Question:
In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 4
node 0 should be visited before node 1
node 2 should be visited before node 1
node 3 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.
Since visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.
Since visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.
Since visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.

In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 1
node 1 should be visited before node 2
node 3 should be visited before node 1
node 3 should be visited before node 2
node 4 should be visited before node 3
node 4 should be visited before node 0
node 4 should be visited before node 1
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 4, node 4 can be visited first.
Since visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.
Since visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 3
node 1 should be visited before node 2
node 3 should be visited before node 2
node 4 should be visited before node 1
node 4 should be visited before node 2
node 5 should be visited before node 1
node 5 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.
Since visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.
Since visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 5
node 1 should be visited before node 2
node 1 should be visited before node 0
node 3 should be visited before node 0
node 3 should be visited before node 5
node 4 should be visited before node 3
node 4 should be visited before node 2
node 4 should be visited before node 0
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.
Since visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.
Since visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.
Since visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.
Since visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.

In a directed graph with 7 nodes numbered from 0 to 6:
node 0 should be visited before node 6
node 2 should be visited before node 0
node 2 should be visited before node 5
node 4 should be visited before node 1
node 4 should be visited before node 3
node 6 should be visited before node 3
node 6 should be visited before node 5
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.
Since visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.
Since visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.
Since visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.
Since visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.
Since visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.

In a directed graph with 31 nodes numbered from 0 to 30:
node 0 should be visited before node 7
node 1 should be visited before node 20
node 1 should be visited before node 30
node 1 should be visited before node 15
node 1 should be visited before node 6
node 1 should be visited before node 21
node 1 should be visited before node 28
node 1 should be visited before node 29
node 1 should be visited before node 19
node 1 should be visited before node 11
node 1 should be visited before node 0
node 1 should be visited before node 7
node 2 should be visited before node 27
node 2 should be visited before node 1
node 2 should be visited before node 4
node 2 should be visited before node 10
node 2 should be visited before node 21
node 2 should be visited before node 5
node 2 should be visited before node 29
node 2 should be visited before node 8
node 2 should be visited before node 19
node 2 should be visited before node 11
node 3 should be visited before node 18
node 3 should be visited before node 27
node 3 should be visited before node 30
node 3 should be visited before node 9
node 3 should be visited before node 4
node 3 should be visited before node 15
node 3 should be visited before node 21
node 3 should be visited before node 28
node 3 should be visited before node 14
node 3 should be visited before node 29
node 3 should be visited before node 8
node 3 should be visited before node 13
node 3 should be visited before node 7
node 4 should be visited before node 10
node 4 should be visited before node 6
node 4 should be visited before node 23
node 4 should be visited before node 28
node 4 should be visited before node 5
node 4 should be visited before node 29
node 4 should be visited before node 13
node 4 should be visited before node 0
node 4 should be visited before node 7
node 5 should be visited before node 29
node 5 should be visited before node 19
node 5 should be visited before node 13
node 6 should be visited before node 23
node 6 should be visited before node 28
node 6 should be visited before node 14
node 6 should be visited before node 8
node 6 should be visited before node 19
node 6 should be visited before node 13
node 6 should be visited before node 11
node 8 should be visited before node 13
node 8 should be visited before node 7
node 9 should be visited before node 6
node 9 should be visited before node 28
node 9 should be visited before node 13
node 9 should be visited before node 0
node 9 should be visited before node 7
node 10 should be visited before node 21
node 10 should be visited before node 28
node 10 should be visited before node 14
node 10 should be visited before node 29
node 10 should be visited before node 8
node 10 should be visited before node 11
node 12 should be visited before node 22
node 12 should be visited before node 24
node 12 should be visited before node 17
node 12 should be visited before node 3
node 12 should be visited before node 18
node 12 should be visited before node 16
node 12 should be visited before node 2
node 12 should be visited before node 27
node 12 should be visited before node 20
node 12 should be visited before node 30
node 12 should be visited before node 4
node 12 should be visited before node 28
node 12 should be visited before node 5
node 12 should be visited before node 14
node 12 should be visited before node 13
node 12 should be visited before node 0
node 12 should be visited before node 7
node 13 should be visited before node 11
node 14 should be visited before node 8
node 14 should be visited before node 19
node 14 should be visited before node 13
node 14 should be visited before node 0
node 15 should be visited before node 23
node 15 should be visited before node 28
node 15 should be visited before node 5
node 15 should be visited before node 29
node 15 should be visited before node 8
node 15 should be visited before node 13
node 15 should be visited before node 11
node 16 should be visited before node 27
node 16 should be visited before node 30
node 16 should be visited before node 9
node 16 should be visited before node 4
node 16 should be visited before node 10
node 16 should be visited before node 6
node 16 should be visited before node 21
node 16 should be visited before node 23
node 16 should be visited before node 28
node 16 should be visited before node 5
node 16 should be visited before node 19
node 16 should be visited before node 11
node 16 should be visited before node 0
node 17 should be visited before node 3
node 17 should be visited before node 18
node 17 should be visited before node 25
node 17 should be visited before node 2
node 17 should be visited before node 1
node 17 should be visited before node 20
node 17 should be visited before node 9
node 17 should be visited before node 4
node 17 should be visited before node 6
node 17 should be visited before node 21
node 17 should be visited before node 28
node 17 should be visited before node 5
node 17 should be visited before node 14
node 17 should be visited before node 29
node 17 should be visited before node 8
node 17 should be visited before node 19
node 17 should be visited before node 11
node 17 should be visited before node 0
node 18 should be visited before node 25
node 18 should be visited before node 2
node 18 should be visited before node 27
node 18 should be visited before node 20
node 18 should be visited before node 4
node 18 should be visited before node 10
node 18 should be visited before node 6
node 18 should be visited before node 28
node 18 should be visited before node 14
node 18 should be visited before node 29
node 18 should be visited before node 13
node 18 should be visited before node 11
node 19 should be visited before node 11
node 20 should be visited before node 30
node 20 should be visited before node 9
node 20 should be visited before node 15
node 20 should be visited before node 10
node 20 should be visited before node 6
node 20 should be visited before node 21
node 20 should be visited before node 29
node 20 should be visited before node 8
node 20 should be visited before node 19
node 20 should be visited before node 0
node 20 should be visited before node 7
node 21 should be visited before node 23
node 21 should be visited before node 28
node 21 should be visited before node 14
node 21 should be visited before node 13
node 21 should be visited before node 11
node 22 should be visited before node 24
node 22 should be visited before node 25
node 22 should be visited before node 16
node 22 should be visited before node 27
node 22 should be visited before node 1
node 22 should be visited before node 30
node 22 should be visited before node 9
node 22 should be visited before node 4
node 22 should be visited before node 15
node 22 should be visited before node 6
node 22 should be visited before node 21
node 22 should be visited before node 5
node 22 should be visited before node 14
node 22 should be visited before node 8
node 22 should be visited before node 19
node 22 should be visited before node 0
node 22 should be visited before node 7
node 23 should be visited before node 28
node 23 should be visited before node 5
node 23 should be visited before node 14
node 23 should be visited before node 19
node 23 should be visited before node 13
node 23 should be visited before node 11
node 24 should be visited before node 17
node 24 should be visited before node 3
node 24 should be visited before node 2
node 24 should be visited before node 27
node 24 should be visited before node 20
node 24 should be visited before node 30
node 24 should be visited before node 4
node 24 should be visited before node 15
node 24 should be visited before node 10
node 24 should be visited before node 6
node 24 should be visited before node 21
node 24 should be visited before node 23
node 24 should be visited before node 28
node 24 should be visited before node 0
node 24 should be visited before node 7
node 25 should be visited before node 16
node 25 should be visited before node 27
node 25 should be visited before node 4
node 25 should be visited before node 15
node 25 should be visited before node 28
node 25 should be visited before node 14
node 25 should be visited before node 29
node 25 should be visited before node 13
node 25 should be visited before node 7
node 26 should be visited before node 18
node 26 should be visited before node 25
node 26 should be visited before node 16
node 26 should be visited before node 2
node 26 should be visited before node 4
node 26 should be visited before node 21
node 26 should be visited before node 23
node 26 should be visited before node 8
node 26 should be visited before node 0
node 26 should be visited before node 7
node 27 should be visited before node 30
node 27 should be visited before node 4
node 27 should be visited before node 6
node 27 should be visited before node 28
node 27 should be visited before node 19
node 27 should be visited before node 13
node 27 should be visited before node 11
node 27 should be visited before node 0
node 27 should be visited before node 7
node 28 should be visited before node 14
node 28 should be visited before node 29
node 28 should be visited before node 8
node 28 should be visited before node 0
node 28 should be visited before node 7
node 29 should be visited before node 11
node 30 should be visited before node 9
node 30 should be visited before node 4
node 30 should be visited before node 15
node 30 should be visited before node 5
node 30 should be visited before node 29
node 30 should be visited before node 8
node 30 should be visited before node 19
node 30 should be visited before node 0
node 30 should be visited before node 7
Q: Can all the nodes be visited? Give the solution.
A:

