Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 8, and the edges are:
an edge from node 0 to node 8 with capacity 3,
an edge from node 1 to node 3 with capacity 6,
an edge from node 2 to node 5 with capacity 7,
an edge from node 2 to node 4 with capacity 4,
an edge from node 2 to node 3 with capacity 6,
an edge from node 3 to node 5 with capacity 5,
an edge from node 3 to node 6 with capacity 10,
an edge from node 4 to node 2 with capacity 2,
an edge from node 5 to node 8 with capacity 7,
an edge from node 8 to node 4 with capacity 8,
an edge from node 8 to node 6 with capacity 6.
Q: What is the maximum flow from node 2 to node 6?
A:

Answer: The maximum flow from node 2 to node 6 is 12.


Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 4 with capacity 3,
an edge from node 1 to node 2 with capacity 9,
an edge from node 1 to node 0 with capacity 8,
an edge from node 2 to node 1 with capacity 9,
an edge from node 2 to node 0 with capacity 5,
an edge from node 3 to node 5 with capacity 9,
an edge from node 4 to node 2 with capacity 6,
an edge from node 5 to node 4 with capacity 2,
an edge from node 5 to node 2 with capacity 9.
Q: What is the maximum flow from node 2 to node 4?
A:

Answer: The maximum flow from node 2 to node 4 is 13.


Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 15, and the edges are:
an edge from node 0 to node 8 with capacity 17,
an edge from node 0 to node 3 with capacity 8,
an edge from node 0 to node 12 with capacity 1,
an edge from node 0 to node 2 with capacity 15,
an edge from node 0 to node 15 with capacity 10,
an edge from node 1 to node 10 with capacity 9,
an edge from node 1 to node 4 with capacity 5,
an edge from node 1 to node 12 with capacity 18,
an edge from node 1 to node 0 with capacity 19,
an edge from node 1 to node 11 with capacity 10,
an edge from node 1 to node 2 with capacity 10,
an edge from node 2 to node 11 with capacity 4,
an edge from node 2 to node 14 with capacity 13,
an edge from node 3 to node 5 with capacity 9,
an edge from node 3 to node 10 with capacity 3,
an edge from node 3 to node 12 with capacity 4,
an edge from node 3 to node 13 with capacity 6,
an edge from node 3 to node 7 with capacity 3,
an edge from node 3 to node 11 with capacity 10,
an edge from node 4 to node 5 with capacity 13,
an edge from node 4 to node 10 with capacity 14,
an edge from node 4 to node 11 with capacity 19,
an edge from node 4 to node 2 with capacity 1,
an edge from node 4 to node 14 with capacity 13,
an edge from node 5 to node 2 with capacity 11,
an edge from node 6 to node 10 with capacity 11,
an edge from node 7 to node 10 with capacity 12,
an edge from node 7 to node 3 with capacity 13,
an edge from node 7 to node 1 with capacity 19,
an edge from node 7 to node 11 with capacity 11,
an edge from node 7 to node 14 with capacity 9,
an edge from node 8 to node 12 with capacity 3,
an edge from node 8 to node 13 with capacity 20,
an edge from node 8 to node 2 with capacity 17,
an edge from node 8 to node 9 with capacity 6,
an edge from node 8 to node 14 with capacity 13,
an edge from node 9 to node 12 with capacity 4,
an edge from node 9 to node 7 with capacity 13,
an edge from node 9 to node 2 with capacity 9,
an edge from node 10 to node 6 with capacity 8,
an edge from node 11 to node 5 with capacity 16,
an edge from node 12 to node 3 with capacity 12,
an edge from node 12 to node 4 with capacity 9,
an edge from node 13 to node 4 with capacity 19,
an edge from node 13 to node 7 with capacity 9,
an edge from node 13 to node 1 with capacity 3,
an edge from node 13 to node 14 with capacity 8,
an edge from node 14 to node 10 with capacity 8,
an edge from node 14 to node 13 with capacity 11,
an edge from node 14 to node 2 with capacity 10,
an edge from node 15 to node 10 with capacity 9,
an edge from node 15 to node 12 with capacity 2,
an edge from node 15 to node 13 with capacity 15,
an edge from node 15 to node 7 with capacity 12,
an edge from node 15 to node 11 with capacity 5.
Q: What is the maximum flow from node 7 to node 13?
A:

Answer: The maximum flow from node 7 to node 13 is 36.


Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 0 with capacity 10,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 9,
an edge from node 2 to node 4 with capacity 10,
an edge from node 3 to node 0 with capacity 6,
an edge from node 4 to node 1 with capacity 8,
an edge from node 4 to node 2 with capacity 2.
Q: What is the maximum flow from node 4 to node 0?
A:

Answer: The maximum flow from node 4 to node 0 is 10.


Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 17, and the edges are:
an edge from node 0 to node 7 with capacity 3,
an edge from node 0 to node 14 with capacity 3,
an edge from node 0 to node 13 with capacity 10,
an edge from node 0 to node 9 with capacity 17,
an edge from node 1 to node 6 with capacity 5,
an edge from node 1 to node 10 with capacity 3,
an edge from node 1 to node 16 with capacity 3,
an edge from node 2 to node 14 with capacity 4,
an edge from node 2 to node 1 with capacity 17,
an edge from node 2 to node 5 with capacity 9,
an edge from node 2 to node 17 with capacity 18,
an edge from node 2 to node 15 with capacity 4,
an edge from node 2 to node 12 with capacity 12,
an edge from node 2 to node 8 with capacity 13,
an edge from node 2 to node 0 with capacity 12,
an edge from node 3 to node 14 with capacity 3,
an edge from node 3 to node 1 with capacity 18,
an edge from node 3 to node 12 with capacity 13,
an edge from node 3 to node 8 with capacity 4,
an edge from node 3 to node 16 with capacity 10,
an edge from node 4 to node 6 with capacity 8,
an edge from node 4 to node 14 with capacity 20,
an edge from node 4 to node 3 with capacity 1,
an edge from node 4 to node 17 with capacity 19,
an edge from node 4 to node 9 with capacity 3,
an edge from node 4 to node 16 with capacity 6,
an edge from node 5 to node 6 with capacity 13,
an edge from node 5 to node 14 with capacity 11,
an edge from node 5 to node 15 with capacity 10,
an edge from node 5 to node 4 with capacity 15,
an edge from node 5 to node 2 with capacity 17,
an edge from node 5 to node 0 with capacity 3,
an edge from node 6 to node 7 with capacity 15,
an edge from node 6 to node 13 with capacity 11,
an edge from node 6 to node 1 with capacity 12,
an edge from node 6 to node 5 with capacity 10,
an edge from node 6 to node 17 with capacity 20,
an edge from node 7 to node 3 with capacity 14,
an edge from node 7 to node 11 with capacity 16,
an edge from node 7 to node 8 with capacity 6,
an edge from node 8 to node 13 with capacity 16,
an edge from node 8 to node 12 with capacity 1,
an edge from node 8 to node 0 with capacity 11,
an edge from node 8 to node 16 with capacity 16,
an edge from node 9 to node 1 with capacity 1,
an edge from node 9 to node 17 with capacity 9,
an edge from node 9 to node 10 with capacity 1,
an edge from node 9 to node 12 with capacity 11,
an edge from node 9 to node 4 with capacity 6,
an edge from node 10 to node 1 with capacity 1,
an edge from node 10 to node 11 with capacity 12,
an edge from node 10 to node 4 with capacity 7,
an edge from node 10 to node 0 with capacity 17,
an edge from node 11 to node 14 with capacity 5,
an edge from node 11 to node 2 with capacity 1,
an edge from node 12 to node 14 with capacity 16,
an edge from node 12 to node 13 with capacity 6,
an edge from node 12 to node 15 with capacity 16,
an edge from node 12 to node 2 with capacity 9,
an edge from node 12 to node 8 with capacity 7,
an edge from node 13 to node 14 with capacity 18,
an edge from node 13 to node 2 with capacity 1,
an edge from node 13 to node 8 with capacity 12,
an edge from node 13 to node 0 with capacity 12,
an edge from node 13 to node 16 with capacity 3,
an edge from node 14 to node 17 with capacity 16,
an edge from node 14 to node 12 with capacity 4,
an edge from node 15 to node 1 with capacity 15,
an edge from node 15 to node 10 with capacity 7,
an edge from node 15 to node 12 with capacity 1,
an edge from node 15 to node 0 with capacity 7,
an edge from node 16 to node 5 with capacity 17,
an edge from node 16 to node 10 with capacity 15,
an edge from node 16 to node 9 with capacity 13,
an edge from node 16 to node 11 with capacity 17,
an edge from node 16 to node 15 with capacity 13,
an edge from node 16 to node 2 with capacity 10,
an edge from node 16 to node 8 with capacity 17,
an edge from node 17 to node 3 with capacity 2,
an edge from node 17 to node 9 with capacity 9,
an edge from node 17 to node 12 with capacity 17,
an edge from node 17 to node 2 with capacity 19,
an edge from node 17 to node 16 with capacity 1.
Q: What is the maximum flow from node 4 to node 15?
A:

Answer: The maximum flow from node 4 to node 15 is 43.


Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 14, and the edges are:
an edge from node 0 to node 11 with capacity 20,
an edge from node 0 to node 14 with capacity 20,
an edge from node 0 to node 10 with capacity 17,
an edge from node 0 to node 4 with capacity 8,
an edge from node 0 to node 6 with capacity 7,
an edge from node 1 to node 14 with capacity 18,
an edge from node 1 to node 10 with capacity 19,
an edge from node 1 to node 4 with capacity 18,
an edge from node 1 to node 6 with capacity 15,
an edge from node 1 to node 2 with capacity 14,
an edge from node 1 to node 12 with capacity 9,
an edge from node 2 to node 7 with capacity 17,
an edge from node 2 to node 8 with capacity 8,
an edge from node 2 to node 1 with capacity 7,
an edge from node 2 to node 9 with capacity 14,
an edge from node 3 to node 13 with capacity 15,
an edge from node 3 to node 14 with capacity 17,
an edge from node 3 to node 4 with capacity 20,
an edge from node 3 to node 0 with capacity 3,
an edge from node 3 to node 5 with capacity 10,
an edge from node 3 to node 12 with capacity 1,
an edge from node 4 to node 8 with capacity 18,
an edge from node 4 to node 5 with capacity 1,
an edge from node 5 to node 11 with capacity 2,
an edge from node 5 to node 13 with capacity 9,
an edge from node 5 to node 3 with capacity 20,
an edge from node 5 to node 0 with capacity 9,
an edge from node 5 to node 1 with capacity 11,
an edge from node 6 to node 10 with capacity 12,
an edge from node 6 to node 0 with capacity 11,
an edge from node 6 to node 1 with capacity 17,
an edge from node 7 to node 13 with capacity 13,
an edge from node 7 to node 10 with capacity 13,
an edge from node 7 to node 4 with capacity 20,
an edge from node 7 to node 9 with capacity 3,
an edge from node 8 to node 11 with capacity 10,
an edge from node 8 to node 10 with capacity 7,
an edge from node 8 to node 4 with capacity 20,
an edge from node 8 to node 1 with capacity 19,
an edge from node 8 to node 9 with capacity 8,
an edge from node 9 to node 11 with capacity 10,
an edge from node 9 to node 13 with capacity 19,
an edge from node 9 to node 14 with capacity 1,
an edge from node 9 to node 7 with capacity 19,
an edge from node 9 to node 8 with capacity 2,
an edge from node 10 to node 13 with capacity 8,
an edge from node 10 to node 8 with capacity 17,
an edge from node 10 to node 0 with capacity 3,
an edge from node 10 to node 12 with capacity 5,
an edge from node 11 to node 4 with capacity 13,
an edge from node 11 to node 3 with capacity 13,
an edge from node 11 to node 1 with capacity 20,
an edge from node 11 to node 12 with capacity 16,
an edge from node 12 to node 13 with capacity 11,
an edge from node 12 to node 6 with capacity 13,
an edge from node 12 to node 2 with capacity 12,
an edge from node 12 to node 5 with capacity 7,
an edge from node 13 to node 14 with capacity 11,
an edge from node 13 to node 5 with capacity 15,
an edge from node 14 to node 13 with capacity 5,
an edge from node 14 to node 0 with capacity 5,
an edge from node 14 to node 5 with capacity 17,
an edge from node 14 to node 12 with capacity 14.
Q: What is the maximum flow from node 4 to node 10?
A:

Answer: The maximum flow from node 4 to node 10 is 19.


Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 19, and the edges are:
an edge from node 0 to node 7 with capacity 12,
an edge from node 0 to node 18 with capacity 17,
an edge from node 0 to node 8 with capacity 10,
an edge from node 0 to node 15 with capacity 5,
an edge from node 0 to node 2 with capacity 17,
an edge from node 0 to node 14 with capacity 4,
an edge from node 1 to node 7 with capacity 2,
an edge from node 1 to node 10 with capacity 7,
an edge from node 1 to node 18 with capacity 7,
an edge from node 1 to node 15 with capacity 9,
an edge from node 1 to node 14 with capacity 4,
an edge from node 2 to node 9 with capacity 18,
an edge from node 2 to node 7 with capacity 16,
an edge from node 2 to node 0 with capacity 13,
an edge from node 2 to node 18 with capacity 1,
an edge from node 3 to node 19 with capacity 9,
an edge from node 3 to node 8 with capacity 20,
an edge from node 4 to node 0 with capacity 2,
an edge from node 4 to node 15 with capacity 9,
an edge from node 4 to node 14 with capacity 11,
an edge from node 5 to node 12 with capacity 1,
an edge from node 5 to node 19 with capacity 14,
an edge from node 5 to node 2 with capacity 20,
an edge from node 6 to node 3 with capacity 4,
an edge from node 6 to node 7 with capacity 2,
an edge from node 6 to node 12 with capacity 3,
an edge from node 6 to node 19 with capacity 15,
an edge from node 6 to node 10 with capacity 11,
an edge from node 6 to node 4 with capacity 4,
an edge from node 6 to node 14 with capacity 20,
an edge from node 7 to node 19 with capacity 18,
an edge from node 7 to node 0 with capacity 1,
an edge from node 7 to node 5 with capacity 6,
an edge from node 7 to node 2 with capacity 1,
an edge from node 8 to node 7 with capacity 7,
an edge from node 8 to node 12 with capacity 19,
an edge from node 8 to node 6 with capacity 4,
an edge from node 8 to node 10 with capacity 10,
an edge from node 8 to node 0 with capacity 4,
an edge from node 8 to node 5 with capacity 2,
an edge from node 8 to node 1 with capacity 9,
an edge from node 8 to node 14 with capacity 11,
an edge from node 9 to node 3 with capacity 1,
an edge from node 9 to node 19 with capacity 7,
an edge from node 9 to node 1 with capacity 5,
an edge from node 9 to node 14 with capacity 1,
an edge from node 10 to node 19 with capacity 4,
an edge from node 10 to node 6 with capacity 6,
an edge from node 10 to node 5 with capacity 15,
an edge from node 10 to node 15 with capacity 11,
an edge from node 10 to node 13 with capacity 17,
an edge from node 10 to node 11 with capacity 5,
an edge from node 11 to node 3 with capacity 18,
an edge from node 11 to node 7 with capacity 19,
an edge from node 11 to node 19 with capacity 8,
an edge from node 11 to node 18 with capacity 4,
an edge from node 11 to node 8 with capacity 19,
an edge from node 11 to node 5 with capacity 3,
an edge from node 11 to node 13 with capacity 13,
an edge from node 11 to node 14 with capacity 11,
an edge from node 12 to node 7 with capacity 4,
an edge from node 12 to node 19 with capacity 3,
an edge from node 12 to node 16 with capacity 17,
an edge from node 12 to node 17 with capacity 13,
an edge from node 13 to node 12 with capacity 17,
an edge from node 13 to node 10 with capacity 16,
an edge from node 13 to node 18 with capacity 15,
an edge from node 13 to node 15 with capacity 3,
an edge from node 13 to node 2 with capacity 6,
an edge from node 13 to node 16 with capacity 6,
an edge from node 13 to node 14 with capacity 1,
an edge from node 14 to node 12 with capacity 11,
an edge from node 14 to node 6 with capacity 6,
an edge from node 14 to node 0 with capacity 9,
an edge from node 14 to node 2 with capacity 11,
an edge from node 14 to node 4 with capacity 3,
an edge from node 14 to node 17 with capacity 18,
an edge from node 15 to node 6 with capacity 5,
an edge from node 15 to node 11 with capacity 2,
an edge from node 15 to node 14 with capacity 1,
an edge from node 16 to node 10 with capacity 4,
an edge from node 16 to node 18 with capacity 16,
an edge from node 16 to node 15 with capacity 16,
an edge from node 16 to node 14 with capacity 8,
an edge from node 17 to node 9 with capacity 3,
an edge from node 17 to node 10 with capacity 8,
an edge from node 17 to node 0 with capacity 18,
an edge from node 17 to node 18 with capacity 4,
an edge from node 17 to node 5 with capacity 20,
an edge from node 17 to node 15 with capacity 4,
an edge from node 17 to node 1 with capacity 16,
an edge from node 17 to node 11 with capacity 3,
an edge from node 17 to node 14 with capacity 6,
an edge from node 18 to node 9 with capacity 15,
an edge from node 18 to node 3 with capacity 17,
an edge from node 18 to node 10 with capacity 12,
an edge from node 18 to node 8 with capacity 15,
an edge from node 19 to node 3 with capacity 13,
an edge from node 19 to node 2 with capacity 14,
an edge from node 19 to node 11 with capacity 14.
Q: What is the maximum flow from node 16 to node 10?
A:

Answer: The maximum flow from node 16 to node 10 is 36.


Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 11, and the edges are:
an edge from node 0 to node 3 with capacity 4,
an edge from node 0 to node 5 with capacity 6,
an edge from node 1 to node 6 with capacity 9,
an edge from node 1 to node 2 with capacity 17,
an edge from node 1 to node 10 with capacity 3,
an edge from node 2 to node 3 with capacity 12,
an edge from node 2 to node 11 with capacity 17,
an edge from node 2 to node 4 with capacity 14,
an edge from node 3 to node 2 with capacity 9,
an edge from node 3 to node 1 with capacity 5,
an edge from node 3 to node 8 with capacity 8,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 7 with capacity 12,
an edge from node 4 to node 2 with capacity 10,
an edge from node 4 to node 3 with capacity 12,
an edge from node 4 to node 5 with capacity 20,
an edge from node 5 to node 9 with capacity 17,
an edge from node 5 to node 2 with capacity 5,
an edge from node 5 to node 3 with capacity 6,
an edge from node 5 to node 8 with capacity 17,
an edge from node 5 to node 10 with capacity 10,
an edge from node 6 to node 7 with capacity 20,
an edge from node 6 to node 0 with capacity 19,
an edge from node 6 to node 10 with capacity 10,
an edge from node 7 to node 2 with capacity 20,
an edge from node 8 to node 5 with capacity 10,
an edge from node 8 to node 4 with capacity 12,
an edge from node 9 to node 7 with capacity 13,
an edge from node 9 to node 6 with capacity 6,
an edge from node 9 to node 0 with capacity 17,
an edge from node 10 to node 1 with capacity 16,
an edge from node 10 to node 5 with capacity 19,
an edge from node 11 to node 0 with capacity 13.
Q: What is the maximum flow from node 4 to node 2?
A:

Answer: The maximum flow from node 4 to node 2 is 54.


Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 11, and the edges are:
an edge from node 0 to node 2 with capacity 3,
an edge from node 0 to node 6 with capacity 12,
an edge from node 1 to node 5 with capacity 18,
an edge from node 2 to node 5 with capacity 13,
an edge from node 3 to node 0 with capacity 3,
an edge from node 3 to node 10 with capacity 1,
an edge from node 4 to node 10 with capacity 12,
an edge from node 5 to node 2 with capacity 11,
an edge from node 5 to node 8 with capacity 5,
an edge from node 5 to node 6 with capacity 4,
an edge from node 5 to node 10 with capacity 11,
an edge from node 5 to node 1 with capacity 20,
an edge from node 5 to node 11 with capacity 14,
an edge from node 6 to node 0 with capacity 9,
an edge from node 6 to node 8 with capacity 14,
an edge from node 6 to node 4 with capacity 6,
an edge from node 6 to node 5 with capacity 6,
an edge from node 7 to node 8 with capacity 16,
an edge from node 8 to node 0 with capacity 4,
an edge from node 8 to node 2 with capacity 12,
an edge from node 8 to node 6 with capacity 4,
an edge from node 8 to node 1 with capacity 9,
an edge from node 8 to node 4 with capacity 10,
an edge from node 8 to node 11 with capacity 2,
an edge from node 8 to node 5 with capacity 20,
an edge from node 9 to node 11 with capacity 14,
an edge from node 10 to node 1 with capacity 1,
an edge from node 10 to node 4 with capacity 1,
an edge from node 11 to node 6 with capacity 10,
an edge from node 11 to node 3 with capacity 4,
an edge from node 11 to node 1 with capacity 17.
Q: What is the maximum flow from node 0 to node 3?
A:

Answer: The maximum flow from node 0 to node 3 is 4.


Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 2 to node 5 with capacity 9,
an edge from node 2 to node 0 with capacity 6,
an edge from node 2 to node 3 with capacity 5,
an edge from node 3 to node 1 with capacity 8,
an edge from node 3 to node 0 with capacity 5,
an edge from node 4 to node 5 with capacity 4,
an edge from node 4 to node 0 with capacity 3,
an edge from node 4 to node 3 with capacity 9,
an edge from node 5 to node 2 with capacity 9,
an edge from node 5 to node 3 with capacity 2.
Q: What is the maximum flow from node 5 to node 0?
A:

Answer: The maximum flow from node 5 to node 0 is 11.


Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 9, and the edges are:
an edge from node 0 to node 1 with capacity 7,
an edge from node 0 to node 2 with capacity 6,
an edge from node 0 to node 3 with capacity 5,
an edge from node 1 to node 0 with capacity 4,
an edge from node 1 to node 7 with capacity 10,
an edge from node 2 to node 7 with capacity 2,
an edge from node 2 to node 3 with capacity 2,
an edge from node 3 to node 1 with capacity 1,
an edge from node 3 to node 2 with capacity 4,
an edge from node 3 to node 0 with capacity 4,
an edge from node 3 to node 5 with capacity 9,
an edge from node 4 to node 5 with capacity 10,
an edge from node 5 to node 0 with capacity 2,
an edge from node 5 to node 3 with capacity 2,
an edge from node 6 to node 1 with capacity 8,
an edge from node 6 to node 0 with capacity 9,
an edge from node 7 to node 9 with capacity 4,
an edge from node 8 to node 0 with capacity 10,
an edge from node 8 to node 7 with capacity 6,
an edge from node 8 to node 5 with capacity 9,
an edge from node 8 to node 6 with capacity 10,
an edge from node 9 to node 2 with capacity 6,
an edge from node 9 to node 0 with capacity 4,
an edge from node 9 to node 4 with capacity 1,
an edge from node 9 to node 5 with capacity 4,
an edge from node 9 to node 8 with capacity 2.
Q: What is the maximum flow from node 4 to node 6?
A:

Answer: The maximum flow from node 4 to node 6 is 2.


Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 8, and the edges are:
an edge from node 0 to node 4 with capacity 7,
an edge from node 0 to node 3 with capacity 6,
an edge from node 2 to node 7 with capacity 8,
an edge from node 2 to node 8 with capacity 2,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 8 with capacity 9,
an edge from node 3 to node 1 with capacity 3,
an edge from node 5 to node 2 with capacity 6,
an edge from node 5 to node 4 with capacity 7,
an edge from node 5 to node 3 with capacity 5,
an edge from node 6 to node 3 with capacity 10,
an edge from node 7 to node 2 with capacity 6,
an edge from node 7 to node 4 with capacity 1,
an edge from node 7 to node 1 with capacity 6,
an edge from node 8 to node 4 with capacity 7,
an edge from node 8 to node 0 with capacity 10.
Q: What is the maximum flow from node 5 to node 4?
A:

Answer: The maximum flow from node 5 to node 4 is 15.


Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 16, and the edges are:
an edge from node 0 to node 16 with capacity 2,
an edge from node 0 to node 15 with capacity 10,
an edge from node 0 to node 8 with capacity 10,
an edge from node 1 to node 16 with capacity 2,
an edge from node 1 to node 14 with capacity 1,
an edge from node 1 to node 2 with capacity 11,
an edge from node 1 to node 11 with capacity 19,
an edge from node 1 to node 12 with capacity 3,
an edge from node 1 to node 4 with capacity 18,
an edge from node 2 to node 10 with capacity 14,
an edge from node 2 to node 9 with capacity 10,
an edge from node 2 to node 4 with capacity 4,
an edge from node 3 to node 5 with capacity 13,
an edge from node 3 to node 11 with capacity 12,
an edge from node 3 to node 0 with capacity 7,
an edge from node 3 to node 15 with capacity 6,
an edge from node 3 to node 12 with capacity 18,
an edge from node 4 to node 2 with capacity 16,
an edge from node 4 to node 15 with capacity 18,
an edge from node 5 to node 7 with capacity 2,
an edge from node 5 to node 16 with capacity 20,
an edge from node 5 to node 12 with capacity 7,
an edge from node 6 to node 7 with capacity 15,
an edge from node 6 to node 3 with capacity 10,
an edge from node 7 to node 10 with capacity 7,
an edge from node 7 to node 6 with capacity 6,
an edge from node 8 to node 7 with capacity 3,
an edge from node 8 to node 14 with capacity 11,
an edge from node 8 to node 9 with capacity 4,
an edge from node 8 to node 2 with capacity 10,
an edge from node 8 to node 1 with capacity 12,
an edge from node 9 to node 8 with capacity 5,
an edge from node 10 to node 5 with capacity 17,
an edge from node 10 to node 13 with capacity 1,
an edge from node 10 to node 12 with capacity 10,
an edge from node 10 to node 1 with capacity 4,
an edge from node 11 to node 5 with capacity 15,
an edge from node 11 to node 2 with capacity 12,
an edge from node 11 to node 1 with capacity 18,
an edge from node 12 to node 7 with capacity 12,
an edge from node 12 to node 10 with capacity 8,
an edge from node 12 to node 5 with capacity 4,
an edge from node 12 to node 9 with capacity 17,
an edge from node 12 to node 0 with capacity 20,
an edge from node 12 to node 8 with capacity 17,
an edge from node 12 to node 4 with capacity 17,
an edge from node 13 to node 3 with capacity 9,
an edge from node 13 to node 2 with capacity 13,
an edge from node 13 to node 11 with capacity 7,
an edge from node 13 to node 1 with capacity 7,
an edge from node 14 to node 16 with capacity 19,
an edge from node 14 to node 5 with capacity 7,
an edge from node 14 to node 11 with capacity 4,
an edge from node 14 to node 6 with capacity 4,
an edge from node 14 to node 8 with capacity 3,
an edge from node 15 to node 10 with capacity 10,
an edge from node 15 to node 3 with capacity 5,
an edge from node 15 to node 13 with capacity 14,
an edge from node 15 to node 2 with capacity 15,
an edge from node 15 to node 12 with capacity 6,
an edge from node 16 to node 14 with capacity 17,
an edge from node 16 to node 8 with capacity 11,
an edge from node 16 to node 4 with capacity 3.
Q: What is the maximum flow from node 12 to node 8?
A:

Answer: The maximum flow from node 12 to node 8 is 46.


Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 17, and the edges are:
an edge from node 0 to node 6 with capacity 9,
an edge from node 0 to node 10 with capacity 5,
an edge from node 0 to node 8 with capacity 7,
an edge from node 0 to node 13 with capacity 11,
an edge from node 0 to node 17 with capacity 19,
an edge from node 0 to node 15 with capacity 6,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 11 with capacity 14,
an edge from node 1 to node 4 with capacity 14,
an edge from node 2 to node 16 with capacity 2,
an edge from node 2 to node 17 with capacity 9,
an edge from node 2 to node 12 with capacity 9,
an edge from node 2 to node 14 with capacity 3,
an edge from node 3 to node 11 with capacity 6,
an edge from node 3 to node 9 with capacity 15,
an edge from node 3 to node 17 with capacity 17,
an edge from node 3 to node 0 with capacity 7,
an edge from node 3 to node 1 with capacity 4,
an edge from node 4 to node 11 with capacity 6,
an edge from node 4 to node 9 with capacity 1,
an edge from node 5 to node 6 with capacity 18,
an edge from node 5 to node 11 with capacity 19,
an edge from node 5 to node 12 with capacity 8,
an edge from node 5 to node 14 with capacity 1,
an edge from node 6 to node 8 with capacity 20,
an edge from node 6 to node 9 with capacity 10,
an edge from node 6 to node 17 with capacity 4,
an edge from node 6 to node 3 with capacity 13,
an edge from node 6 to node 4 with capacity 9,
an edge from node 7 to node 11 with capacity 20,
an edge from node 7 to node 13 with capacity 5,
an edge from node 7 to node 17 with capacity 17,
an edge from node 7 to node 1 with capacity 12,
an edge from node 8 to node 6 with capacity 17,
an edge from node 8 to node 11 with capacity 10,
an edge from node 8 to node 9 with capacity 5,
an edge from node 8 to node 3 with capacity 14,
an edge from node 8 to node 15 with capacity 19,
an edge from node 8 to node 12 with capacity 13,
an edge from node 8 to node 5 with capacity 15,
an edge from node 8 to node 1 with capacity 2,
an edge from node 9 to node 12 with capacity 3,
an edge from node 9 to node 4 with capacity 13,
an edge from node 10 to node 7 with capacity 10,
an edge from node 10 to node 9 with capacity 2,
an edge from node 10 to node 5 with capacity 14,
an edge from node 10 to node 1 with capacity 1,
an edge from node 10 to node 14 with capacity 13,
an edge from node 11 to node 2 with capacity 12,
an edge from node 11 to node 15 with capacity 12,
an edge from node 11 to node 14 with capacity 14,
an edge from node 12 to node 6 with capacity 17,
an edge from node 12 to node 17 with capacity 18,
an edge from node 12 to node 0 with capacity 6,
an edge from node 12 to node 5 with capacity 19,
an edge from node 12 to node 4 with capacity 3,
an edge from node 12 to node 14 with capacity 12,
an edge from node 13 to node 17 with capacity 8,
an edge from node 13 to node 12 with capacity 3,
an edge from node 13 to node 5 with capacity 12,
an edge from node 14 to node 7 with capacity 15,
an edge from node 14 to node 17 with capacity 1,
an edge from node 14 to node 3 with capacity 16,
an edge from node 14 to node 15 with capacity 6,
an edge from node 15 to node 13 with capacity 20,
an edge from node 15 to node 2 with capacity 3,
an edge from node 15 to node 4 with capacity 14,
an edge from node 16 to node 7 with capacity 5,
an edge from node 16 to node 3 with capacity 14,
an edge from node 16 to node 0 with capacity 10,
an edge from node 16 to node 4 with capacity 3,
an edge from node 17 to node 11 with capacity 13.
Q: What is the maximum flow from node 10 to node 9?
A:

Answer: The maximum flow from node 10 to node 9 is 33.


Question:
In a directed graph, the nodes are numbered from 0 to 3, and the edges are:
an edge from node 1 to node 0 with capacity 10,
an edge from node 0 to node 2 with capacity 6,
an edge from node 2 to node 3 with capacity 4.
Q: What is the maximum flow from node 1 to node 3?
A: From the source (node 1), we can send 10 units of flow to node 0.
10 units of flow arrive at node 0, then we can send 6 units of flow from node 0 to node 2.
6 units of flow arrive at node 0, then we can send 4 units of flow from node 2 to node 3.
The total unit of flow arrives at node 3 is 4. So the maximum flow from node 1 to node 3 is 4.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 3 with capacity 3,
an edge from node 0 to node 4 with capacity 10,
an edge from node 1 to node 3 with capacity 3,
an edge from node 1 to node 4 with capacity 5,
an edge from node 2 to node 1 with capacity 10,
an edge from node 3 to node 1 with capacity 10,
an edge from node 3 to node 4 with capacity 1,
an edge from node 4 to node 3 with capacity 2.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 4, and 3 units of flow to node 3.
3 units of flow arrive at node 3, then we can send 3 units of flow from node 3 to node 1.
3 units of flow arrive at node 1, then we can send 3 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 0 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 4, and the edges are:
an edge from node 0 to node 1 with capacity 10,
an edge from node 1 to node 2 with capacity 6,
an edge from node 0 to node 2 with capacity 2,
an edge from node 1 to node 3 with capacity 6,
an edge from node 3 to node 2 with capacity 3,
an edge from node 2 to node 4 with capacity 5,
an edge from node 3 to node 4 with capacity 8.
Q: What is the maximum flow from node 0 to node 4?
A: From the source (node 0), we can send 10 units of flow to node 1, and 2 units of flow to node 2.
10 units of flow arrive at node 1, then we can send 6 units of flow from node 3 to node 1, and 4 units of flow from node 3 to node 2.
6 units of flow arrive at node 2, then we can send 5 units of flow from node 2 to node 4.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 4.
The total unit of flow arrives at node 4 is 11. So the maximum flow from node 0 to node 4 is 11.

