[Miladkhoshdel]

Fixes #2785

Bug

Both bellman_ford and bellman_ford_paths incorrectly report a negative cycle when a destination vertex appears only as a neighbor.

For example:

graph = {"a": {"b": 1}}

bellman_ford(graph, "a")
# Actual: False
# Expected: True

bellman_ford_paths(graph, "a")
# Actual: (None, None, True)
# Expected: ({"a": 0, "b": 1}, {"a": None, "b": "a"}, False)

This graph contains two vertices and one positive edge, with no cycle.

Initialization correctly discovers both vertices. However, both functions use len(graph) to calculate the vertex count, counting only top-level dictionary keys.

Here, that count is 1, so the V - 1 relaxation loop performs zero passes. The distance to b remains infinity, and the subsequent negative-cycle check incorrectly interprets the unprocessed edge as evidence of a negative cycle.

For longer paths, insufficient relaxation passes can also make results depend on dictionary insertion order.

Fix

Use len(distance) to count vertices in both functions. The initialized distance dictionary includes neighbor-only vertices, providing the correct number of relaxation passes before checking for negative cycles.

Regression tests

Added coverage for both functions:

• A single positive edge to a neighbor-only vertex.
• A chain ending at a neighbor-only sink, with different insertion orders.
• A negative edge without a cycle.
• A reachable negative cycle with a neighbor-only sink.

Validation

• Full test suite: 604 passed.
• git diff --check: passed.

Summary by CodeRabbit

• Bug Fixes
  • Bellman-Ford now correctly handles vertices that appear only as neighbors, including when calculating shortest paths and detecting reachable negative cycles.
• Tests
  • Added coverage for positive and negative edges, multi-edge paths with different vertex orders, and negative-cycle detection.

[coderabbitai]

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ℹ️ Recent review info

⚙️ Run configuration

• Configuration used: defaults
• Review profile: CHILL
• Plan: Advanced
• Run ID: aefde835-dfca-42c7-9247-0142815954d0

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📥 Commits

Reviewing files that changed from the base of the PR and between bd1d152 and 6e48195.

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📒 Files selected for processing (2)

• algorithms/graph/bellman_ford.py
• tests/test_graph.py

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📝 Walkthrough

Walkthrough

Both Bellman-Ford functions now count initialized distance entries when setting the relaxation-pass count. New tests cover neighbor-only destinations, paths in different insertion orders, and negative-cycle detection.

Changes

Bellman-Ford vertex counting

Layer / File(s)	Summary
Relaxation count and regression coverage algorithms/graph/bellman_ford.py, tests/test_graph.py	Both functions use the initialized distance map to set the relaxation-pass count. Tests cover single edges, two-edge paths in different insertion orders, and a reachable negative cycle. The tests check distances and predecessors from bellman_ford_paths.

Priority: ⬇️ Low

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

Change: Bug fix · Severity of issue fixed: Low

Suggested reviewers: keon

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Merge Risk: ⚪ Minimal · up to 6e481

No actionable merge-blocking risk is identified; the change is mergeable 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 2 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: fixing false negative-cycle detection for neighbor-only vertices in Bellman-Ford.
Linked Issues check		Issue #2785 requires both bellman_ford and bellman_ford_paths to count neighbor-only vertices during relaxation. The PR changes both functions to use the initialized distance dictionary for the …
Out of Scope Changes check		The changes are limited to algorithms/graph/bellman_ford.py and regression tests in tests/test_graph.py. The implementation change and tests directly support Issue #2785. No unrelated change is id…

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