Answer: The solution is: 12,26,22,24,17,3,18,25,2,16,1,27,20,30,9,4,15,10,6,21,23,28,5,14,29,8,19,0,13,7,11.


Question:
In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 4
node 0 should be visited before node 1
node 2 should be visited before node 1
node 3 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.
Since visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.
Since visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.
Since visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.

In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 1
node 1 should be visited before node 2
node 3 should be visited before node 1
node 3 should be visited before node 2
node 4 should be visited before node 3
node 4 should be visited before node 0
node 4 should be visited before node 1
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 4, node 4 can be visited first.
Since visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.
Since visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 3
node 1 should be visited before node 2
node 3 should be visited before node 2
node 4 should be visited before node 1
node 4 should be visited before node 2
node 5 should be visited before node 1
node 5 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.
Since visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.
Since visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 5
node 1 should be visited before node 2
node 1 should be visited before node 0
node 3 should be visited before node 0
node 3 should be visited before node 5
node 4 should be visited before node 3
node 4 should be visited before node 2
node 4 should be visited before node 0
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.
Since visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.
Since visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.
Since visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.
Since visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.

In a directed graph with 7 nodes numbered from 0 to 6:
node 0 should be visited before node 6
node 2 should be visited before node 0
node 2 should be visited before node 5
node 4 should be visited before node 1
node 4 should be visited before node 3
node 6 should be visited before node 3
node 6 should be visited before node 5
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.
Since visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.
Since visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.
Since visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.
Since visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.
Since visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.

In a directed graph with 11 nodes numbered from 0 to 10:
node 0 should be visited before node 5
node 0 should be visited before node 3
node 0 should be visited before node 10
node 0 should be visited before node 8
node 0 should be visited before node 4
node 0 should be visited before node 7
node 1 should be visited before node 5
node 1 should be visited before node 3
node 1 should be visited before node 2
node 1 should be visited before node 4
node 1 should be visited before node 7
node 2 should be visited before node 8
node 2 should be visited before node 9
node 3 should be visited before node 10
node 3 should be visited before node 2
node 3 should be visited before node 8
node 3 should be visited before node 4
node 3 should be visited before node 7
node 3 should be visited before node 9
node 4 should be visited before node 7
node 4 should be visited before node 9
node 5 should be visited before node 10
node 5 should be visited before node 4
node 5 should be visited before node 7
node 5 should be visited before node 9
node 6 should be visited before node 0
node 6 should be visited before node 5
node 6 should be visited before node 10
node 6 should be visited before node 2
node 6 should be visited before node 8
node 6 should be visited before node 4
node 6 should be visited before node 7
node 6 should be visited before node 9
node 7 should be visited before node 9
node 8 should be visited before node 7
node 8 should be visited before node 9
node 10 should be visited before node 2
node 10 should be visited before node 8
node 10 should be visited before node 4
node 10 should be visited before node 7
node 10 should be visited before node 9
Q: Can all the nodes be visited? Give the solution.
A:

Answer: The solution is: 1,6,0,5,3,10,2,4,8,7,9.


Question:
In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 4
node 0 should be visited before node 1
node 2 should be visited before node 1
node 3 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.
Since visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.
Since visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.
Since visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.

In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 1
node 1 should be visited before node 2
node 3 should be visited before node 1
node 3 should be visited before node 2
node 4 should be visited before node 3
node 4 should be visited before node 0
node 4 should be visited before node 1
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 4, node 4 can be visited first.
Since visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.
Since visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 3
node 1 should be visited before node 2
node 3 should be visited before node 2
node 4 should be visited before node 1
node 4 should be visited before node 2
node 5 should be visited before node 1
node 5 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.
Since visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.
Since visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 5
node 1 should be visited before node 2
node 1 should be visited before node 0
node 3 should be visited before node 0
node 3 should be visited before node 5
node 4 should be visited before node 3
node 4 should be visited before node 2
node 4 should be visited before node 0
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.
Since visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.
Since visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.
Since visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.
Since visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.

In a directed graph with 7 nodes numbered from 0 to 6:
node 0 should be visited before node 6
node 2 should be visited before node 0
node 2 should be visited before node 5
node 4 should be visited before node 1
node 4 should be visited before node 3
node 6 should be visited before node 3
node 6 should be visited before node 5
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.
Since visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.
Since visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.
Since visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.
Since visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.
Since visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.