In a directed graph, the nodes are numbered from 0 to 5, and the edges are:
an edge from node 0 to node 4 with capacity 8,
an edge from node 2 to node 0 with capacity 2,
an edge from node 2 to node 4 with capacity 6,
an edge from node 3 to node 1 with capacity 7,
an edge from node 4 to node 3 with capacity 10,
an edge from node 4 to node 1 with capacity 2,
an edge from node 4 to node 5 with capacity 2,
an edge from node 5 to node 4 with capacity 7.
Q: What is the maximum flow from node 2 to node 1?
A: From the source (node 1), we can send 2 units of flow to node 0, and 6 units of flow to node 4.
2 units of flow arrive at node 0, then we can send 2 units of flow from node 0 to node 4.
8 units of flow arrive at node 4, then we can send 2 units of flow from node 4 to node 1, and 6 units of flow from node 4 to node 3.
6 units of flow arrive at node 3, then we can send 6 units of flow from node 3 to node 1.
The total unit of flow arrives at node 4 is 8. So the maximum flow from node 2 to node 1 is 8.

In a directed graph, the nodes are numbered from 0 to 6, and the edges are:
an edge from node 0 to node 3 with capacity 1,
an edge from node 1 to node 4 with capacity 7,
an edge from node 2 to node 6 with capacity 1,
an edge from node 2 to node 4 with capacity 6,
an edge from node 2 to node 1 with capacity 6,
an edge from node 3 to node 4 with capacity 4,
an edge from node 3 to node 1 with capacity 7,
an edge from node 5 to node 1 with capacity 9,
an edge from node 6 to node 4 with capacity 10.
Q: What is the maximum flow from node 2 to node 4?
A: From the source (node 2), we can send 1 units of flow to node 0, 6 units of flow to node 1, and 6 units of flow to node 4.
1 unit of flow arrive at node 0, then we can send 1 unit of flow from node 0 to node 4.
6 units of flow arrive at node 1, then we can send 6 units of flow from node 1 to node 4.
The total unit of flow arrives at node 4 is 13. So the maximum flow from node 2 to node 4 is 13.

In a directed graph, the nodes are numbered from 0 to 14, and the edges are:
an edge from node 1 to node 3 with capacity 13,
an edge from node 1 to node 0 with capacity 5,
an edge from node 1 to node 13 with capacity 18,
an edge from node 1 to node 10 with capacity 11,
an edge from node 1 to node 5 with capacity 16,
an edge from node 1 to node 2 with capacity 18,
an edge from node 2 to node 8 with capacity 20,
an edge from node 2 to node 1 with capacity 15,
an edge from node 2 to node 5 with capacity 1,
an edge from node 3 to node 6 with capacity 20,
an edge from node 3 to node 11 with capacity 19,
an edge from node 4 to node 12 with capacity 14,
an edge from node 4 to node 1 with capacity 14,
an edge from node 5 to node 14 with capacity 4,
an edge from node 5 to node 9 with capacity 20,
an edge from node 5 to node 7 with capacity 1,
an edge from node 5 to node 0 with capacity 16,
an edge from node 5 to node 2 with capacity 17,
an edge from node 6 to node 9 with capacity 1,
an edge from node 8 to node 7 with capacity 15,
an edge from node 8 to node 3 with capacity 2,
an edge from node 8 to node 0 with capacity 3,
an edge from node 9 to node 12 with capacity 12,
an edge from node 9 to node 5 with capacity 13,
an edge from node 10 to node 6 with capacity 9,
an edge from node 10 to node 0 with capacity 5,
an edge from node 10 to node 12 with capacity 7,
an edge from node 10 to node 11 with capacity 14,
an edge from node 11 to node 6 with capacity 20,
an edge from node 11 to node 12 with capacity 17,
an edge from node 12 to node 7 with capacity 12,
an edge from node 12 to node 0 with capacity 11,
an edge from node 12 to node 13 with capacity 10,
an edge from node 12 to node 1 with capacity 15,
an edge from node 12 to node 4 with capacity 20,
an edge from node 13 to node 6 with capacity 9,
an edge from node 13 to node 8 with capacity 17,
an edge from node 13 to node 0 with capacity 16,
an edge from node 13 to node 10 with capacity 16,
an edge from node 13 to node 2 with capacity 13,
an edge from node 13 to node 11 with capacity 3,
an edge from node 14 to node 3 with capacity 1,
an edge from node 14 to node 4 with capacity 13.
Q: What is the maximum flow from node 9 to node 7?
A:

Answer: The maximum flow from node 9 to node 7 is 25.