CS253: Topological Sort (2019)

https://github.com/emory-courses/cs253/

Transcript

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2. Cycle Detection 2 0 1 2 3 4
3. Cycle Detection 2 0 1 2 3 4
4. Cycle Detection 2 0 1 2 3 4 No incoming edge
5. Cycle Detection 2 0 1 2 3 4 No incoming edge
6. Cycle Detection 2 0 1 2 3 4 No incoming edge
7. Cycle Detection 2 0 1 2 3 4 No incoming edge No cycle
8. Cycle Detection 2 0 1 2 3 4 No incoming edge No cycle
9. Cycle Detection 2 0 1 2 3 4 No incoming edge No cycle
10. Cycle Detection 2 0 1 2 3 4 No incoming edge No cycle
11. Cycle Detection 2 0 1 2 3 4 No incoming edge No cycle No cycle
12. Cycle Detection 2 0 1 2 3 4 No incoming edge No cycle No cycle
13. Cycle Detection 2 0 1 2 3 4 No incoming edge No cycle No cycle
14. Cycle Detection 2 0 1 2 3 4 No incoming edge No cycle No cycle
15. Cycle Detection 2 0 1 2 3 4 No incoming edge No cycle No cycle
16. Cycle Detection 2 0 1 2 3 4 No incoming edge No cycle Cycle! No cycle
17. Cycle Detection 3 public boolean containsCycle() { Deque<Integer> notVisited = new ArrayDeque<>(); for (int i=0; i<size(); i++) notVisited.add(i); while (!notVisited.isEmpty()) { if (containsCycleAux(notVisited.poll(), notVisited, new HashSet<>())) return true; } return false; }
18. Cycle Detection 3 public boolean containsCycle() { Deque<Integer> notVisited = new ArrayDeque<>(); for (int i=0; i<size(); i++) notVisited.add(i); while (!notVisited.isEmpty()) { if (containsCycleAux(notVisited.poll(), notVisited, new HashSet<>())) return true; } return false; } boolean containsCycleAux(int target, Deque<Integer> notVisited, Set<Integer> visited)
19. Cycle Detection 4 private boolean containsCycleAux(int target, Deque<Integer> notVisited,
 Set<Integer> visited) { notVisited.remove(target); visited.add(target); for (Edge edge : getIncomingEdges(target)) { if (visited.contains(edge.getSource())) return true; if (containsCycleAux(edge.getSource(), notVisited, new HashSet<>(visited))) return true; } return false; }
20. Topological Sort 5
21. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first.
22. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7
23. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores
24. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores
25. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores
26. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores
27. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores
28. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores
29. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores
30. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores
31. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores
32. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores Depth-First
33. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores Depth-First
34. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores Depth-First
35. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores Depth-First
36. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores Depth-First
37. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores Depth-First
38. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores Depth-First
39. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores Depth-First
40. Topological Sort 5 Sort vertices in a linear order such that for each vertex, all vertices associated with its incoming edges must appear first. 0 1 2 3 4 5 6 7 Incoming scores Depth-First
41. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7
42. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Keep adding vertices with no incoming edge.
43. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices Keep adding vertices with no incoming edge.
44. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 Keep adding vertices with no incoming edge.
45. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 Keep adding vertices with no incoming edge.
46. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 Keep adding vertices with no incoming edge.
47. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 Keep adding vertices with no incoming edge.
48. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 Keep adding vertices with no incoming edge.
49. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 Keep adding vertices with no incoming edge.
50. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 3 Keep adding vertices with no incoming edge.
51. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 3 Keep adding vertices with no incoming edge.
52. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 3 Keep adding vertices with no incoming edge.
53. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 3 Keep adding vertices with no incoming edge. 4
54. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 3 Keep adding vertices with no incoming edge. 4
55. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 3 Keep adding vertices with no incoming edge. 4
56. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 3 Keep adding vertices with no incoming edge. 4
57. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 3 Keep adding vertices with no incoming edge. 4 5
58. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 3 Keep adding vertices with no incoming edge. 4 5
59. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 3 Keep adding vertices with no incoming edge. 4 5
60. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 3 Keep adding vertices with no incoming edge. 4 5 7
61. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 3 Keep adding vertices with no incoming edge. 4 5 7
62. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 3 Keep adding vertices with no incoming edge. 4 5 7
