LinearProgramming (Algorithms 4/e)

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 an 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 solution.
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 determine the entering and leaving variables. It is not suitable for use on large inputs.
This computes correct results if all arithmetic performed is without floating-point rounding error or arithmetic overflow. In practice, there will be floating-point rounding error and this implementation is not robust in the presence of such errors.
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	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 an m-by-n matrix, b is an m-length vector, and c is an n-length vector.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	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.

Methods inherited from class java.lang.Object
clone, equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- 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 an 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