[Miladkhoshdel]

Closes #2787

Problem

maximum_flow_bfs and maximum_flow_dfs can return a flow smaller than the true maximum when reaching the optimal result requires rerouting an earlier augmenting path.

Both functions subtract the amount of flow sent from each edge’s forward capacity, but they never increase the corresponding reverse residual capacity. As a result, subsequent searches cannot cancel earlier flow and choose a better route.

For example, the BFS regression network supports two paths, each carrying one unit:

• 0 → 1 → 4 → 5
• 0 → 2 → 3 → 5

However, BFS first selects 0 → 1 → 3 → 5. Reaching the maximum flow then requires traversing the reverse residual edge 3 → 1 to reroute that flow. Without this edge, the function stops and returns 1 instead of 2.

The DFS implementation has the same defect, reproduced with a different vertex ordering of the same network.

Changes

• Add reverse residual capacity updates during augmentation in both functions.
• Add a regression test for each function covering flow rerouting.
• Preserve the existing function signatures and input-copying behavior.

After sending flow along an edge u → v, the residual graph now reduces capacity on u → v and increases capacity on v → u by the same amount.

Validation

• Both regression cases returned 1 before the fix and now correctly return 2.
• All 40 graph tests pass with python3 -m unittest tests.test_graph -q.
• git diff --check passes.

Summary by CodeRabbit

• Bug Fixes
  • Corrected maximum-flow calculations so earlier path choices can be reversed when finding the optimal flow.
• Tests
  • Added regression coverage for graphs that require revising an earlier path to reach the maximum flow.

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ℹ️ Recent review info

⚙️ Run configuration

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• Run ID: de68c42e-2767-425f-8b92-6d875d5d472b

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📥 Commits

Reviewing files that changed from the base of the PR and between bd1d152 and d190efb.

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📒 Files selected for processing (3)

• algorithms/graph/maximum_flow_bfs.py
• algorithms/graph/maximum_flow_dfs.py
• tests/test_graph.py

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📝 Walkthrough

Walkthrough

The BFS and DFS maximum-flow implementations now add reverse residual capacity during augmentation. New regression tests check that both return a maximum flow of 2 when rerouting is required.

Changes

Maximum-flow rerouting

Layer / File(s)	Summary
Reverse residual capacity and rerouting tests algorithms/graph/maximum_flow_bfs.py, algorithms/graph/maximum_flow_dfs.py, tests/test_graph.py	Both algorithms add flow to reverse residual capacity during augmentation. Regression tests verify that each algorithm returns 2 for a network that requires rerouting.

Priority: ➖ Normal

Estimated code review effort: 2 (Simple) | ~10 minutes

Change: Bug fix · Severity of issue fixed: Medium

Suggested reviewers: keon

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Merge Risk: ⚪ Minimal · up to d190e

The change appears ready to merge after normal checks.

Pre-merge checks | 4 | 1

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Docstring Coverage		Docstring coverage is 28.57% which is insufficient. The required threshold is 80.00%. Docstring coverage is scoped to functions touched by this diff. Analyzed 7 functions across 3 files.	Write docstrings for the functions missing them to satisfy the coverage threshold.

✅ Passed checks (4 passed)

Check name	Status	Explanation
Description Check		Check skipped - CodeRabbit’s high-level summary is enabled.
Title check		The title clearly and concisely describes the main change: restoring reverse residual capacity in both BFS and DFS maximum-flow implementations.
Linked Issues check		Issue [#2787] requires reverse residual-capacity updates in maximum_flow_bfs and maximum_flow_dfs, plus rerouting regression tests that return 2 for the supplied networks. The change summary rep…
Out of Scope Changes check		The reported changes are limited to the two functions named by issue [#2787] and their regression tests. The summaries report no public declaration changes. These changes directly support the issue ob…

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