In a directed graph with 21 nodes numbered from 0 to 20:
node 0 should be visited before node 13
node 0 should be visited before node 12
node 0 should be visited before node 10
node 0 should be visited before node 4
node 1 should be visited before node 6
node 1 should be visited before node 9
node 1 should be visited before node 5
node 1 should be visited before node 2
node 1 should be visited before node 0
node 1 should be visited before node 13
node 1 should be visited before node 15
node 1 should be visited before node 10
node 1 should be visited before node 18
node 1 should be visited before node 4
node 2 should be visited before node 3
node 2 should be visited before node 13
node 2 should be visited before node 10
node 2 should be visited before node 18
node 2 should be visited before node 11
node 2 should be visited before node 4
node 3 should be visited before node 13
node 3 should be visited before node 12
node 3 should be visited before node 15
node 3 should be visited before node 10
node 3 should be visited before node 7
node 3 should be visited before node 8
node 5 should be visited before node 3
node 5 should be visited before node 18
node 5 should be visited before node 11
node 6 should be visited before node 9
node 6 should be visited before node 5
node 6 should be visited before node 2
node 6 should be visited before node 3
node 6 should be visited before node 13
node 6 should be visited before node 12
node 6 should be visited before node 10
node 6 should be visited before node 7
node 6 should be visited before node 11
node 7 should be visited before node 11
node 7 should be visited before node 8
node 7 should be visited before node 4
node 8 should be visited before node 4
node 9 should be visited before node 2
node 9 should be visited before node 3
node 9 should be visited before node 13
node 9 should be visited before node 15
node 9 should be visited before node 7
node 9 should be visited before node 11
node 10 should be visited before node 18
node 10 should be visited before node 11
node 10 should be visited before node 4
node 12 should be visited before node 11
node 12 should be visited before node 4
node 13 should be visited before node 12
node 13 should be visited before node 11
node 13 should be visited before node 8
node 13 should be visited before node 4
node 14 should be visited before node 1
node 14 should be visited before node 9
node 14 should be visited before node 16
node 14 should be visited before node 2
node 14 should be visited before node 3
node 14 should be visited before node 0
node 14 should be visited before node 15
node 14 should be visited before node 18
node 14 should be visited before node 8
node 15 should be visited before node 18
node 15 should be visited before node 7
node 15 should be visited before node 11
node 15 should be visited before node 8
node 16 should be visited before node 5
node 16 should be visited before node 2
node 16 should be visited before node 0
node 16 should be visited before node 12
node 16 should be visited before node 15
node 16 should be visited before node 10
node 16 should be visited before node 18
node 16 should be visited before node 11
node 16 should be visited before node 8
node 16 should be visited before node 4
node 17 should be visited before node 5
node 17 should be visited before node 2
node 17 should be visited before node 3
node 17 should be visited before node 13
node 17 should be visited before node 12
node 17 should be visited before node 15
node 17 should be visited before node 18
node 17 should be visited before node 7
node 17 should be visited before node 8
node 18 should be visited before node 7
node 18 should be visited before node 4
node 19 should be visited before node 16
node 19 should be visited before node 13
node 19 should be visited before node 12
node 19 should be visited before node 18
node 19 should be visited before node 11
node 19 should be visited before node 8
node 19 should be visited before node 4
node 20 should be visited before node 1
node 20 should be visited before node 6
node 20 should be visited before node 9
node 20 should be visited before node 17
node 20 should be visited before node 16
node 20 should be visited before node 5
node 20 should be visited before node 2
node 20 should be visited before node 13
node 20 should be visited before node 15
node 20 should be visited before node 10
node 20 should be visited before node 11
node 20 should be visited before node 4
Q: Can all the nodes be visited? Give the solution.
A:

Answer: The solution is: 14,19,20,1,17,16,6,0,9,5,2,3,13,15,10,12,18,7,11,8,4.


Question:
In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 4
node 0 should be visited before node 1
node 2 should be visited before node 1
node 3 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.
Since visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.
Since visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.
Since visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.

In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 1
node 1 should be visited before node 2
node 3 should be visited before node 1
node 3 should be visited before node 2
node 4 should be visited before node 3
node 4 should be visited before node 0
node 4 should be visited before node 1
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 4, node 4 can be visited first.
Since visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.
Since visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 3
node 1 should be visited before node 2
node 3 should be visited before node 2
node 4 should be visited before node 1
node 4 should be visited before node 2
node 5 should be visited before node 1
node 5 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.
Since visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.
Since visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 5
node 1 should be visited before node 2
node 1 should be visited before node 0
node 3 should be visited before node 0
node 3 should be visited before node 5
node 4 should be visited before node 3
node 4 should be visited before node 2
node 4 should be visited before node 0
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.
Since visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.
Since visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.
Since visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.
Since visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.

In a directed graph with 7 nodes numbered from 0 to 6:
node 0 should be visited before node 6
node 2 should be visited before node 0
node 2 should be visited before node 5
node 4 should be visited before node 1
node 4 should be visited before node 3
node 6 should be visited before node 3
node 6 should be visited before node 5
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.
Since visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.
Since visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.
Since visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.
Since visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.
Since visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.

In a directed graph with 16 nodes numbered from 0 to 15:
node 1 should be visited before node 0
node 1 should be visited before node 14
node 2 should be visited before node 6
node 2 should be visited before node 4
node 2 should be visited before node 15
node 2 should be visited before node 7
node 2 should be visited before node 1
node 2 should be visited before node 12
node 2 should be visited before node 8
node 3 should be visited before node 10
node 3 should be visited before node 5
node 3 should be visited before node 4
node 3 should be visited before node 9
node 3 should be visited before node 8
node 3 should be visited before node 14
node 4 should be visited before node 12
node 4 should be visited before node 8
node 4 should be visited before node 0
node 5 should be visited before node 2
node 5 should be visited before node 6
node 5 should be visited before node 15
node 5 should be visited before node 1
node 5 should be visited before node 12
node 5 should be visited before node 8
node 5 should be visited before node 0
node 6 should be visited before node 4
node 6 should be visited before node 15
node 6 should be visited before node 12
node 6 should be visited before node 9
node 6 should be visited before node 8
node 7 should be visited before node 12
node 7 should be visited before node 9
node 7 should be visited before node 8
node 7 should be visited before node 0
node 7 should be visited before node 14
node 9 should be visited before node 8
node 9 should be visited before node 0
node 10 should be visited before node 5
node 10 should be visited before node 6
node 10 should be visited before node 7
node 10 should be visited before node 8
node 10 should be visited before node 0
node 10 should be visited before node 14
node 11 should be visited before node 10
node 11 should be visited before node 5
node 11 should be visited before node 6
node 11 should be visited before node 15
node 11 should be visited before node 12
node 11 should be visited before node 9
node 11 should be visited before node 8
node 11 should be visited before node 0
node 12 should be visited before node 9
node 12 should be visited before node 0
node 13 should be visited before node 2
node 13 should be visited before node 4
node 13 should be visited before node 15
node 13 should be visited before node 7
node 13 should be visited before node 12
node 13 should be visited before node 9
node 13 should be visited before node 8
node 15 should be visited before node 7
node 15 should be visited before node 12
Q: Can all the nodes be visited? Give the solution.
A:

Answer: The solution is: 3,11,13,10,5,2,6,1,4,15,7,12,14,9,8,0.


