深度优先搜索DFS-图
深度优先搜索的代码：
public class DepthFirstSearch { private boolean[] marked; // marked[v] = is there an s-v path? private int count; // number of vertices connected to s public DepthFirstSearch(Graph G, int s) { marked = new boolean[G.V()]; validateVertex(s); dfs(G, s); } // depth first search from v private void dfs(Graph G, int v) { count++; marked[v] = true; for (int w : G.adj(v)) { if (!marked[w]) { dfs(G, w); } } } public boolean marked(int v) { validateVertex(v); return marked[v]; } public int count() { return count; } private void validateVertex(int v) { int V = marked.length; if (v < 0 || v >= V) throw new IllegalArgumentException("vertex " + v + " is not between 0 and " + (V-1)); } public static void main(String[] args) { In in = new In(args[0]); Graph G = new Graph(in); int s = Integer.parseInt(args[1]); DepthFirstSearch search = new DepthFirstSearch(G, s); for (int v = 0; v < G.V(); v++) { if (search.marked(v)) StdOut.print(v + " "); } StdOut.println(); if (search.count() != G.V()) StdOut.println("NOT connected"); else StdOut.println("connected"); } }
深度优先搜索查找图中的路径：
public class BreadthFirstPaths { private static final int INFINITY = Integer.MAX_VALUE; private boolean[] marked; // marked[v] = is there an s-v path private int[] edgeTo; // edgeTo[v] = previous edge on shortest s-v path private int[] distTo; // distTo[v] = number of edges shortest s-v path /** * Computes the shortest path between the source vertex {@code s} * and every other vertex in the graph {@code G}. * @param G the graph * @param s the source vertex * @throws IllegalArgumentException unless {@code 0 <= s < V} */ public BreadthFirstPaths(Graph G, int s) { marked = new boolean[G.V()]; distTo = new int[G.V()]; edgeTo = new int[G.V()]; validateVertex(s); bfs(G, s); assert check(G, s); } /** * Computes the shortest path between any one of the source vertices in {@code sources} * and every other vertex in graph {@code G}. * @param G the graph * @param sources the source vertices * @throws IllegalArgumentException if {@code sources} is {@code null} * @throws IllegalArgumentException unless {@code 0 <= s < V} for each vertex * {@code s} in {@code sources} */ public BreadthFirstPaths(Graph G, Iterable<Integer> sources) { marked = new boolean[G.V()]; distTo = new int[G.V()]; edgeTo = new int[G.V()]; for (int v = 0; v < G.V(); v++) distTo[v] = INFINITY; validateVertices(sources); bfs(G, sources); } // breadth-first search from a single source private void bfs(Graph G, int s) { Queue<Integer> q = new Queue<Integer>(); 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(); for (int w : G.adj(v)) { if (!marked[w]) { edgeTo[w] = v; distTo[w] = distTo[v] + 1; marked[w] = true; q.enqueue(w); } } } } // breadth-first search from multiple sources private void bfs(Graph G, Iterable<Integer> sources) { Queue<Integer> q = new Queue<Integer>(); for (int s : sources) { marked[s] = true; distTo[s] = 0; q.enqueue(s); } while (!q.isEmpty()) { int v = q.dequeue(); for (int w : G.adj(v)) { if (!marked[w]) { edgeTo[w] = v; distTo[w] = distTo[v] + 1; marked[w] = true; q.enqueue(w); } } } } /** * Is there a path between the source vertex {@code s} (or sources) and vertex {@code v}? * @param v the vertex * @return {@code true} if there is a path, and {@code false} otherwise * @throws IllegalArgumentException unless {@code 0 <= v < V} */ public boolean hasPathTo(int v) { validateVertex(v); return marked[v]; } /** * Returns the number of edges in a shortest path between the source vertex {@code s} * (or sources) and vertex {@code v}? * @param v the vertex * @return the number of edges in a shortest path * @throws IllegalArgumentException unless {@code 0 <= v < V} */ public int distTo(int v) { validateVertex(v); return distTo[v]; } /** * Returns a shortest path between the source vertex {@code s} (or sources) * and {@code v}, or {@code null} if no such path. * @param v the vertex * @return the sequence of vertices on a shortest path, as an Iterable * @throws IllegalArgumentException unless {@code 0 <= v < V} */ public Iterable<Integer> pathTo(int v) { validateVertex(v); if (!hasPathTo(v)) return null; Stack<Integer> path = new Stack<Integer>(); int x; for (x = v; distTo[x] != 0; x = edgeTo[x]) path.push(x); path.push(x); return path; } // check optimality conditions for single source private boolean 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++) { for (int w : 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; } // throw an IllegalArgumentException unless {@code 0 <= v < V} private void validateVertex(int v) { int V = marked.length; if (v < 0 || v >= V) throw new IllegalArgumentException("vertex " + v + " is not between 0 and " + (V-1)); } // throw an IllegalArgumentException unless {@code 0 <= v < V} private void validateVertices(Iterable<Integer> vertices) { if (vertices == null) { throw new IllegalArgumentException("argument is null"); } for (Integer v : vertices) { if (v == null) { throw new IllegalArgumentException("vertex is null"); } validateVertex(v); } } /** * Unit tests the {@code BreadthFirstPaths} data type. * * @param args the command-line arguments */ public static void main(String[] args) { In in = new In(args[0]); Graph G = new Graph(in); // StdOut.println(G); int s = Integer.parseInt(args[1]); BreadthFirstPaths bfs = new BreadthFirstPaths(G, s); for (int v = 0; v < G.V(); v++) { if (bfs.hasPathTo(v)) { StdOut.printf("%d to %d (%d): ", s, v, bfs.distTo(v)); for (int x : bfs.pathTo(v)) { if (x == s) StdOut.print(x); else StdOut.print("-" + x); } StdOut.println(); } else { StdOut.printf("%d to %d (-): not connected\n", s, v); } } } }
