Add 10 graph algorithms by gangs2314 · Pull Request #14316 · TheAlgorithms/Python

gangs2314 · 2026-03-01T08:45:29Z

Describe your change:

Add an algorithm?
Fix a bug or typo in an existing algorithm?
Documentation change?

Checklist:

I have read CONTRIBUTING.md.
This PR only changes one algorithm file or relates to only one algorithm.
All new algorithms include comprehensive docstrings with complexity analysis.
All functions have type hints.
All new algorithms include doctests with examples.
Tests have been added and all tests pass.
I have NOT edited the README or any other documentation files.

Description

Implemented 10 advanced graph algorithms with comprehensive tests.

algorithms-keeper

Click here to look at the relevant links ⬇️

🔗 Relevant Links

Repository:

Contributing guidelines

Project Euler solution guidelines

Python:

Formatted string literals (f-strings)

Type hints

doctest

unittest

pytest

Automated review generated by algorithms-keeper. If there's any problem regarding this review, please open an issue about it.

algorithms-keeper commands and options

algorithms-keeper actions can be triggered by commenting on this PR:

@algorithms-keeper review to trigger the checks for only added pull request files

@algorithms-keeper review-all to trigger the checks for all the pull request files, including the modified files. As we cannot post review comments on lines not part of the diff, this command will post all the messages in one comment.

NOTE: Commands are in beta and so this feature is restricted only to a member or owner of the organization.

algorithms-keeper · 2026-03-01T08:45:44Z

+    Solve Chinese Postman Problem for weighted undirected graphs.
+    """
+
+    def __init__(self, n: int):


Please provide return type hint for the function: __init__. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide descriptive name for the parameter: n

algorithms-keeper · 2026-03-01T08:45:44Z

+        self.adj: List[List[Tuple[int, int]]] = [[] for _ in range(n)]
+        self.total_weight = 0
+
+    def add_edge(self, u: int, v: int, w: int) -> None:


Please provide descriptive name for the parameter: u

Please provide descriptive name for the parameter: v

Please provide descriptive name for the parameter: w

algorithms-keeper · 2026-03-01T08:45:44Z

+
+
+def chinese_postman(
+    n: int, edges: List[Tuple[int, int, int]]


Please provide descriptive name for the parameter: n

algorithms-keeper · 2026-03-01T08:45:44Z

+    import random
+    import time
+
+    def benchmark():


Please provide return type hint for the function: benchmark. If the function does not return a value, please provide the type hint as: def function() -> None:

algorithms-keeper · 2026-03-01T08:45:44Z

+    Maximum flow using Ford-Fulkerson with Edmonds-Karp (BFS).
+    """
+
+    def __init__(self, n: int):


Please provide return type hint for the function: __init__. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide descriptive name for the parameter: n

algorithms-keeper · 2026-03-01T08:45:45Z

+        self.rev_graph[b].append(not_a)
+        self.rev_graph[a].append(not_b)
+
+    def add_implication(self, i: int, val_i: bool, j: int, val_j: bool) -> None:


Please provide descriptive name for the parameter: i

Please provide descriptive name for the parameter: j

algorithms-keeper · 2026-03-01T08:45:45Z

+        self.graph[a].append(b)
+        self.rev_graph[b].append(a)
+
+    def add_nand(self, i: int, val_i: bool, j: int, val_j: bool) -> None:


Please provide descriptive name for the parameter: i

Please provide descriptive name for the parameter: j

algorithms-keeper · 2026-03-01T08:45:45Z

+        visited = [False] * n
+        order = []
+
+        def dfs1(u: int):


Please provide return type hint for the function: dfs1. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide descriptive name for the parameter: u

algorithms-keeper · 2026-03-01T08:45:45Z

+        component = [-1] * n
+        current_comp = 0
+
+        def dfs2(u: int):


Please provide return type hint for the function: dfs2. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide descriptive name for the parameter: u

algorithms-keeper · 2026-03-01T08:45:45Z

+
+
+def solve_2sat(
+    n: int, clauses: List[Tuple[int, bool, int, bool]]


Please provide descriptive name for the parameter: n

algorithms-keeper

Click here to look at the relevant links ⬇️

🔗 Relevant Links

Repository:

Contributing guidelines

Project Euler solution guidelines

Python:

Formatted string literals (f-strings)

Type hints

doctest

unittest

pytest

Automated review generated by algorithms-keeper. If there's any problem regarding this review, please open an issue about it.

algorithms-keeper commands and options

algorithms-keeper actions can be triggered by commenting on this PR:

@algorithms-keeper review to trigger the checks for only added pull request files

@algorithms-keeper review-all to trigger the checks for all the pull request files, including the modified files. As we cannot post review comments on lines not part of the diff, this command will post all the messages in one comment.