Question:
In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 4
node 0 should be visited before node 1
node 2 should be visited before node 1
node 3 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.
Since visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.
Since visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.
Since visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.

In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 1
node 1 should be visited before node 2
node 3 should be visited before node 1
node 3 should be visited before node 2
node 4 should be visited before node 3
node 4 should be visited before node 0
node 4 should be visited before node 1
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 4, node 4 can be visited first.
Since visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.
Since visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 3
node 1 should be visited before node 2
node 3 should be visited before node 2
node 4 should be visited before node 1
node 4 should be visited before node 2
node 5 should be visited before node 1
node 5 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.
Since visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.
Since visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 5
node 1 should be visited before node 2
node 1 should be visited before node 0
node 3 should be visited before node 0
node 3 should be visited before node 5
node 4 should be visited before node 3
node 4 should be visited before node 2
node 4 should be visited before node 0
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.
Since visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.
Since visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.
Since visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.
Since visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.

In a directed graph with 7 nodes numbered from 0 to 6:
node 0 should be visited before node 6
node 2 should be visited before node 0
node 2 should be visited before node 5
node 4 should be visited before node 1
node 4 should be visited before node 3
node 6 should be visited before node 3
node 6 should be visited before node 5
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.
Since visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.
Since visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.
Since visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.
Since visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.
Since visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.

In a directed graph with 21 nodes numbered from 0 to 20:
node 0 should be visited before node 6
node 0 should be visited before node 5
node 0 should be visited before node 9
node 0 should be visited before node 19
node 0 should be visited before node 10
node 1 should be visited before node 16
node 1 should be visited before node 7
node 1 should be visited before node 10
node 1 should be visited before node 8
node 1 should be visited before node 11
node 1 should be visited before node 3
node 1 should be visited before node 14
node 2 should be visited before node 16
node 2 should be visited before node 19
node 2 should be visited before node 10
node 2 should be visited before node 11
node 2 should be visited before node 3
node 2 should be visited before node 14
node 4 should be visited before node 18
node 4 should be visited before node 13
node 4 should be visited before node 0
node 4 should be visited before node 1
node 4 should be visited before node 16
node 4 should be visited before node 19
node 4 should be visited before node 15
node 4 should be visited before node 8
node 4 should be visited before node 11
node 4 should be visited before node 3
node 4 should be visited before node 14
node 5 should be visited before node 2
node 5 should be visited before node 1
node 5 should be visited before node 15
node 5 should be visited before node 10
node 5 should be visited before node 17
node 5 should be visited before node 11
node 5 should be visited before node 3
node 6 should be visited before node 5
node 6 should be visited before node 9
node 6 should be visited before node 20
node 6 should be visited before node 2
node 6 should be visited before node 1
node 6 should be visited before node 19
node 6 should be visited before node 7
node 6 should be visited before node 10
node 6 should be visited before node 17
node 6 should be visited before node 11
node 6 should be visited before node 3
node 7 should be visited before node 3
node 7 should be visited before node 14
node 8 should be visited before node 17
node 8 should be visited before node 11
node 8 should be visited before node 3
node 8 should be visited before node 14
node 9 should be visited before node 20
node 9 should be visited before node 2
node 9 should be visited before node 1
node 9 should be visited before node 16
node 9 should be visited before node 19
node 9 should be visited before node 7
node 9 should be visited before node 15
node 9 should be visited before node 10
node 9 should be visited before node 11
node 9 should be visited before node 3
node 9 should be visited before node 14
node 10 should be visited before node 17
node 10 should be visited before node 3
node 11 should be visited before node 3
node 12 should be visited before node 13
node 12 should be visited before node 0
node 12 should be visited before node 6
node 12 should be visited before node 5
node 12 should be visited before node 9
node 12 should be visited before node 20
node 12 should be visited before node 19
node 12 should be visited before node 10
node 12 should be visited before node 17
node 12 should be visited before node 11
node 13 should be visited before node 6
node 13 should be visited before node 20
node 13 should be visited before node 2
node 13 should be visited before node 1
node 13 should be visited before node 19
node 13 should be visited before node 7
node 13 should be visited before node 10
node 13 should be visited before node 17
node 13 should be visited before node 3
node 13 should be visited before node 14
node 15 should be visited before node 10
node 15 should be visited before node 17
node 15 should be visited before node 11
node 15 should be visited before node 3
node 16 should be visited before node 19
node 16 should be visited before node 11
node 17 should be visited before node 14
node 18 should be visited before node 13
node 18 should be visited before node 6
node 18 should be visited before node 9
node 18 should be visited before node 2
node 18 should be visited before node 16
node 18 should be visited before node 19
node 18 should be visited before node 7
node 18 should be visited before node 10
node 18 should be visited before node 14
node 19 should be visited before node 15
node 19 should be visited before node 17
node 19 should be visited before node 14
node 20 should be visited before node 2
node 20 should be visited before node 1
node 20 should be visited before node 16
node 20 should be visited before node 7
node 20 should be visited before node 15
node 20 should be visited before node 17
node 20 should be visited before node 11
Q: Can all the nodes be visited? Give the solution.
A:

Answer: The solution is: 4,12,18,0,13,6,5,9,20,2,1,16,7,8,19,15,10,11,17,3,14.


Question:
In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 4
node 0 should be visited before node 1
node 2 should be visited before node 1
node 3 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.
Since visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.
Since visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.
Since visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.

In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 1
node 1 should be visited before node 2
node 3 should be visited before node 1
node 3 should be visited before node 2
node 4 should be visited before node 3
node 4 should be visited before node 0
node 4 should be visited before node 1
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 4, node 4 can be visited first.
Since visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.
Since visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 3
node 1 should be visited before node 2
node 3 should be visited before node 2
node 4 should be visited before node 1
node 4 should be visited before node 2
node 5 should be visited before node 1
node 5 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.
Since visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.
Since visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 5
node 1 should be visited before node 2
node 1 should be visited before node 0
node 3 should be visited before node 0
node 3 should be visited before node 5
node 4 should be visited before node 3
node 4 should be visited before node 2
node 4 should be visited before node 0
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.
Since visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.
Since visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.
Since visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.
Since visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.

In a directed graph with 7 nodes numbered from 0 to 6:
node 0 should be visited before node 6
node 2 should be visited before node 0
node 2 should be visited before node 5
node 4 should be visited before node 1
node 4 should be visited before node 3
node 6 should be visited before node 3
node 6 should be visited before node 5
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.
Since visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.
Since visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.
Since visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.
Since visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.
Since visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.

In a directed graph with 16 nodes numbered from 0 to 15:
node 0 should be visited before node 8
node 0 should be visited before node 5
node 0 should be visited before node 4
node 0 should be visited before node 3
node 0 should be visited before node 11
node 0 should be visited before node 12
node 0 should be visited before node 2
node 1 should be visited before node 13
node 1 should be visited before node 0
node 1 should be visited before node 8
node 1 should be visited before node 4
node 1 should be visited before node 11
node 1 should be visited before node 12
node 1 should be visited before node 2
node 1 should be visited before node 9
node 2 should be visited before node 9
node 2 should be visited before node 10
node 3 should be visited before node 11
node 3 should be visited before node 12
node 3 should be visited before node 2
node 3 should be visited before node 9
node 4 should be visited before node 3
node 4 should be visited before node 11
node 4 should be visited before node 12
node 4 should be visited before node 10
node 5 should be visited before node 4
node 5 should be visited before node 3
node 5 should be visited before node 11
node 5 should be visited before node 12
node 5 should be visited before node 2
node 5 should be visited before node 9
node 6 should be visited before node 1
node 6 should be visited before node 15
node 6 should be visited before node 8
node 6 should be visited before node 5
node 6 should be visited before node 4
node 6 should be visited before node 3
node 6 should be visited before node 12
node 6 should be visited before node 2
node 6 should be visited before node 9
node 6 should be visited before node 10
node 7 should be visited before node 14
node 7 should be visited before node 6
node 7 should be visited before node 1
node 7 should be visited before node 13
node 7 should be visited before node 0
node 7 should be visited before node 5
node 7 should be visited before node 4
node 7 should be visited before node 3
node 7 should be visited before node 11
node 7 should be visited before node 12
node 8 should be visited before node 4
node 8 should be visited before node 3
node 8 should be visited before node 11
node 8 should be visited before node 12
node 8 should be visited before node 2
node 8 should be visited before node 9
node 8 should be visited before node 10
node 9 should be visited before node 10
node 11 should be visited before node 12
node 11 should be visited before node 9
node 12 should be visited before node 9
node 12 should be visited before node 10
node 13 should be visited before node 0
node 13 should be visited before node 5
node 13 should be visited before node 4
node 13 should be visited before node 3
node 13 should be visited before node 11
node 13 should be visited before node 12
node 13 should be visited before node 2
node 13 should be visited before node 9
node 13 should be visited before node 10
node 14 should be visited before node 6
node 14 should be visited before node 15
node 14 should be visited before node 13
node 14 should be visited before node 0
node 14 should be visited before node 8
node 14 should be visited before node 5
node 14 should be visited before node 3
node 14 should be visited before node 11
node 14 should be visited before node 12
node 14 should be visited before node 2
node 14 should be visited before node 9
node 14 should be visited before node 10
node 15 should be visited before node 13
node 15 should be visited before node 0
node 15 should be visited before node 8
node 15 should be visited before node 5
node 15 should be visited before node 4
node 15 should be visited before node 3
node 15 should be visited before node 11
node 15 should be visited before node 12
node 15 should be visited before node 2
node 15 should be visited before node 10
Q: Can all the nodes be visited? Give the solution.
A:

Answer: The solution is: 7,14,6,1,15,13,0,8,5,4,3,11,2,12,9,10.


Question:
In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 4
node 0 should be visited before node 1
node 2 should be visited before node 1
node 3 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.
Since visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.
Since visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.
Since visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.

In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 1
node 1 should be visited before node 2
node 3 should be visited before node 1
node 3 should be visited before node 2
node 4 should be visited before node 3
node 4 should be visited before node 0
node 4 should be visited before node 1
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 4, node 4 can be visited first.
Since visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.
Since visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 3
node 1 should be visited before node 2
node 3 should be visited before node 2
node 4 should be visited before node 1
node 4 should be visited before node 2
node 5 should be visited before node 1
node 5 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.
Since visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.
Since visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 5
node 1 should be visited before node 2
node 1 should be visited before node 0
node 3 should be visited before node 0
node 3 should be visited before node 5
node 4 should be visited before node 3
node 4 should be visited before node 2
node 4 should be visited before node 0
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.
Since visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.
Since visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.
Since visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.
Since visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.

In a directed graph with 7 nodes numbered from 0 to 6:
node 0 should be visited before node 6
node 2 should be visited before node 0
node 2 should be visited before node 5
node 4 should be visited before node 1
node 4 should be visited before node 3
node 6 should be visited before node 3
node 6 should be visited before node 5
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.
Since visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.
Since visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.
Since visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.
Since visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.
Since visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.

In a directed graph with 12 nodes numbered from 0 to 11:
node 1 should be visited before node 4
node 1 should be visited before node 2
node 1 should be visited before node 3
node 1 should be visited before node 9
node 1 should be visited before node 7
node 1 should be visited before node 10
node 1 should be visited before node 0
node 2 should be visited before node 11
node 2 should be visited before node 3
node 2 should be visited before node 7
node 2 should be visited before node 8
node 2 should be visited before node 10
node 2 should be visited before node 6
node 3 should be visited before node 9
node 3 should be visited before node 10
node 4 should be visited before node 11
node 4 should be visited before node 7
node 4 should be visited before node 10
node 4 should be visited before node 0
node 5 should be visited before node 2
node 5 should be visited before node 7
node 5 should be visited before node 0
node 6 should be visited before node 0
node 7 should be visited before node 8
node 7 should be visited before node 10
node 8 should be visited before node 10
node 8 should be visited before node 6
node 9 should be visited before node 7
node 9 should be visited before node 8
node 10 should be visited before node 6
node 11 should be visited before node 9
node 11 should be visited before node 7
node 11 should be visited before node 10
node 11 should be visited before node 6
Q: Can all the nodes be visited? Give the solution.
A:

Answer: The solution is: 1,5,4,2,11,3,9,7,8,10,6,0.


Question:
In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 4
node 0 should be visited before node 1
node 2 should be visited before node 1
node 3 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.
Since visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.
Since visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.
Since visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.

