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广度优先搜索

定义

给定一幅图和一个起点S，找到从S到给定目的顶点V的一条最短路径。

使用一个队列来保存所有已经被标记过但其邻接表还未被检查过的顶点。先将顶点加入队列，然后重复以下步骤直到队列为空：

  • 取队列中的下一个顶点V并标记它。
  • 将与V相邻的所有未被标记过的顶点加入队列。

代码

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

    public BreadthFirstPaths(Graph G, int s) {
        marked = new boolean[G.V()];
        distTo = new int[G.V()];
        edgeTo = new int[G.V()];
        bfs(G, s);
    }

    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);
                }
            }
        }
    }

    public boolean hasPathTo(int v) {
        return marked[v];
    }

    public int distTo(int v) {
        return distTo[v];
    }

    public Iterable<Integer> pathTo(int 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;
    }
}

轨迹图