NOTE: Commands are in beta and so this feature is restricted only to a member or owner of the organization.

algorithms-keeper · 2026-03-04T13:36:36Z

+    Solve Chinese Postman Problem for weighted undirected graphs.
+    """
+
+    def __init__(self, n: int):


Please provide return type hint for the function: __init__. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide descriptive name for the parameter: n

algorithms-keeper · 2026-03-04T13:36:36Z

+        self.adj: List[List[Tuple[int, int]]] = [[] for _ in range(n)]
+        self.total_weight = 0
+
+    def add_edge(self, u: int, v: int, w: int) -> None:


Please provide descriptive name for the parameter: u

Please provide descriptive name for the parameter: v

Please provide descriptive name for the parameter: w

algorithms-keeper · 2026-03-04T13:36:37Z

+
+
+def chinese_postman(
+    n: int, edges: List[Tuple[int, int, int]]


Please provide descriptive name for the parameter: n

algorithms-keeper · 2026-03-04T13:36:37Z

+    import random
+    import time
+
+    def benchmark():


Please provide return type hint for the function: benchmark. If the function does not return a value, please provide the type hint as: def function() -> None:

algorithms-keeper · 2026-03-04T13:36:37Z

+    Maximum flow using Ford-Fulkerson with Edmonds-Karp (BFS).
+    """
+
+    def __init__(self, n: int):


Please provide return type hint for the function: __init__. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide descriptive name for the parameter: n

algorithms-keeper · 2026-03-04T13:36:38Z

+        self.rev_graph[b].append(not_a)
+        self.rev_graph[a].append(not_b)
+
+    def add_implication(self, i: int, val_i: bool, j: int, val_j: bool) -> None:


Please provide descriptive name for the parameter: i

Please provide descriptive name for the parameter: j

algorithms-keeper · 2026-03-04T13:36:38Z

+        self.graph[a].append(b)
+        self.rev_graph[b].append(a)
+
+    def add_nand(self, i: int, val_i: bool, j: int, val_j: bool) -> None:


Please provide descriptive name for the parameter: i

Please provide descriptive name for the parameter: j

algorithms-keeper · 2026-03-04T13:36:38Z

+        visited = [False] * n
+        order = []
+
+        def dfs1(u: int):


Please provide return type hint for the function: dfs1. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide descriptive name for the parameter: u

algorithms-keeper · 2026-03-04T13:36:38Z

+        component = [-1] * n
+        current_comp = 0
+
+        def dfs2(u: int):


Please provide return type hint for the function: dfs2. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide descriptive name for the parameter: u

algorithms-keeper · 2026-03-04T13:36:38Z

+
+
+def solve_2sat(
+    n: int, clauses: List[Tuple[int, bool, int, bool]]


Please provide descriptive name for the parameter: n

New Algorithms: 1. Floyd-Warshall (all-pairs shortest path) - O(V³) 2. Johnson's Algorithm (sparse graph all-pairs) - O(V² log V + VE) 3. Hopcroft-Karp (maximum bipartite matching) - O(E√V) 4. Ford-Fulkerson with Edmonds-Karp (max flow) - O(VE²) 5. Push-Relabel (faster max flow) - O(V²√E) 6. 2-SAT Solver (using SCC) - O(V + E) 7. Chinese Postman Problem (route inspection) - O(V³ + 2^k k²) 8. Traveling Salesman (Held-Karp DP) - O(n² 2ⁿ) 9. Heavy-Light Decomposition (path queries) - O(n log² n) 10. Maximum Bipartite Independent Set - O(E√V) All algorithms include: - Type hints and docstrings with complexity analysis - Doctests with examples - Comprehensive pytest test suite (50+ tests) Test coverage: Added 50+ unit tests

for more information, see https://pre-commit.ci

algorithms-keeper

Click here to look at the relevant links ⬇️

🔗 Relevant Links

Repository:

Contributing guidelines

Project Euler solution guidelines

Python:

Formatted string literals (f-strings)

Type hints

doctest

unittest

pytest

Automated review generated by algorithms-keeper. If there's any problem regarding this review, please open an issue about it.

algorithms-keeper commands and options

algorithms-keeper actions can be triggered by commenting on this PR:

@algorithms-keeper review to trigger the checks for only added pull request files

@algorithms-keeper review-all to trigger the checks for all the pull request files, including the modified files. As we cannot post review comments on lines not part of the diff, this command will post all the messages in one comment.

