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A lot of new additions to algs4, these are the last classes that othe…
…r classes depends on, from now on all other classes have all their dependencies in algs4. Adding: - BreadthFirstPaths - Complex - FordFulkerson - GrahamScan - NFA - SequentialSearchST - SymbolGraph
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,259 @@ | ||
| using System.Collections.Generic; | ||
| using algs4.stdlib; | ||
|
|
||
| namespace algs4.algs4 | ||
| { | ||
| public class BreadthFirstPaths | ||
| { | ||
| private const int Infinity = int.MaxValue; | ||
|
|
||
| /// <summary> | ||
| /// marked[v] = is there an s-v path | ||
| /// </summary> | ||
| private readonly bool[] _marked; | ||
|
|
||
| /// <summary> | ||
| /// edgeTo[v] = previous edge on shortest s-v path | ||
| /// </summary> | ||
| private readonly int[] _edgeTo; | ||
|
|
||
| /// <summary> | ||
| /// distTo[v] = number of edges shortest s-v path | ||
| /// </summary> | ||
| private readonly int[] _distTo; | ||
|
|
||
| /// <summary> | ||
| /// Computes the shortest path between the source vertex s | ||
| /// and every other vertex in the graph G. | ||
| /// </summary> | ||
| /// <param name="g">the graph</param> | ||
| /// <param name="s">the source vertex</param> | ||
| public BreadthFirstPaths(Graph g, int s) | ||
| { | ||
| _marked = new bool[g.V()]; | ||
| _distTo = new int[g.V()]; | ||
| _edgeTo = new int[g.V()]; | ||
| BFS(g, s); | ||
| } | ||
|
|
||
| /// <summary> | ||
| /// Computes the shortest path between any one of the source vertices in sources | ||
| /// and every other vertex in graph G. | ||
| /// </summary> | ||
| /// <param name="g">the graph</param> | ||
| /// <param name="sources">the source vertices</param> | ||
| public BreadthFirstPaths(Graph g, IEnumerable<int> sources) | ||
| { | ||
| _marked = new bool[g.V()]; | ||
| _distTo = new int[g.V()]; | ||
| _edgeTo = new int[g.V()]; | ||
| for (int v = 0; v < g.V(); v++) | ||
| { | ||
| _distTo[v] = Infinity; | ||
| } | ||
| BFS(g, sources); | ||
| } | ||
|
|
||
| /// <summary> | ||
| /// Breadth-first search from a single source | ||
| /// </summary> | ||
| /// <param name="g"></param> | ||
| /// <param name="s"></param> | ||
| private void BFS(Graph g, int s) | ||
| { | ||
| Queue<int> q = new Queue<int>(); | ||
| for (int v = 0; v < g.V(); v++) | ||
| { | ||
| _distTo[v] = Infinity; | ||
| } | ||
| _distTo[s] = 0; | ||
| _marked[s] = true; | ||
| q.Enqueue(s); | ||
|
|
||
| while (!q.IsEmpty()) | ||
| { | ||
| int v = q.Dequeue(); | ||
| foreach (int w in g.Adj(v)) | ||
| { | ||
| if (!_marked[w]) | ||
| { | ||
| _edgeTo[w] = v; | ||
| _distTo[w] = _distTo[v] + 1; | ||
| _marked[w] = true; | ||
| q.Enqueue(w); | ||
| } | ||
| } | ||
| } | ||
| } | ||
|
|
||
| /// <summary> | ||
| /// Breadth-first search from multiple sources | ||
| /// </summary> | ||
| /// <param name="g"></param> | ||
| /// <param name="sources"></param> | ||
| private void BFS(Graph g, IEnumerable<int> sources) | ||
| { | ||
| Queue<int> q = new Queue<int>(); | ||
| foreach (int s in sources) | ||
| { | ||
| _marked[s] = true; | ||
| _distTo[s] = 0; | ||
| q.Enqueue(s); | ||
| } | ||
| while (!q.IsEmpty()) | ||
| { | ||
| int v = q.Dequeue(); | ||
| foreach (int w in g.Adj(v)) | ||
| { | ||
| if (!_marked[w]) | ||
| { | ||
| _edgeTo[w] = v; | ||
| _distTo[w] = _distTo[v] + 1; | ||
| _marked[w] = true; | ||
| q.Enqueue(w); | ||
| } | ||
| } | ||
| } | ||
| } | ||
|
|
||
| /// <summary> | ||
| /// Is there a path between the source vertex s (or sources) and vertex v? | ||
| /// </summary> | ||
| /// <param name="v">the vertex</param> | ||
| /// <returns>true if there is a path, and false otherwise</returns> | ||
| public bool HasPathTo(int v) | ||
| { | ||