In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 1
node 1 should be visited before node 2
node 3 should be visited before node 1
node 3 should be visited before node 2
node 4 should be visited before node 3
node 4 should be visited before node 0
node 4 should be visited before node 1
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 4, node 4 can be visited first.
Since visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.
Since visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 3
node 1 should be visited before node 2
node 3 should be visited before node 2
node 4 should be visited before node 1
node 4 should be visited before node 2
node 5 should be visited before node 1
node 5 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.
Since visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.
Since visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 5
node 1 should be visited before node 2
node 1 should be visited before node 0
node 3 should be visited before node 0
node 3 should be visited before node 5
node 4 should be visited before node 3
node 4 should be visited before node 2
node 4 should be visited before node 0
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.
Since visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.
Since visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.
Since visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.
Since visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.

In a directed graph with 7 nodes numbered from 0 to 6:
node 0 should be visited before node 6
node 2 should be visited before node 0
node 2 should be visited before node 5
node 4 should be visited before node 1
node 4 should be visited before node 3
node 6 should be visited before node 3
node 6 should be visited before node 5
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.
Since visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.
Since visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.
Since visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.
Since visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.
Since visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.

In a directed graph with 24 nodes numbered from 0 to 23:
node 0 should be visited before node 19
node 0 should be visited before node 23
node 0 should be visited before node 18
node 0 should be visited before node 15
node 1 should be visited before node 6
node 1 should be visited before node 12
node 1 should be visited before node 18
node 2 should be visited before node 22
node 2 should be visited before node 21
node 2 should be visited before node 13
node 2 should be visited before node 7
node 2 should be visited before node 1
node 2 should be visited before node 6
node 2 should be visited before node 19
node 2 should be visited before node 5
node 2 should be visited before node 18
node 2 should be visited before node 15
node 3 should be visited before node 9
node 3 should be visited before node 17
node 3 should be visited before node 13
node 3 should be visited before node 7
node 3 should be visited before node 5
node 3 should be visited before node 23
node 3 should be visited before node 8
node 3 should be visited before node 15
node 4 should be visited before node 2
node 4 should be visited before node 22
node 4 should be visited before node 17
node 4 should be visited before node 10
node 4 should be visited before node 21
node 4 should be visited before node 7
node 4 should be visited before node 1
node 4 should be visited before node 6
node 4 should be visited before node 19
node 4 should be visited before node 5
node 4 should be visited before node 14
node 4 should be visited before node 8
node 4 should be visited before node 15
node 5 should be visited before node 12
node 5 should be visited before node 23
node 5 should be visited before node 8
node 5 should be visited before node 15
node 6 should be visited before node 0
node 6 should be visited before node 19
node 6 should be visited before node 5
node 6 should be visited before node 23
node 6 should be visited before node 14
node 7 should be visited before node 6
node 7 should be visited before node 19
node 7 should be visited before node 5
node 7 should be visited before node 23
node 7 should be visited before node 18
node 7 should be visited before node 14
node 8 should be visited before node 15
node 9 should be visited before node 17
node 9 should be visited before node 21
node 9 should be visited before node 7
node 9 should be visited before node 1
node 9 should be visited before node 0
node 9 should be visited before node 5
node 9 should be visited before node 18
node 10 should be visited before node 13
node 10 should be visited before node 0
node 10 should be visited before node 5
node 10 should be visited before node 12
node 10 should be visited before node 18
node 10 should be visited before node 14
node 11 should be visited before node 16
node 11 should be visited before node 2
node 11 should be visited before node 10
node 11 should be visited before node 21
node 11 should be visited before node 7
node 11 should be visited before node 1
node 11 should be visited before node 19
node 11 should be visited before node 5
node 11 should be visited before node 12
node 11 should be visited before node 14
node 11 should be visited before node 8
node 12 should be visited before node 23
node 12 should be visited before node 15
node 13 should be visited before node 1
node 13 should be visited before node 6
node 13 should be visited before node 5
node 13 should be visited before node 18
node 14 should be visited before node 15
node 16 should be visited before node 4
node 16 should be visited before node 2
node 16 should be visited before node 22
node 16 should be visited before node 17
node 16 should be visited before node 10
node 16 should be visited before node 21
node 16 should be visited before node 13
node 16 should be visited before node 7
node 16 should be visited before node 1
node 16 should be visited before node 6
node 16 should be visited before node 0
node 16 should be visited before node 5
node 16 should be visited before node 8
node 16 should be visited before node 15
node 17 should be visited before node 13
node 17 should be visited before node 7
node 17 should be visited before node 0
node 17 should be visited before node 5
node 17 should be visited before node 12
node 17 should be visited before node 23
node 17 should be visited before node 15
node 18 should be visited before node 15
node 19 should be visited before node 23
node 19 should be visited before node 15
node 20 should be visited before node 3
node 20 should be visited before node 22
node 20 should be visited before node 17
node 20 should be visited before node 13
node 20 should be visited before node 0
node 20 should be visited before node 5
node 20 should be visited before node 12
node 20 should be visited before node 18
node 20 should be visited before node 8
node 21 should be visited before node 7
node 21 should be visited before node 6
node 21 should be visited before node 19
node 21 should be visited before node 12
node 21 should be visited before node 18
node 21 should be visited before node 15
node 22 should be visited before node 17
node 22 should be visited before node 10
node 22 should be visited before node 21
node 22 should be visited before node 13
node 22 should be visited before node 7
node 22 should be visited before node 5
node 22 should be visited before node 14
node 22 should be visited before node 8
node 22 should be visited before node 15
node 23 should be visited before node 15
Q: Can all the nodes be visited? Give the solution.
A:

Answer: The solution is: 11,20,16,3,4,9,2,22,17,10,21,13,7,1,6,0,5,14,19,18,12,8,23,15.


Question:
In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 4
node 0 should be visited before node 1
node 2 should be visited before node 1
node 3 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.
Since visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.
Since visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.
Since visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.

In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 1
node 1 should be visited before node 2
node 3 should be visited before node 1
node 3 should be visited before node 2
node 4 should be visited before node 3
node 4 should be visited before node 0
node 4 should be visited before node 1
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 4, node 4 can be visited first.
Since visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.
Since visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 3
node 1 should be visited before node 2
node 3 should be visited before node 2
node 4 should be visited before node 1
node 4 should be visited before node 2
node 5 should be visited before node 1
node 5 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.
Since visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.
Since visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 5
node 1 should be visited before node 2
node 1 should be visited before node 0
node 3 should be visited before node 0
node 3 should be visited before node 5
node 4 should be visited before node 3
node 4 should be visited before node 2
node 4 should be visited before node 0
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.
Since visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.
Since visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.
Since visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.
Since visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.