NOTE: Commands are in beta and so this feature is restricted only to a member or owner of the organization.

algorithms-keeper · 2026-06-19T07:11:22Z

+from pathlib import Path
+
+
+def fix_floyd_warshall():


Please provide return type hint for the function: fix_floyd_warshall. If the function does not return a value, please provide the type hint as: def function() -> None:

algorithms-keeper · 2026-06-19T07:11:22Z

+    print("fixed graphs/floyd_warshall.py")
+
+
+def fix_ford_fulkerson():


Please provide return type hint for the function: fix_ford_fulkerson. If the function does not return a value, please provide the type hint as: def function() -> None:

algorithms-keeper · 2026-06-19T07:11:22Z

+    p.write_text(text)
+    print("fixed graphs/ford_fulkerson.py")
+
+


Please provide return type hint for the function: fix_heavy_light_decomposition. If the function does not return a value, please provide the type hint as: def function() -> None:

algorithms-keeper · 2026-06-19T07:11:22Z

+    p.write_text(text)
+    print("fixed graphs/heavy_light_decomposition.py")
+
+


Please provide return type hint for the function: fix_hopcroft_karp. If the function does not return a value, please provide the type hint as: def function() -> None:

algorithms-keeper · 2026-06-19T07:11:22Z

+    p.write_text(text)
+    print("fixed graphs/hopcroft_karp.py")
+
+


Please provide return type hint for the function: fix_max_bipartite_independent_set. If the function does not return a value, please provide the type hint as: def function() -> None:

algorithms-keeper · 2026-06-19T07:11:24Z

+        self.rev_graph[b].append(not_a)
+        self.rev_graph[a].append(not_b)
+
+    def add_implication(self, i: int, val_i: bool, j: int, val_j: bool) -> None:


Please provide descriptive name for the parameter: i

Please provide descriptive name for the parameter: j

algorithms-keeper · 2026-06-19T07:11:24Z

+        self.graph[a].append(b)
+        self.rev_graph[b].append(a)
+
+    def add_nand(self, i: int, val_i: bool, j: int, val_j: bool) -> None:


Please provide descriptive name for the parameter: i

Please provide descriptive name for the parameter: j

algorithms-keeper · 2026-06-19T07:11:24Z

+        visited = [False] * n
+        order = []
+
+        def dfs1(u: int):


Please provide return type hint for the function: dfs1. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide descriptive name for the parameter: u

algorithms-keeper · 2026-06-19T07:11:24Z

+        component = [-1] * n
+        current_comp = 0
+
+        def dfs2(u: int):


Please provide return type hint for the function: dfs2. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide descriptive name for the parameter: u

algorithms-keeper · 2026-06-19T07:11:24Z

+        return assignment
+
+
+def solve_2sat(n: int, clauses: list[tuple[int, bool, int, bool]]) -> list[bool] | None:


Please provide descriptive name for the parameter: n

for more information, see https://pre-commit.ci

algorithms-keeper

Click here to look at the relevant links ⬇️

🔗 Relevant Links

Repository:

Contributing guidelines

Project Euler solution guidelines

Python:

Formatted string literals (f-strings)

Type hints

doctest

unittest

pytest

Automated review generated by algorithms-keeper. If there's any problem regarding this review, please open an issue about it.

algorithms-keeper commands and options

algorithms-keeper actions can be triggered by commenting on this PR:

@algorithms-keeper review to trigger the checks for only added pull request files

@algorithms-keeper review-all to trigger the checks for all the pull request files, including the modified files. As we cannot post review comments on lines not part of the diff, this command will post all the messages in one comment.

NOTE: Commands are in beta and so this feature is restricted only to a member or owner of the organization.

algorithms-keeper · 2026-06-19T07:20:04Z

+from pathlib import Path
+
+
+def fix_floyd_warshall():


Please provide return type hint for the function: fix_floyd_warshall. If the function does not return a value, please provide the type hint as: def function() -> None:

algorithms-keeper · 2026-06-19T07:20:04Z

+    print("fixed graphs/floyd_warshall.py")
+
+
+def fix_ford_fulkerson():


Please provide return type hint for the function: fix_ford_fulkerson. If the function does not return a value, please provide the type hint as: def function() -> None:

algorithms-keeper · 2026-06-19T07:20:04Z

+    print("fixed graphs/ford_fulkerson.py")
+
+
+def fix_heavy_light_decomposition():


Please provide return type hint for the function: fix_heavy_light_decomposition. If the function does not return a value, please provide the type hint as: def function() -> None:

algorithms-keeper · 2026-06-19T07:20:04Z

+    print("fixed graphs/heavy_light_decomposition.py")
+
+
+def fix_hopcroft_karp():


Please provide return type hint for the function: fix_hopcroft_karp. If the function does not return a value, please provide the type hint as: def function() -> None:

algorithms-keeper · 2026-06-19T07:20:04Z

+    print("fixed graphs/hopcroft_karp.py")
+
+
+def fix_max_bipartite_independent_set():