| return _marked[v]; | ||
| } | ||
|
|
||
| /// <summary> | ||
| /// Returns the number of edges in a shortest path between the source vertex s | ||
| /// (or sources) and vertex v? | ||
| /// </summary> | ||
| /// <param name="v">the vertex</param> | ||
| /// <returns>the number of edges in a shortest path</returns> | ||
| public int DistTo(int v) | ||
| { | ||
| return _distTo[v]; | ||
| } | ||
|
|
||
| /// <summary> | ||
| /// Returns a shortest path between the source vertex s (or sources) | ||
| /// and v, or null if no such path. | ||
| /// </summary> | ||
| /// <param name="v">the vertex</param> | ||
| /// <returns>the sequence of vertices on a shortest path, as an IEnumerable</returns> | ||
| public IEnumerable<int> PathTo(int v) | ||
| { | ||
| if (!HasPathTo(v)) | ||
| { | ||
| return null; | ||
| } | ||
| Stack<int> path = new Stack<int>(); | ||
| int x; | ||
| for (x = v; _distTo[x] != 0; x = _edgeTo[x]) | ||
| { | ||
| path.Push(x); | ||
| } | ||
| path.Push(x); | ||
| return path; | ||
| } | ||
|
|
||
| /// <summary> | ||
| /// Check optimality conditions for single source | ||
| /// </summary> | ||
| /// <param name="g"></param> | ||
| /// <param name="s"></param> | ||
| /// <returns></returns> | ||
| public bool Check(Graph g, int s) | ||
| { | ||
| // check that the distance of s = 0 | ||
| if (_distTo[s] != 0) | ||
| { | ||
| StdOut.PrintLn("distance of source " + s + " to itself = " + _distTo[s]); | ||
| return false; | ||
| } | ||
|
|
||
| // check that for each edge v-w dist[w] <= dist[v] + 1 | ||
| // provided v is reachable from s | ||
| for (int v = 0; v < g.V(); v++) | ||
| { | ||
| foreach (int w in g.Adj(v)) | ||
| { | ||
| if (HasPathTo(v) != HasPathTo(w)) | ||
| { | ||
| StdOut.PrintLn("edge " + v + "-" + w); | ||
| StdOut.PrintLn("hasPathTo(" + v + ") = " + HasPathTo(v)); | ||
| StdOut.PrintLn("hasPathTo(" + w + ") = " + HasPathTo(w)); | ||
| return false; | ||
| } | ||
| if (HasPathTo(v) && (_distTo[w] > _distTo[v] + 1)) | ||
| { | ||
| StdOut.PrintLn("edge " + v + "-" + w); | ||
| StdOut.PrintLn("distTo[" + v + "] = " + _distTo[v]); | ||
| StdOut.PrintLn("distTo[" + w + "] = " + _distTo[w]); | ||
| return false; | ||
| } | ||
| } | ||
| } | ||
|
|
||
| // check that v = edgeTo[w] satisfies distTo[w] + distTo[v] + 1 | ||
| // provided v is reachable from s | ||
| for (int w = 0; w < g.V(); w++) | ||
| { | ||
| if (!HasPathTo(w) || w == s) | ||
| { | ||
| continue; | ||
| } | ||
| int v = _edgeTo[w]; | ||
| if (_distTo[w] != _distTo[v] + 1) | ||
| { | ||
| StdOut.PrintLn("shortest path edge " + v + "-" + w); | ||
| StdOut.PrintLn("distTo[" + v + "] = " + _distTo[v]); | ||
| StdOut.PrintLn("distTo[" + w + "] = " + _distTo[w]); | ||
| return false; | ||
| } | ||
| } | ||
|
|
||
| return true; | ||
| } | ||
|
|
||
| /// <summary> | ||
| /// Unit tests the BreadthFirstPaths data type. | ||
| /// </summary> | ||
| /// <param name="args"></param> | ||
| public static void RunMain(string[] args) | ||
| { | ||
| In input = new In(args[0]); | ||
| Graph g = new Graph(input); | ||
|
|
||
| int s = int.Parse(args[1]); | ||
| BreadthFirstPaths bfs = new BreadthFirstPaths(g, s); | ||
|
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| for (int v = 0; v < g.V(); v++) | ||
| { | ||
| if (bfs.HasPathTo(v)) | ||
| { | ||
| StdOut.PrintF("{0} to {1} ({2}): ", s, v, bfs.DistTo(v)); | ||
| foreach (int x in bfs.PathTo(v)) | ||
| { | ||
| if (x == s) | ||
| { | ||
| StdOut.Print(x); | ||
| } | ||
| else | ||
| { | ||
| StdOut.Print("-" + x); | ||
| } | ||
| } | ||
| StdOut.PrintLn(); | ||
| } | ||
|
|
||
| else | ||
| { | ||
| StdOut.PrintF("{0} to {1} (-): not connected\n", s, v); | ||
| } | ||
| } | ||
| } | ||
| } | ||
| } |
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