Added Johnson's algorithm for all-pairs shortest paths#13340
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cclauss merged 7 commits intoMay 20, 2026
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Hi @cclauss @MaximSmolskiy Could you review this pr and give some feedback. Could you please merge this after reviewing it ? |
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Hi @cclauss , I wanted to kindly ask if there’s any feedback or required changes for this PR. |
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Pull request overview
This PR adds a new graph algorithm implementation for Johnson’s all-pairs shortest paths, including support for negative edge weights and negative-cycle detection, plus pytest coverage.
Changes:
- Adds
graphs/johnson.pywith Bellman-Ford potentials and repeated Dijkstra runs. - Adds
graphs/tests/test_johnson.pycovering a basic graph and a negative-cycle case.
Reviewed changes
Copilot reviewed 2 out of 2 changed files in this pull request and generated 5 comments.
| File | Description |
|---|---|
graphs/johnson.py |
Implements Johnson’s algorithm and helper routines. |
graphs/tests/test_johnson.py |
Adds tests for successful shortest-path computation and negative-cycle rejection. |
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| new_dist = d_u + w_prime | ||
| if new_dist < dist[v]: | ||
| dist[v] = new_dist | ||
| heapq.heappush(heap, (new_dist, v)) |
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| assert math.isclose(dist[0][3], 2.0, abs_tol=1e-9) | ||
| assert math.isclose(dist[3][2], -5.0, abs_tol=1e-9) | ||
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| Example: | ||
| >>> g = { | ||
| ... 0: [(1, 3), (2, 8), (4, -4)], | ||
| ... 1: [(3, 1), (4, 7)], | ||
| ... 2: [(1, 4)], |
| Compute all-pairs shortest paths using Johnson's algorithm. | ||
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| Args: | ||
| graph: adjacency list {u: [(v, weight), ...], ...} |
cclauss
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May 20, 2026
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| heap: list[tuple[float, Node]] = [(0.0, start)] | ||
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| w_prime = w + potentials[u] - potentials[v] | ||
| if w_prime < 0: | ||
| raise ValueError( | ||
| "Negative edge weight after reweighting: numeric error" | ||
| ) |
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| Node = Hashable | ||
| edge = tuple[Node, Node, float] | ||
| adjacency = dict[Node, list[tuple[Node, float]]] |
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| Raises: | ||
| ValueError: if a negative weight cycle is detected | ||
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Describe your change:
This PR adds Johnson's algorithm for computing all-pairs shortest paths in a weighted graph. The implementation handles graphs with negative edge weights (but no negative cycles) by combining Bellman-Ford and Dijkstra algorithms. A corresponding test file
test_johnson.pyis also included to validate correctness.Checklist: