mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-27 15:01:08 +00:00
bc8df6de31
* [pre-commit.ci] pre-commit autoupdate updates: - [github.com/astral-sh/ruff-pre-commit: v0.2.2 → v0.3.2](https://github.com/astral-sh/ruff-pre-commit/compare/v0.2.2...v0.3.2) - [github.com/pre-commit/mirrors-mypy: v1.8.0 → v1.9.0](https://github.com/pre-commit/mirrors-mypy/compare/v1.8.0...v1.9.0) * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
114 lines
2.9 KiB
Python
114 lines
2.9 KiB
Python
"""
|
|
Ford-Fulkerson Algorithm for Maximum Flow Problem
|
|
* https://en.wikipedia.org/wiki/Ford%E2%80%93Fulkerson_algorithm
|
|
|
|
Description:
|
|
(1) Start with initial flow as 0
|
|
(2) Choose the augmenting path from source to sink and add the path to flow
|
|
"""
|
|
|
|
graph = [
|
|
[0, 16, 13, 0, 0, 0],
|
|
[0, 0, 10, 12, 0, 0],
|
|
[0, 4, 0, 0, 14, 0],
|
|
[0, 0, 9, 0, 0, 20],
|
|
[0, 0, 0, 7, 0, 4],
|
|
[0, 0, 0, 0, 0, 0],
|
|
]
|
|
|
|
|
|
def breadth_first_search(graph: list, source: int, sink: int, parents: list) -> bool:
|
|
"""
|
|
This function returns True if there is a node that has not iterated.
|
|
|
|
Args:
|
|
graph: Adjacency matrix of graph
|
|
source: Source
|
|
sink: Sink
|
|
parents: Parent list
|
|
|
|
Returns:
|
|
True if there is a node that has not iterated.
|
|
|
|
>>> breadth_first_search(graph, 0, 5, [-1, -1, -1, -1, -1, -1])
|
|
True
|
|
>>> breadth_first_search(graph, 0, 6, [-1, -1, -1, -1, -1, -1])
|
|
Traceback (most recent call last):
|
|
...
|
|
IndexError: list index out of range
|
|
"""
|
|
visited = [False] * len(graph) # Mark all nodes as not visited
|
|
queue = [] # breadth-first search queue
|
|
|
|
# Source node
|
|
queue.append(source)
|
|
visited[source] = True
|
|
|
|
while queue:
|
|
u = queue.pop(0) # Pop the front node
|
|
# Traverse all adjacent nodes of u
|
|
for ind, node in enumerate(graph[u]):
|
|
if visited[ind] is False and node > 0:
|
|
queue.append(ind)
|
|
visited[ind] = True
|
|
parents[ind] = u
|
|
return visited[sink]
|
|
|
|
|
|
def ford_fulkerson(graph: list, source: int, sink: int) -> int:
|
|
"""
|
|
This function returns the maximum flow from source to sink in the given graph.
|
|
|
|
CAUTION: This function changes the given graph.
|
|
|
|
Args:
|
|
graph: Adjacency matrix of graph
|
|
source: Source
|
|
sink: Sink
|
|
|
|
Returns:
|
|
Maximum flow
|
|
|
|
>>> test_graph = [
|
|
... [0, 16, 13, 0, 0, 0],
|
|
... [0, 0, 10, 12, 0, 0],
|
|
... [0, 4, 0, 0, 14, 0],
|
|
... [0, 0, 9, 0, 0, 20],
|
|
... [0, 0, 0, 7, 0, 4],
|
|
... [0, 0, 0, 0, 0, 0],
|
|
... ]
|
|
>>> ford_fulkerson(test_graph, 0, 5)
|
|
23
|
|
"""
|
|
# This array is filled by breadth-first search and to store path
|
|
parent = [-1] * (len(graph))
|
|
max_flow = 0
|
|
|
|
# While there is a path from source to sink
|
|
while breadth_first_search(graph, source, sink, parent):
|
|
path_flow = int(1e9) # Infinite value
|
|
s = sink
|
|
|
|
while s != source:
|
|
# Find the minimum value in the selected path
|
|
path_flow = min(path_flow, graph[parent[s]][s])
|
|
s = parent[s]
|
|
|
|
max_flow += path_flow
|
|
v = sink
|
|
|
|
while v != source:
|
|
u = parent[v]
|
|
graph[u][v] -= path_flow
|
|
graph[v][u] += path_flow
|
|
v = parent[v]
|
|
|
|
return max_flow
|
|
|
|
|
|
if __name__ == "__main__":
|
|
from doctest import testmod
|
|
|
|
testmod()
|
|
print(f"{ford_fulkerson(graph, source=0, sink=5) = }")
|