``` 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056 057 058 059 060 061 062 063 064 065 066 067 068 069 070 071 072 073 074 075 076 077 078 079 080 081 082 083 084 085 086 087 088 089 090 091 092 093 094 095 096 097 098 099 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 ``` ```// Exercise 4.2.39 (Solution published at http://algs4.cs.princeton.edu/) package algs42; import stdlib.*; import algs13.Queue; /* *********************************************************************** * Compilation: javac TopologicalQueue.java * Execution: java TopologicalQueue V E F * Dependencies: Queue.java * * Compute topological ordering of a DAG using queue-based algorithm. * Runs in O(E + V) time. * * *************************************************************************/ public class XTopologicalQueue { private final Queue order; // vertices in topological order private final int[] indegree; // indegree[v] = indegree of vertex v private final int[] rank; // rank[v] = order where vertex v appers in order private int count; // for computing the ranks public XTopologicalQueue(Digraph G) { indegree = new int[G.V()]; rank = new int[G.V()]; order = new Queue<>(); // compute indegrees for (int v = 0; v < G.V(); v++) { for (int w : G.adj(v)) { indegree[w]++; } } // initialize queue to contain all vertices with indegree = 0 Queue queue = new Queue<>(); for (int v = 0; v < G.V(); v++) if (indegree[v] == 0) queue.enqueue(v); while (!queue.isEmpty()) { int v = queue.dequeue(); order.enqueue(v); rank[v] = count++; for (int w : G.adj(v)) { indegree[w]--; if (indegree[w] == 0) queue.enqueue(w); } } } // is G a directed acyclic graph? public boolean isDAG() { for (int element : indegree) if (element != 0) return false; return true; } // the vertices in topological order (assuming G is a DAG) public Iterable order() { return order; } // the rank of vertex v in topological order public int rank(int v) { return rank[v]; } // certify that digraph is acyclic private boolean check(Digraph G) { // digraph is acyclic if (isDAG()) { // check that ranks are a permutation of 0 to V-1 boolean[] found = new boolean[G.V()]; for (int i = 0; i < G.V(); i++) { found[rank(i)] = true; } for (int i = 0; i < G.V(); i++) { if (!found[i]) { System.err.println("No vertex with rank " + i); return false; } } // check that ranks provide a valid toplogical order for (int v = 0; v < G.V(); v++) { for (int w : G.adj(v)) { if (rank(v) > rank(w)) { System.err.format("%d-%d: rank(%d) = %d, rank(%d) = %d\n", v, w, v, rank(v), w, rank(w)); return false; } } } // check that order() is consistent with rank() int r = 0; for (int v : order()) { if (rank(v) != r) { System.err.println("order() and rank() inconsistent"); return false; } r++; } } return true; } public static void main(String[] args) { args = new String[] { "10", "20", "2" }; // create random DAG with V vertices and E edges; then add F random edges int V = Integer.parseInt(args[0]); int E = Integer.parseInt(args[1]); int F = Integer.parseInt(args[2]); Digraph G = new Digraph(V); int[] vertices = new int[V]; for (int i = 0; i < V; i++) vertices[i] = i; StdRandom.shuffle(vertices); for (int i = 0; i < E; i++) { int v, w; do { v = StdRandom.uniform(V); w = StdRandom.uniform(V); } while (v >= w); G.addEdge(vertices[v], vertices[w]); } // add F extra edges for (int i = 0; i < F; i++) { int v = (int) (Math.random() * V); int w = (int) (Math.random() * V); G.addEdge(v, w); } StdOut.println(G); // find a directed cycle XTopologicalQueue topological = new XTopologicalQueue(G); if (!topological.isDAG()) { StdOut.println("Not a DAG"); } // or give topologial sort else { StdOut.print("Topological order: "); for (int v : topological.order()) { StdOut.print(v + " "); } StdOut.println(); } } } ```