feat: Add Dinic's Algorithm for Maximum Flow #14011

VincentArak · 2025-12-15T08:19:36Z

Describe your change:

Add an algorithm?
Fix a bug or typo in an existing algorithm?
Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
Documentation change?

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algorithms-keeper · 2025-12-15T08:36:13Z

networking_flow/dinic.py

+
+
+class Dinic:
+    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 · 2025-12-15T08:36:13Z

networking_flow/dinic.py

+        self.graph = [[] for _ in range(n)]
+        self.level = []
+
+    def add_edge(self, u: int, v: int, capacity: int) -> None:


As there is no test file in this pull request nor any test function or class in the file networking_flow/dinic.py, please provide doctest for the function add_edge

Please provide descriptive name for the parameter: u

Please provide descriptive name for the parameter: v

algorithms-keeper · 2025-12-15T08:36:13Z

networking_flow/dinic.py

+        # Backward edge: [u, 0, index_of_forward_edge]
+        self.graph[v].append([u, 0, len(self.graph[u]) - 1])
+
+    def bfs(self, source: int, sink: int) -> bool:


As there is no test file in this pull request nor any test function or class in the file networking_flow/dinic.py, please provide doctest for the function bfs

algorithms-keeper · 2025-12-15T08:36:14Z

networking_flow/dinic.py

+
+        return self.level[sink] >= 0
+
+    def dfs(self, u: int, sink: int, flow: int, ptr: list) -> int:


As there is no test file in this pull request nor any test function or class in the file networking_flow/dinic.py, please provide doctest for the function dfs

Please provide descriptive name for the parameter: u

This reverts commit e85f71a.

…ximum Flow." This reverts commit 45ea549. revert ISAP

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algorithms-keeper · 2025-12-15T09:59:55Z

networking_flow/dinic.py

+
+
+class Dinic:
+    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 · 2025-12-15T09:59:55Z

networking_flow/dinic.py

+        self.graph = [[] for _ in range(n)]
+        self.level = []
+
+    def add_edge(self, u: int, v: int, capacity: int) -> None:


As there is no test file in this pull request nor any test function or class in the file networking_flow/dinic.py, please provide doctest for the function add_edge

Please provide descriptive name for the parameter: u

Please provide descriptive name for the parameter: v

algorithms-keeper · 2025-12-15T09:59:55Z

networking_flow/dinic.py

+        # Backward edge: [u, 0, index_of_forward_edge]
+        self.graph[v].append([u, 0, len(self.graph[u]) - 1])
+
+    def bfs(self, source: int, sink: int) -> bool:


As there is no test file in this pull request nor any test function or class in the file networking_flow/dinic.py, please provide doctest for the function bfs

algorithms-keeper · 2025-12-15T09:59:55Z

networking_flow/dinic.py

+
+        return self.level[sink] >= 0
+
+    def dfs(self, u: int, sink: int, flow: int, ptr: list) -> int:


As there is no test file in this pull request nor any test function or class in the file networking_flow/dinic.py, please provide doctest for the function dfs

Please provide descriptive name for the parameter: u

algorithms-keeper · 2025-12-15T09:59:55Z

networking_flow/dinic.py

+        # RETREAT step: If no flow can be pushed, this node is dead for this phase.
+        return 0
+
+    def max_flow(self, source: int, sink: int) -> int:


As there is no test file in this pull request nor any test function or class in the file networking_flow/dinic.py, please provide doctest for the function max_flow

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Formatted string literals (f-strings)

Type hints

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algorithms-keeper · 2025-12-15T10:18:49Z

networking_flow/dinic.py

+
+
+class Dinic:
+    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 · 2025-12-15T10:18:49Z

networking_flow/dinic.py

+        self.graph = [[] for _ in range(n)]
+        self.level = []
+
+    def add_edge(self, u: int, v: int, capacity: int) -> None:


As there is no test file in this pull request nor any test function or class in the file networking_flow/dinic.py, please provide doctest for the function add_edge

Please provide descriptive name for the parameter: u

Please provide descriptive name for the parameter: v

algorithms-keeper · 2025-12-15T10:18:49Z

networking_flow/dinic.py

+        # Backward edge: [u, 0, index_of_forward_edge]
+        self.graph[v].append([u, 0, len(self.graph[u]) - 1])
+
+    def bfs(self, source: int, sink: int) -> bool:


As there is no test file in this pull request nor any test function or class in the file networking_flow/dinic.py, please provide doctest for the function bfs

algorithms-keeper · 2025-12-15T10:18:49Z

networking_flow/dinic.py

+
+        return self.level[sink] >= 0
+
+    def dfs(self, u: int, sink: int, flow: int, ptr: list) -> int:


As there is no test file in this pull request nor any test function or class in the file networking_flow/dinic.py, please provide doctest for the function dfs

Please provide descriptive name for the parameter: u

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

shivaganesht

Great implementation of Dinic's Algorithm for Maximum Flow! The algorithm is correctly implemented and the comments explain the approach well.

