TransitiveClosure (Algorithms 4/e)

Object
- edu.princeton.cs.algs4.TransitiveClosure

```
public class TransitiveClosure
extends Object
```
The TransitiveClosure class represents a data type for computing the transitive closure of a digraph.
This implementation runs depth-first search from each vertex. The constructor takes Θ(V(V + E)) in the worst case, where V is the number of vertices and E is the number of edges. Each instance method takes Θ(1) time. It uses Θ(V²) extra space (not including the digraph).
For large digraphs, you may want to consider a more sophisticated algorithm. Nuutila proposes two algorithm for the problem (based on strong components and an interval representation) that runs in Θ(E + V) time on typical digraphs. For additional documentation, see Section 4.2 of Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.

Author:

Robert Sedgewick, Kevin Wayne

Constructor Summary

Constructors
Constructor Description

TransitiveClosure(Digraph digraph)
Computes the transitive closure of a digraph.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`static void`	`main(String[] args)`	Unit tests the `TransitiveClosure` data type.
`boolean`	`reachable(int v, int w)`	Is there a directed path from vertex `v` to vertex `w` in the digraph?

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

- Constructor Detail
  - TransitiveClosure
```
public TransitiveClosure(Digraph digraph)
```
    Computes the transitive closure of a digraph.
    
    Parameters:
    
    digraph - the digraph
- Method Detail
  - reachable
```
public boolean reachable(int v,
                         int w)
```
    Is there a directed path from vertex v to vertex w in the digraph?
    
    Parameters:
    
    v - the source vertex
    
    w - the target vertex
    
    Returns:
    
    true if there is a directed path from v to w, false otherwise
    
    Throws:
    
    IllegalArgumentException - unless 0 <= v < V
    
    IllegalArgumentException - unless 0 <= w < V
  - main
```
public static void main(String[] args)
```
    Unit tests the TransitiveClosure data type.
    
    Parameters:
    
    args - the command-line arguments