In a directed graph with 7 nodes numbered from 0 to 6:
node 0 should be visited before node 6
node 2 should be visited before node 0
node 2 should be visited before node 5
node 4 should be visited before node 1
node 4 should be visited before node 3
node 6 should be visited before node 3
node 6 should be visited before node 5
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.
Since visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.
Since visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.
Since visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.
Since visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.
Since visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.

In a directed graph with 25 nodes numbered from 0 to 24:
node 0 should be visited before node 15
node 0 should be visited before node 22
node 0 should be visited before node 20
node 0 should be visited before node 10
node 0 should be visited before node 18
node 0 should be visited before node 8
node 1 should be visited before node 11
node 1 should be visited before node 24
node 1 should be visited before node 18
node 1 should be visited before node 9
node 2 should be visited before node 21
node 2 should be visited before node 16
node 2 should be visited before node 0
node 2 should be visited before node 15
node 2 should be visited before node 1
node 2 should be visited before node 4
node 2 should be visited before node 20
node 2 should be visited before node 9
node 3 should be visited before node 21
node 3 should be visited before node 7
node 3 should be visited before node 0
node 3 should be visited before node 19
node 3 should be visited before node 6
node 3 should be visited before node 24
node 3 should be visited before node 20
node 3 should be visited before node 18
node 3 should be visited before node 13
node 3 should be visited before node 23
node 4 should be visited before node 5
node 4 should be visited before node 11
node 4 should be visited before node 10
node 4 should be visited before node 18
node 4 should be visited before node 14
node 4 should be visited before node 13
node 5 should be visited before node 24
node 5 should be visited before node 22
node 5 should be visited before node 14
node 5 should be visited before node 13
node 6 should be visited before node 15
node 6 should be visited before node 1
node 6 should be visited before node 4
node 6 should be visited before node 20
node 6 should be visited before node 10
node 6 should be visited before node 13
node 7 should be visited before node 16
node 7 should be visited before node 4
node 7 should be visited before node 14
node 7 should be visited before node 9
node 8 should be visited before node 23
node 8 should be visited before node 9
node 10 should be visited before node 18
node 10 should be visited before node 23
node 11 should be visited before node 24
node 11 should be visited before node 22
node 11 should be visited before node 18
node 11 should be visited before node 9
node 12 should be visited before node 16
node 12 should be visited before node 19
node 12 should be visited before node 15
node 12 should be visited before node 5
node 12 should be visited before node 11
node 12 should be visited before node 20
node 12 should be visited before node 10
node 12 should be visited before node 14
node 15 should be visited before node 11
node 15 should be visited before node 18
node 15 should be visited before node 13
node 16 should be visited before node 0
node 16 should be visited before node 19
node 16 should be visited before node 17
node 16 should be visited before node 6
node 16 should be visited before node 1
node 16 should be visited before node 11
node 16 should be visited before node 22
node 16 should be visited before node 14
node 17 should be visited before node 24
node 17 should be visited before node 8
node 17 should be visited before node 23
node 17 should be visited before node 9
node 18 should be visited before node 8
node 19 should be visited before node 1
node 19 should be visited before node 5
node 19 should be visited before node 11
node 19 should be visited before node 24
node 19 should be visited before node 18
node 19 should be visited before node 8
node 19 should be visited before node 23
node 20 should be visited before node 10
node 21 should be visited before node 17
node 21 should be visited before node 22
node 21 should be visited before node 20
node 21 should be visited before node 8
node 21 should be visited before node 9
node 22 should be visited before node 14
node 24 should be visited before node 14
Q: Can all the nodes be visited? Give the solution.
A:

Answer: The solution is: 2,3,12,21,7,16,0,19,17,6,15,1,4,20,5,11,10,13,24,22,18,14,8,23,9.


Question:
In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 4
node 0 should be visited before node 1
node 2 should be visited before node 1
node 3 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.
Since visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.
Since visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.
Since visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.

In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 1
node 1 should be visited before node 2
node 3 should be visited before node 1
node 3 should be visited before node 2
node 4 should be visited before node 3
node 4 should be visited before node 0
node 4 should be visited before node 1
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 4, node 4 can be visited first.
Since visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.
Since visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 3
node 1 should be visited before node 2
node 3 should be visited before node 2
node 4 should be visited before node 1
node 4 should be visited before node 2
node 5 should be visited before node 1
node 5 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.
Since visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.
Since visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 5
node 1 should be visited before node 2
node 1 should be visited before node 0
node 3 should be visited before node 0
node 3 should be visited before node 5
node 4 should be visited before node 3
node 4 should be visited before node 2
node 4 should be visited before node 0
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.
Since visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.
Since visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.
Since visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.
Since visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.

In a directed graph with 7 nodes numbered from 0 to 6:
node 0 should be visited before node 6
node 2 should be visited before node 0
node 2 should be visited before node 5
node 4 should be visited before node 1
node 4 should be visited before node 3
node 6 should be visited before node 3
node 6 should be visited before node 5
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.
Since visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.
Since visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.
Since visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.
Since visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.
Since visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.