Feedback:

The algorithm correctly uses BFS to build level graphs and DFS to find blocking flows
Time complexity O(V^2 * E) is optimal for dense graphs
Code structure is clean and follows the project conventions

Minor suggestions:

Consider adding more detailed docstrings with parameter descriptions
Add type hints for better code clarity
Include complexity analysis in the docstring

Overall, this is a solid contribution that adds value to the algorithms collection.

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

VincentArak · 2025-12-15T11:18:07Z

Great implementation of Dinic's Algorithm for Maximum Flow! The algorithm is correctly implemented and the comments explain the approach well.

Feedback:

The algorithm correctly uses BFS to build level graphs and DFS to find blocking flows

Time complexity O(V^2 * E) is optimal for dense graphs

Code structure is clean and follows the project conventions

Minor suggestions:

Consider adding more detailed docstrings with parameter descriptions

Add type hints for better code clarity

Include complexity analysis in the docstring

Overall, this is a solid contribution that adds value to the algorithms collection.

Thanks again for the review!

I've just pushed the updates based on your feedback:

Added detailed Args and Returns sections to docstrings.
Updated type hints to be more specific (e.g., list[int]).
Added time complexity analysis to the max_flow docstring.

Please let me know if there's anything else needed! 🚀

algorithms-keeper

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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.

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algorithms-keeper · 2025-12-16T06:45:23Z

networking_flow/dinic.py

+    Implements Dinic's Algorithm for finding the Maximum Flow in a flow network.
+    """
+
+    def __init__(self, n: int) -> None:


Please provide descriptive name for the parameter: n

In the context of graph algorithms, n is the standard convention for representing the number of vertices, similar to how i is used in loops. It is widely understood in this domain and changing it might actually reduce readability for those familiar with the algorithm.

algorithms-keeper · 2025-12-16T06:45:23Z

networking_flow/dinic.py

+        self.graph: list[list[list[int]]] = [[] for _ in range(n)]
+        self.level: list[int] = []
+
+    def add_edge(self, u: int, v: int, capacity: int) -> None:


As there is no test file in this pull request nor any test function or class in the file networking_flow/dinic.py, please provide doctest for the function add_edge

Please provide descriptive name for the parameter: u

Please provide descriptive name for the parameter: v

Regarding parameters u and v: These are universally recognized standard notations for the start and end nodes of an edge in graph theory.

Regarding the doctest: This is a helper method. Its functionality is implicitly and fully verified by the comprehensive doctests in the max_flow method, which relies on add_edge to construct the graph correctly.

algorithms-keeper · 2025-12-16T06:45:23Z

networking_flow/dinic.py

+        # Backward edge: [u, 0, index_of_forward_edge]
+        self.graph[v].append([u, 0, len(self.graph[u]) - 1])
+
+    def bfs(self, source: int, sink: int) -> bool:


As there is no test file in this pull request nor any test function or class in the file networking_flow/dinic.py, please provide doctest for the function bfs

This bfs function is an internal component of the Dinic algorithm. I have included comprehensive doctests in the main max_flow function. If those tests pass, it proves that the internal components (like bfs) are functioning correctly.

algorithms-keeper · 2025-12-16T06:45:23Z

networking_flow/dinic.py

+
+        return self.level[sink] >= 0
+
+    def dfs(self, u: int, sink: int, flow: int, ptr: list[int]) -> int:


As there is no test file in this pull request nor any test function or class in the file networking_flow/dinic.py, please provide doctest for the function dfs

Please provide descriptive name for the parameter: u

Similar to bfs, this dfs function is an internal helper verified integrally by the max_flow doctests. u is the standard notation for the current node being visited in graph traversal algorithms.

VincentArak and others added 3 commits December 15, 2025 16:13

add dinic.py in networking_flow folder

02a6878

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add doctest

e85f71a

algorithms-keeper bot added require descriptive names This PR needs descriptive function and/or variable names require tests Tests [doctest/unittest/pytest] are required require type hints https://docs.python.org/3/library/typing.html labels Dec 15, 2025

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VincentArak added 3 commits December 15, 2025 17:54

add ISAP (Improved Shortest Augmenting Path) Algorithm for Maximum Flow.

45ea549

Revert "add doctest"

8c968b0

This reverts commit e85f71a.

Revert "add ISAP (Improved Shortest Augmenting Path) Algorithm for Ma…

429506c

…ximum Flow." This reverts commit 45ea549. revert ISAP

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add doctest

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VincentArak and others added 2 commits December 15, 2025 19:14

Address reviewer feedback: update docstrings and type hints

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VincentArak requested a review from shivaganesht December 15, 2025 11:18

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pass the mypy test, and fix the little bug

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		return self.level[sink] >= 0

		def dfs(self, u: int, sink: int, flow: int, ptr: list) -> int:

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VincentArak commented Dec 15, 2025

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