Please provide return type hint for the function: fix_max_bipartite_independent_set. If the function does not return a value, please provide the type hint as: def function() -> None:

algorithms-keeper · 2026-06-19T07:20:05Z

+        self.rev_graph[b].append(not_a)
+        self.rev_graph[a].append(not_b)
+
+    def add_implication(self, i: int, val_i: bool, j: int, val_j: bool) -> None:


Please provide descriptive name for the parameter: i

Please provide descriptive name for the parameter: j

algorithms-keeper · 2026-06-19T07:20:05Z

+        self.graph[a].append(b)
+        self.rev_graph[b].append(a)
+
+    def add_nand(self, i: int, val_i: bool, j: int, val_j: bool) -> None:


Please provide descriptive name for the parameter: i

Please provide descriptive name for the parameter: j

algorithms-keeper · 2026-06-19T07:20:05Z

+        visited = [False] * n
+        order = []
+
+        def dfs1(u: int):


Please provide return type hint for the function: dfs1. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide descriptive name for the parameter: u

algorithms-keeper · 2026-06-19T07:20:05Z

+        component = [-1] * n
+        current_comp = 0
+
+        def dfs2(u: int):


Please provide return type hint for the function: dfs2. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide descriptive name for the parameter: u

algorithms-keeper · 2026-06-19T07:20:05Z

+        return assignment
+
+
+def solve_2sat(n: int, clauses: list[tuple[int, bool, int, bool]]) -> list[bool] | None:


Please provide descriptive name for the parameter: n

algorithms-keeper Bot added require descriptive names This PR needs descriptive function and/or variable names require type hints https://docs.python.org/3/library/typing.html labels Mar 1, 2026

algorithms-keeper Bot reviewed Mar 1, 2026

View reviewed changes

algorithms-keeper Bot added awaiting reviews This PR is ready to be reviewed tests are failing Do not merge until tests pass labels Mar 1, 2026

algorithms-keeper Bot reviewed Mar 4, 2026

View reviewed changes

gangs2314 and others added 5 commits June 19, 2026 12:38

[pre-commit.ci] auto fixes from pre-commit.com hooks

46e575b

for more information, see https://pre-commit.ci

Fix flake8 errors and add __init__.py files

9718a3e

Fix style issues (flake8)

cee0636

fix: resolve ruff linting, naming, and type hint issues

d063a89

gangs2314 force-pushed the add-10-graph-algorithms branch from 4cca9f1 to d063a89 Compare June 19, 2026 07:10

algorithms-keeper Bot reviewed Jun 19, 2026

View reviewed changes

fix: correct push-relabel active condition and johnson test expectation

22d5ba3

gangs2314 force-pushed the add-10-graph-algorithms branch from cda6b3f to 22d5ba3 Compare June 19, 2026 07:19

[pre-commit.ci] auto fixes from pre-commit.com hooks

70b94f1

for more information, see https://pre-commit.ci

algorithms-keeper Bot reviewed Jun 19, 2026

View reviewed changes



		def chinese_postman(
		n: int, edges: List[Tuple[int, int, int]]



		def solve_2sat(
		n: int, clauses: List[Tuple[int, bool, int, bool]]

		print("fixed graphs/floyd_warshall.py")


		def fix_ford_fulkerson():

		p.write_text(text)
		print("fixed graphs/heavy_light_decomposition.py")

		return assignment


		def solve_2sat(n: int, clauses: list[tuple[int, bool, int, bool]]) -> list[bool] \| None:

		print("fixed graphs/ford_fulkerson.py")


		def fix_heavy_light_decomposition():

		print("fixed graphs/heavy_light_decomposition.py")


		def fix_hopcroft_karp():

		print("fixed graphs/hopcroft_karp.py")


		def fix_max_bipartite_independent_set():

Uh oh!

Conversation

gangs2314 commented Mar 1, 2026

Describe your change:

Checklist:

Description

Uh oh!

algorithms-keeper Bot left a comment

Choose a reason for hiding this comment

🔗 Relevant Links

Repository:

Python:

Automated review generated by algorithms-keeper. If there's any problem regarding this review, please open an issue about it.

algorithms-keeper actions can be triggered by commenting on this PR:

Uh oh!

algorithms-keeper Bot Mar 1, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 1, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 1, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 1, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 1, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 1, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 1, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 1, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 1, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 1, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot left a comment

Choose a reason for hiding this comment

🔗 Relevant Links

Repository:

Python:

Automated review generated by algorithms-keeper. If there's any problem regarding this review, please open an issue about it.

algorithms-keeper actions can be triggered by commenting on this PR:

Uh oh!

algorithms-keeper Bot Mar 4, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 4, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 4, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 4, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 4, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 4, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 4, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 4, 2026

Choose a reason for hiding this comment

Uh oh!

algorithms-keeper Bot Mar 4, 2026

Choose a reason for hiding this comment

Uh oh!