In a directed graph with 19 nodes numbered from 0 to 18:
node 0 should be visited before node 2
node 1 should be visited before node 0
node 1 should be visited before node 2
node 1 should be visited before node 17
node 2 should be visited before node 17
node 3 should be visited before node 14
node 3 should be visited before node 8
node 3 should be visited before node 11
node 3 should be visited before node 16
node 3 should be visited before node 5
node 3 should be visited before node 10
node 3 should be visited before node 18
node 3 should be visited before node 12
node 3 should be visited before node 4
node 3 should be visited before node 1
node 4 should be visited before node 1
node 4 should be visited before node 0
node 4 should be visited before node 17
node 5 should be visited before node 9
node 5 should be visited before node 10
node 5 should be visited before node 18
node 5 should be visited before node 1
node 5 should be visited before node 2
node 5 should be visited before node 17
node 6 should be visited before node 14
node 6 should be visited before node 8
node 6 should be visited before node 15
node 6 should be visited before node 11
node 6 should be visited before node 5
node 6 should be visited before node 18
node 6 should be visited before node 12
node 6 should be visited before node 4
node 6 should be visited before node 1
node 6 should be visited before node 0
node 6 should be visited before node 2
node 7 should be visited before node 11
node 7 should be visited before node 5
node 7 should be visited before node 18
node 7 should be visited before node 12
node 7 should be visited before node 4
node 7 should be visited before node 1
node 7 should be visited before node 2
node 7 should be visited before node 17
node 8 should be visited before node 5
node 8 should be visited before node 9
node 8 should be visited before node 18
node 8 should be visited before node 12
node 8 should be visited before node 4
node 8 should be visited before node 1
node 8 should be visited before node 2
node 8 should be visited before node 17
node 9 should be visited before node 10
node 9 should be visited before node 18
node 9 should be visited before node 4
node 9 should be visited before node 1
node 9 should be visited before node 2
node 9 should be visited before node 17
node 10 should be visited before node 18
node 10 should be visited before node 12
node 10 should be visited before node 4
node 10 should be visited before node 1
node 10 should be visited before node 17
node 11 should be visited before node 16
node 11 should be visited before node 5
node 11 should be visited before node 9
node 11 should be visited before node 10
node 11 should be visited before node 4
node 11 should be visited before node 1
node 11 should be visited before node 2
node 11 should be visited before node 17
node 12 should be visited before node 0
node 12 should be visited before node 17
node 13 should be visited before node 6
node 13 should be visited before node 3
node 13 should be visited before node 14
node 13 should be visited before node 7
node 13 should be visited before node 8
node 13 should be visited before node 15
node 13 should be visited before node 11
node 13 should be visited before node 9
node 13 should be visited before node 10
node 13 should be visited before node 18
node 13 should be visited before node 0
node 13 should be visited before node 2
node 13 should be visited before node 17
node 14 should be visited before node 7
node 14 should be visited before node 8
node 14 should be visited before node 15
node 14 should be visited before node 11
node 14 should be visited before node 16
node 14 should be visited before node 5
node 14 should be visited before node 9
node 14 should be visited before node 10
node 14 should be visited before node 18
node 14 should be visited before node 12
node 14 should be visited before node 2
node 14 should be visited before node 17
node 15 should be visited before node 16
node 15 should be visited before node 5
node 15 should be visited before node 12
node 15 should be visited before node 4
node 15 should be visited before node 1
node 16 should be visited before node 5
node 16 should be visited before node 9
node 16 should be visited before node 18
node 16 should be visited before node 12
node 16 should be visited before node 4
node 16 should be visited before node 0
node 16 should be visited before node 2
node 16 should be visited before node 17
node 18 should be visited before node 12
node 18 should be visited before node 4
node 18 should be visited before node 1
node 18 should be visited before node 0
Q: Can all the nodes be visited? Give the solution.
A:

Answer: The solution is: 13,6,3,14,7,8,15,11,16,5,9,10,18,12,4,1,0,2,17.


Question:
In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 4
node 0 should be visited before node 1
node 2 should be visited before node 1
node 3 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 and node 3, node 0 and node 3 can be visited first.
Since visiting node 4 requires visiting node 0 first, after node 0 is visited, node 4 can be visited.
Since visiting node 2 requires visiting node 3 first, after node 3 is visited, node 2 can be visited.
Since visiting node 1 requires visiting node 0, node 2 first, after node 0 and node 2 are visited, node 1 can be visited. So the solution is: 0,3,4,2,1.

In a directed graph with 5 nodes numbered from 0 to 4:
node 0 should be visited before node 1
node 1 should be visited before node 2
node 3 should be visited before node 1
node 3 should be visited before node 2
node 4 should be visited before node 3
node 4 should be visited before node 0
node 4 should be visited before node 1
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 4, node 4 can be visited first.
Since visiting node 0, node 3 requires visiting node 4 first, after node 4 is visited, node 0 and node 3 can be visited.
Since visiting node 1 requires visiting node 0, node 3, node 4 first, after node 0, node 3, and node 4 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3 first, after node 1 and node 3 are visited, node 2 can be visited. So the solution is: 4,0,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 3
node 1 should be visited before node 2
node 3 should be visited before node 2
node 4 should be visited before node 1
node 4 should be visited before node 2
node 5 should be visited before node 1
node 5 should be visited before node 2
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 0 node 4 and node 5, node 0 node 4 and node 5 can be visited first.
Since visiting node 3 requires visiting node 0 first, after node 0 is visited, node 3 can be visited.
Since visiting node 1 requires visiting node 4, node 5 first, after node 4 and node 5 are visited, node 1 can be visited.
Since visiting node 2 requires visiting node 1, node 3, node 4, node 5 first, after node 1, node 3, node 4, and node 5 are visited, node 2 can be visited. So the solution is: 0,4,5,3,1,2.

In a directed graph with 6 nodes numbered from 0 to 5:
node 0 should be visited before node 5
node 1 should be visited before node 2
node 1 should be visited before node 0
node 3 should be visited before node 0
node 3 should be visited before node 5
node 4 should be visited before node 3
node 4 should be visited before node 2
node 4 should be visited before node 0
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 1 and node 4, node 1 and node 4 can be visited first.
Since visiting node 2 requires visiting node 1, node 4 first, after node 1 and node 4 are visited, node 2 can be visited.
Since visiting node 3 requires visiting node 4 first, after node 4 is visited, node 3 can be visited.
Since visiting node 0 requires visiting node 1, node 3, node 4 first, after node 1, node 3, and node 4 are visited, node 0 can be visited.
Since visiting node 5 requires visiting node 0, node 3 first, after node 0 and node 3 are visited, node 5 can be visited. So the solution is: 1,4,2,3,0,5.

In a directed graph with 7 nodes numbered from 0 to 6:
node 0 should be visited before node 6
node 2 should be visited before node 0
node 2 should be visited before node 5
node 4 should be visited before node 1
node 4 should be visited before node 3
node 6 should be visited before node 3
node 6 should be visited before node 5
Q: Can all the nodes be visited? Give the solution.
A: Since no nodes are required to be visited before node 2 and node 4, node 2 and node 4 can be visited first.
Since visiting node 0 requires visiting node 2 first, after node 2 is visited, node 0 can be visited.
Since visiting node 1 requires visiting node 4 first, after node 4 is visited, node 1 can be visited.
Since visiting node 6 requires visiting node 0 first, after node 0 is visited, node 6 can be visited.
Since visiting node 5 requires visiting node 2, node 6 first, after node 2 and node 6 are visited, node 5 can be visited.
Since visiting node 3 requires visiting node 4, node 6 first, after node 4 and node 6 are visited, node 3 can be visited. So the solution is: 2,4,0,1,6,5,3.

In a directed graph with 9 nodes numbered from 0 to 8:
node 2 should be visited before node 1
node 3 should be visited before node 5
node 3 should be visited before node 2
node 4 should be visited before node 3
node 5 should be visited before node 2
node 6 should be visited before node 5
node 7 should be visited before node 4
node 7 should be visited before node 5
node 8 should be visited before node 6
node 8 should be visited before node 4
node 8 should be visited before node 1
Q: Can all the nodes be visited? Give the solution.
A:

Answer: The solution is: 0,7,8,6,4,3,5,2,1.