}
else
{
cout << "INFEASIBLE AS ARTIFICIAL VARIABLES ARE NOT ZERO!!\nSOLUTION DOES NOT EXIST!!\n";
}
return 0;
}