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

Answer: The solution is: 1,12,13,22,29,7,18,28,25,23,31,30,4,15,16,27,17,20,0,24,26,10,14,2,19,9,8,6,5,21,3,11.


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

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


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

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


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

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


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

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


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

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


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

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


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 7
node 0 should be visited before node 2
node 0 should be visited before node 9
node 0 should be visited before node 6
node 0 should be visited before node 3
node 1 should be visited before node 5
node 2 should be visited before node 8
node 2 should be visited before node 9
node 2 should be visited before node 6
node 2 should be visited before node 1
node 2 should be visited before node 5
node 3 should be visited before node 1
node 4 should be visited before node 0
node 4 should be visited before node 2
node 4 should be visited before node 8
node 4 should be visited before node 3
node 4 should be visited before node 1
node 6 should be visited before node 10
node 7 should be visited before node 2
node 7 should be visited before node 8
node 7 should be visited before node 9
node 7 should be visited before node 6
node 7 should be visited before node 1
node 8 should be visited before node 6
node 8 should be visited before node 3
node 8 should be visited before node 1
node 9 should be visited before node 6
node 9 should be visited before node 3
node 9 should be visited before node 1
node 10 should be visited before node 1
Q: Can all the nodes be visited? Give the solution.
A:

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


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

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


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 7 nodes numbered from 0 to 6:
node 0 should be visited before node 1
node 2 should be visited before node 3
node 2 should be visited before node 0
node 3 should be visited before node 6
node 3 should be visited before node 5
node 5 should be visited before node 4
node 6 should be visited before node 0
node 6 should be visited before node 5
Q: Can all the nodes be visited? Give the solution.
A:

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


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

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