## Class AcyclicSP

• Object
• edu.princeton.cs.algs4.AcyclicSP

• ```public class AcyclicSP
extends Object```
The `AcyclicSP` class represents a data type for solving the single-source shortest paths problem in edge-weighted directed acyclic graphs (DAGs). The edge weights can be positive, negative, or zero.

This implementation uses a topological-sort based algorithm. The constructor takes Θ(V + E) time 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(V) extra space (not including the edge-weighted digraph).

This correctly computes shortest paths if all arithmetic performed is without floating-point rounding error or arithmetic overflow. This is the case if all edge weights are integers and if none of the intermediate results exceeds 252. Since all intermediate results are sums of edge weights, they are bounded by V C, where V is the number of vertices and C is the maximum absolute value of any edge weight.

For additional documentation, see Section 4.4 of Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.

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

Constructors
Constructor Description
```AcyclicSP​(EdgeWeightedDigraph G, int s)```
Computes a shortest paths tree from `s` to every other vertex in the directed acyclic graph `G`.
• ### Method Summary

All Methods
Modifier and Type Method Description
`double` `distTo​(int v)`
Returns the length of a shortest path from the source vertex `s` to vertex `v`.
`boolean` `hasPathTo​(int v)`
Is there a path from the source vertex `s` to vertex `v`?
`static void` `main​(String[] args)`
Unit tests the `AcyclicSP` data type.
`Iterable<DirectedEdge>` `pathTo​(int v)`
Returns a shortest path from the source vertex `s` to vertex `v`.
• ### Methods inherited from class java.lang.Object

`clone, equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Constructor Detail

• #### AcyclicSP

```public AcyclicSP​(EdgeWeightedDigraph G,
int s)```
Computes a shortest paths tree from `s` to every other vertex in the directed acyclic graph `G`.
Parameters:
`G` - the acyclic digraph
`s` - the source vertex
Throws:
`IllegalArgumentException` - if the digraph is not acyclic
`IllegalArgumentException` - unless `0 <= s < V`
• ### Method Detail

• #### distTo

`public double distTo​(int v)`
Returns the length of a shortest path from the source vertex `s` to vertex `v`.
Parameters:
`v` - the destination vertex
Returns:
the length of a shortest path from the source vertex `s` to vertex `v`; `Double.POSITIVE_INFINITY` if no such path
Throws:
`IllegalArgumentException` - unless `0 <= v < V`
• #### hasPathTo

`public boolean hasPathTo​(int v)`
Is there a path from the source vertex `s` to vertex `v`?
Parameters:
`v` - the destination vertex
Returns:
`true` if there is a path from the source vertex `s` to vertex `v`, and `false` otherwise
Throws:
`IllegalArgumentException` - unless `0 <= v < V`
• #### pathTo

`public Iterable<DirectedEdge> pathTo​(int v)`
Returns a shortest path from the source vertex `s` to vertex `v`.
Parameters:
`v` - the destination vertex
Returns:
a shortest path from the source vertex `s` to vertex `v` as an iterable of edges, and `null` if no such path
Throws:
`IllegalArgumentException` - unless `0 <= v < V`
• #### main

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