63. Sort by Incoming Scores 6 0 1 2 3 4 5 6 7 Incoming score of each vertex = Σ of all source vertices 0 1 2 3 Keep adding vertices with no incoming edge. 4 5 6 7
64. public List<Integer> sort(Graph graph) { Deque<Integer> global = graph.getVerticesWithNoIncomingEdges(); Deque<Edge>[] outgoingEdgesAll = graph.getOutgoingEdges(); List<Integer> order = new ArrayList<Integer>(); while (!global.isEmpty()) { Deque<Integer> local = new ArrayDeque<>(); int vertex = global.poll(); order.add(vertex); Deque<Edge> outgoingEdges = outgoingEdgesAll[vertex]; while (!outgoingEdges.isEmpty()) { Edge edge = outgoingEdges.poll(); List<Edge> incomingEdges = graph.getIncomingEdges(edge.getTarget()); incomingEdges.remove(edge); if (incomingEdges.isEmpty()) local.add(edge.getTarget()); } while (!local.isEmpty()) global.addLast(local.removeFirst()); } if (!graph.isEmpty()) throw new IllegalArgumentException("Cyclic graph."); return order; } 7
65. public List<Integer> sort(Graph graph) { Deque<Integer> global = graph.getVerticesWithNoIncomingEdges(); Deque<Edge>[] outgoingEdgesAll = graph.getOutgoingEdges(); List<Integer> order = new ArrayList<Integer>(); while (!global.isEmpty()) { Deque<Integer> local = new ArrayDeque<>(); int vertex = global.poll(); order.add(vertex); Deque<Edge> outgoingEdges = outgoingEdgesAll[vertex]; while (!outgoingEdges.isEmpty()) { Edge edge = outgoingEdges.poll(); List<Edge> incomingEdges = graph.getIncomingEdges(edge.getTarget()); incomingEdges.remove(edge); if (incomingEdges.isEmpty()) local.add(edge.getTarget()); } while (!local.isEmpty()) global.addLast(local.removeFirst()); } if (!graph.isEmpty()) throw new IllegalArgumentException("Cyclic graph."); return order; } 7
66. Sort by Depth-First 8 0 1 2 3 4 5 6 7
67. Sort by Depth-First 8 0 1 2 3 4 5 6 7 Keep adding vertices that are illegible.
68. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 Keep adding vertices that are illegible.
69. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 Keep adding vertices that are illegible.
70. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 Keep adding vertices that are illegible.
71. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 Keep adding vertices that are illegible.
72. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 Keep adding vertices that are illegible.
73. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 Keep adding vertices that are illegible.
74. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 Keep adding vertices that are illegible.
75. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 3 Keep adding vertices that are illegible.
76. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 3 Keep adding vertices that are illegible.
77. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 3 Keep adding vertices that are illegible.
78. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 3 Keep adding vertices that are illegible. 5
79. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 3 Keep adding vertices that are illegible. 5
80. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 3 Keep adding vertices that are illegible. 5
81. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 3 Keep adding vertices that are illegible. 5
82. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 2 3 Keep adding vertices that are illegible. 5
83. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 2 3 Keep adding vertices that are illegible. 5
84. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 2 3 Keep adding vertices that are illegible. 5
85. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 2 3 Keep adding vertices that are illegible. 4 5
86. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 2 3 Keep adding vertices that are illegible. 4 5
87. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 2 3 Keep adding vertices that are illegible. 4 5
88. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 2 3 Keep adding vertices that are illegible. 4 5 6
89. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 2 3 Keep adding vertices that are illegible. 4 5 6
90. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 2 3 Keep adding vertices that are illegible. 4 5 6
91. Sort by Depth-First 8 0 1 2 3 4 5 6 7 0 1 2 3 Keep adding vertices that are illegible. 4 5 6 7
92. public List<Integer> sort(Graph graph) { Deque<Integer> global = graph.getVerticesWithNoIncomingEdges(); Deque<Edge>[] outgoingEdgesAll = graph.getOutgoingEdges(); List<Integer> order = new ArrayList<Integer>(); while (!global.isEmpty()) { Deque<Integer> local = new ArrayDeque<>(); int vertex = global.poll(); order.add(vertex); Deque<Edge> outgoingEdges = outgoingEdgesAll[vertex]; while (!outgoingEdges.isEmpty()) { Edge edge = outgoingEdges.poll(); List<Edge> incomingEdges = graph.getIncomingEdges(edge.getTarget()); incomingEdges.remove(edge); if (incomingEdges.isEmpty()) local.add(edge.getTarget()); } while (!local.isEmpty()) global.addLast(local.removeFirst()); } if (!graph.isEmpty()) throw new IllegalArgumentException("Cyclic graph."); return order; } 9
93. public List<Integer> sort(Graph graph) { Deque<Integer> global = graph.getVerticesWithNoIncomingEdges(); Deque<Edge>[] outgoingEdgesAll = graph.getOutgoingEdges(); List<Integer> order = new ArrayList<Integer>(); while (!global.isEmpty()) { Deque<Integer> local = new ArrayDeque<>(); int vertex = global.poll(); order.add(vertex); Deque<Edge> outgoingEdges = outgoingEdgesAll[vertex]; while (!outgoingEdges.isEmpty()) { Edge edge = outgoingEdges.poll(); List<Edge> incomingEdges = graph.getIncomingEdges(edge.getTarget()); incomingEdges.remove(edge); if (incomingEdges.isEmpty()) local.add(edge.getTarget()); } while (!local.isEmpty()) global.addLast(local.removeFirst()); } if (!graph.isEmpty()) throw new IllegalArgumentException("Cyclic graph."); return order; } 9 global.addFirst(local.removeLast());