▶ 书中第四章部分程序，包括在加上自己补充的代码，图中找欧拉路径
● 无向图中寻找欧拉路径，只注释了与欧拉环不同的地方
1 package package01; 2 3 import edu.princeton.cs.algs4.StdOut; 4 import edu.princeton.cs.algs4.StdRandom; 5 import edu.princeton.cs.algs4.GraphGenerator; 6 import edu.princeton.cs.algs4.Graph; 7 import edu.princeton.cs.algs4.Stack; 8 import edu.princeton.cs.algs4.Queue; 9 import edu.princeton.cs.algs4.BreadthFirstPaths; 10 11 public class class01 12 { 13 private Stack<Integer> cycle = new Stack<Integer>(); 14 15 private static class Edge 16 { 17 private final int v; 18 private final int w; 19 private boolean isUsed; 20 21 public Edge(int v, int w) 22 { 23 this.v = v; 24 this.w = w; 25 isUsed = false; 26 } 27 28 public int other(int vertex) 29 { 30 if (vertex == v) 31 return w; 32 if (vertex == w) 33 return v; 34 throw new IllegalArgumentException(" <other> No such vertex. "); 35 } 36 } 37 38 public class01(Graph G) 39 { 40 if (G.E() == 0) 41 return; 42 int oddDegreeVertices = 0; // 记录奇数度点的数量 43 int s = nonIsolatedVertex(G); // 选一个非孤立点为起点，有奇数度点的话要更换 44 if (G.E() == 0) // 认为无边的图也存在欧拉路径，这与欧拉环不同 45 s = 0; 46 else // 其他情况照常处理 47 { 48 for (int v = 0; v < G.V(); v++) 49 { 50 if (G.degree(v) % 2 != 0) 51 { 52 oddDegreeVertices++; 53 s = v; 54 } 55 } 56 if (oddDegreeVertices > 2) // 奇数度点多于 2，不存在欧拉路径 57 return; 58 Queue<Edge>[] adj = (Queue<Edge>[]) new Queue[G.V()]; 59 for (int v = 0; v < G.V(); v++) 60 adj[v] = new Queue<Edge>(); 61 for (int v = 0; v < G.V(); v++) 62 { 63 boolean selfEdge = false; 64 for (int w : G.adj(v)) 65 { 66 if (v == w) 67 { 68 if (!selfEdge) 69 { 70 Edge e = new Edge(v, w); 71 adj[v].enqueue(e); 72 adj[w].enqueue(e); 73 } 74 selfEdge = !selfEdge; 75 } 76 else if (v < w) 77 { 78 Edge e = new Edge(v, w); 79 adj[v].enqueue(e); 80 adj[w].enqueue(e); 81 } 82 } 83 } 84 } 85 Stack<Integer> stack = new Stack<Integer>(); 86 stack.push(s); 87 for (path = new Stack<Integer>(); !stack.isEmpty();) 88 { 89 int v = stack.pop(); 90 for (; !adj[v].isEmpty();) 91 { 92 Edge edge = adj[v].dequeue(); 93 if (edge.isUsed) 94 continue; 95 edge.isUsed = true; 96 stack.push(v); 97 v = edge.other(v); 98 } 99 path.push(v); 100 } 101 if (path.size() != G.E() + 1) 102 path = null; 103 } 104 105 public Iterable<Integer> path() 106 { 107 return path; 108 } 109 110 public boolean hasEulerianPath() 111 { 112 return path != null; 113 } 114 115 private static int nonIsolatedVertex(Graph G) 116 { 117 for (int v = 0; v < G.V(); v++) 118 { 119 if (G.degree(v) > 0) 120 return v; 121 } 122 return -1; 123 } 124 125 private static boolean satisfiesNecessaryAndSufficientConditions(Graph G) 126 { 127 if (G.E() == 0) // 认为没有变的图也有欧拉路径，统计奇数度的顶点 128 return true; 129 int oddDegreeVertices = 0; 130 for (int v = 0; v < G.V(); v++) 131 { 132 if (G.degree(v) % 2 != 0) 133 oddDegreeVertices++; 134 } 135 if (oddDegreeVertices > 2) 136 return false; 137 BreadthFirstPaths bfs = new BreadthFirstPaths(G, nonIsolatedVertex(G)); 138 for (int v = 0; v < G.V(); v++) 139 { 140 if (G.degree(v) > 0 && !bfs.hasPathTo(v)) 141 return false; 142 } 143 return true; 144 } 145 146 private static void unitTest(Graph G, String description) 147 { 148 System.out.printf(" %s-------------------------------- ", description); 149 StdOut.print(G); 150 class01 euler = new class01(G); 151 System.out.printf("Eulerian path: "); 152 if (euler.hasEulerianCycle()) 153 { 154 for (int v : euler.cycle()) 155 System.out.printf(" %d", v); 156 } 157 System.out.println(); 158 } 159 160 public static void main(String[] args) 161 { 162 int V = Integer.parseInt(args[0]); 163 int E = Integer.parseInt(args[1]); 164 165 Graph G1 = GraphGenerator.eulerianCycle(V, E); 166 unitTest(G1, "Eulerian cycle"); 167 168 Graph G2 = GraphGenerator.eulerianPath(V, E); 169 unitTest(G2, "Eulerian path"); 170 171 Graph G3 = new Graph(G2); 172 G3.addEdge(StdRandom.uniform(V), StdRandom.uniform(V)); 173 unitTest(G3, "one random edge added to Eulerian path"); 174 175 Graph G4 = new Graph(V); 176 int v4 = StdRandom.uniform(V); 177 G4.addEdge(v4, v4); 178 unitTest(G4, "single self loop"); 179 180 Graph G5 = new Graph(V); 181 G5.addEdge(StdRandom.uniform(V), StdRandom.uniform(V)); 182 unitTest(G5, "single edge"); 183 184 Graph G6 = new Graph(V); 185 unitTest(G6, "empty graph"); 186 187 Graph G7 = GraphGenerator.simple(V, E); 188 unitTest(G7, "simple graph"); 189 } 190 }
