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fix(graph): restore reverse residual capacity in BFS and DFS maximum flow #2788

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fix(graph): restore reverse residual capacity in BFS and DFS maximum flow #2788

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d0001a5
fix(graph): add reverse residual capacity to BFS maximum flow
Miladkhoshdel Oct 10, 2026
119ac06
fix(graph): add reverse residual capacity to DFS maximum flow
Miladkhoshdel Oct 10, 2026
d190efb
- test(graph): cover flow rerouting in BFS and DFS maximum flow
Miladkhoshdel Oct 10, 2026
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1 change: 1 addition & 0 deletions algorithms/graph/maximum_flow_bfs.py
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Original file line number Diff line number Diff line change
Expand Up @@ -68,6 +68,7 @@ def maximum_flow_bfs(adjacency_matrix: list[list[int]]) -> int:

while tmp != 0:
new_array[path[tmp]][tmp] = new_array[path[tmp]][tmp] - min_flow
new_array[tmp][path[tmp]] += min_flow
tmp = path[tmp]

total = total + min_flow
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1 change: 1 addition & 0 deletions algorithms/graph/maximum_flow_dfs.py
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Expand Up @@ -67,6 +67,7 @@ def maximum_flow_dfs(adjacency_matrix: list[list[int]]) -> int:

while tmp != 0:
new_array[path[tmp]][tmp] = new_array[path[tmp]][tmp] - min_flow
new_array[tmp][path[tmp]] += min_flow
tmp = path[tmp]

total = total + min_flow
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26 changes: 26 additions & 0 deletions tests/test_graph.py
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Expand Up @@ -169,6 +169,19 @@ def test_maximum_flow_bfs(self):

self.assertEqual(maximum_flow, 23)

def test_maximum_flow_bfs_reroutes_earlier_flow(self):
graph = [
[0, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 0],
[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 0],
]
# The first path is 0->1->3->5. Reaching flow 2 requires
# canceling 1->3 so the final paths use 0->1->4->5 and 0->2->3->5.
self.assertEqual(maximum_flow_bfs(graph), 2)


class TestMaximumFlowDfs(unittest.TestCase):
"""
Expand All @@ -190,6 +203,19 @@ def test_maximum_flow_dfs(self):

self.assertEqual(maximum_flow, 23)

def test_maximum_flow_dfs_reroutes_earlier_flow(self):
graph = [
[0, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 1, 1, 0],
[0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 0],
]
# The first path is 0->2->4->5. Reaching flow 2 requires
# canceling 2->4 so the final paths use 0->1->4->5 and 0->2->3->5.
self.assertEqual(maximum_flow_dfs(graph), 2)


class TestAllPairsShortestPath(unittest.TestCase):
def test_all_pairs_shortest_path(self):
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