edu.princeton.cs.algs4

## Class LinearProgramming

• Object
• edu.princeton.cs.algs4.LinearProgramming

• public class LinearProgramming
extends Object
The LinearProgramming class represents a data type for solving a linear program of the form { max cx : Ax ≤ b, x ≥ 0 }, where A is a m-by-n matrix, b is an m-length vector, and c is an n-length vector. For simplicity, we assume that A is of full rank and that b ≥ 0 so that x = 0 is a basic feasible soution.

The data type supplies methods for determining the optimal primal and dual solutions.

This is a bare-bones implementation of the simplex algorithm. It uses Bland's rule to determing the entering and leaving variables. It is not suitable for use on large inputs. It is also not robust in the presence of floating-point roundoff error.

For additional documentation, see Section 6.5 Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.

Author:
Robert Sedgewick, Kevin Wayne
• ### Constructor Summary

Constructors
Constructor and Description
LinearProgramming(double[][] A, double[] b, double[] c)
Determines an optimal solution to the linear program { max cx : Ax ≤ b, x ≥ 0 }, where A is a m-by-n matrix, b is an m-length vector, and c is an n-length vector.
• ### Method Summary

Methods
Modifier and Type Method and Description
double[] dual()
Returns the optimal dual solution to this linear program
static void main(String[] args)
Unit tests the LinearProgramming data type.
double[] primal()
Returns the optimal primal solution to this linear program.
double value()
Returns the optimal value of this linear program.
• ### Constructor Detail

• #### LinearProgramming

public LinearProgramming(double[][] A,
double[] b,
double[] c)
Determines an optimal solution to the linear program { max cx : Ax ≤ b, x ≥ 0 }, where A is a m-by-n matrix, b is an m-length vector, and c is an n-length vector.
Parameters:
A - the m-by-b matrix
b - the m-length RHS vector
c - the n-length cost vector
Throws:
IllegalArgumentException - unless b[i] >= 0 for each i
ArithmeticException - if the linear program is unbounded
• ### Method Detail

• #### value

public double value()
Returns the optimal value of this linear program.
Returns:
the optimal value of this linear program
• #### primal

public double[] primal()
Returns the optimal primal solution to this linear program.
Returns:
the optimal primal solution to this linear program
• #### dual

public double[] dual()
Returns the optimal dual solution to this linear program
Returns:
the optimal dual solution to this linear program
• #### main

public static void main(String[] args)
Unit tests the LinearProgramming data type.
Parameters:
args - the command-line arguments