● 有向图中寻找欧拉路径，只注释了与欧拉环以及无向图欧拉路径不同的地方
1 package package01; 2 3 import java.util.Iterator; 4 import edu.princeton.cs.algs4.StdOut; 5 import edu.princeton.cs.algs4.StdRandom; 6 import edu.princeton.cs.algs4.DigraphGenerator; 7 import edu.princeton.cs.algs4.Graph; 8 import edu.princeton.cs.algs4.Digraph; 9 import edu.princeton.cs.algs4.Stack; 10 import edu.princeton.cs.algs4.BreadthFirstPaths; 11 12 public class class01 13 { 14 private Stack<Integer> path = null; 15 16 public class01(Digraph G) 17 { 18 int s = nonIsolatedVertex(G); 19 if (s == -1) // 没有边 20 s = 0; 21 else 22 { 23 int deficit = 0; // 统计所有顶点总出度与总入度的差 24 for (int v = 0; v < G.V(); v++) 25 { 26 if (G.outdegree(v) > G.indegree(v)) // 计算 deficit 不能直接加总出度和入度的差 27 { // 因为平行边不影响 G.outdegree(v) - G.indegree(v)，但会导致不存在欧拉路径 28 deficit += (G.outdegree(v) - G.indegree(v)); 29 s = v; 30 } 31 } 32 if (deficit > 1) // 差大于 1 则不存在欧拉路径 33 return; 34 } 35 path = new Stack<Integer>(); 36 Iterator<Integer>[] adj = (Iterator<Integer>[]) new Iterator[G.V()]; 37 for (int v = 0; v < G.V(); v++) 38 adj[v] = G.adj(v).iterator(); 39 Stack<Integer> stack = new Stack<Integer>(); 40 for (stack.push(s); !stack.isEmpty(); ) 41 { 42 int v = stack.pop(); 43 for (; adj[v].hasNext(); v = adj[v].next()) 44 stack.push(v); 45 path.push(v); 46 } 47 if (path.size() != G.E() + 1) 48 path = null; 49 } 50 51 public Iterable<Integer> path() 52 { 53 return path; 54 } 55 56 public boolean hasEulerianPath() 57 { 58 return path != null; 59 } 60 61 private static int nonIsolatedVertex(Digraph G) 62 { 63 for (int v = 0; v < G.V(); v++) 64 { 65 if (G.outdegree(v) > 0) 66 return v; 67 } 68 return -1; 69 } 70 71 private static boolean satisfiesNecessaryAndSufficientConditions(Digraph G) 72 { 73 if (G.E() == 0) 74 return true; 75 int deficit = 0; 76 for (int v = 0; v < G.V(); v++) 77 { 78 if (G.outdegree(v) > G.indegree(v)) 79 deficit += (G.outdegree(v) - G.indegree(v)); 80 } 81 if (deficit > 1) 82 return false; 83 Graph H = new Graph(G.V()); 84 for (int v = 0; v < G.V(); v++) 85 { 86 for (int w : G.adj(v)) 87 H.addEdge(v, w); 88 } 89 BreadthFirstPaths bfs = new BreadthFirstPaths(H, nonIsolatedVertex(G)); 90 for (int v = 0; v < G.V(); v++) 91 { 92 if (H.degree(v) > 0 && !bfs.hasPathTo(v)) 93 return false; 94 } 95 return true; 96 } 97 98 private static void unitTest(Digraph G, String description) 99 { 100 System.out.printf(" %s-------------------------------- ", description); 101 StdOut.print(G); 102 class01 euler = new class01(G); 103 System.out.printf("Eulerian path: "); 104 if (euler.hasEulerianPath()) 105 { 106 for (int v : euler.path()) 107 System.out.printf(" %d", v); 108 } 109 StdOut.println(); 110 } 111 112 public static void main(String[] args) 113 { 114 int V = Integer.parseInt(args[0]); 115 int E = Integer.parseInt(args[1]); 116 117 Digraph G1 = DigraphGenerator.eulerianCycle(V, E); 118 unitTest(G1, "Eulerian cycle"); 119 120 Digraph G2 = DigraphGenerator.eulerianPath(V, E); 121 unitTest(G2, "Eulerian path"); 122 123 Digraph G3 = new Digraph(G2); 124 G3.addEdge(StdRandom.uniform(V), StdRandom.uniform(V)); 125 unitTest(G3, "one random edge added to Eulerian path"); 126 127 Digraph G4 = new Digraph(V); 128 int v4 = StdRandom.uniform(V); 129 G4.addEdge(v4, v4); 130 unitTest(G4, "single self loop"); 131 132 Digraph G5 = new Digraph(V); 133 G5.addEdge(StdRandom.uniform(V), StdRandom.uniform(V)); 134 unitTest(G5, "single edge"); 135 136 Digraph G6 = new Digraph(V); 137 unitTest(G6, "empty digraph"); 138 139 Digraph G7 = DigraphGenerator.simple(V, E); 140 unitTest(G7, "simple digraph"); 141 } 142 }