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change the default algorithm to the faster one in {path, cycle}_enumeration #41076

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Oct 27, 2025
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change the default algorithm to the faster one in {path, cycle}_enumeration #41076

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acaab2f
change the default algorithm to the faster one in k shortest path rel…
kappybar Oct 19, 2025
daeb424
specify algorithm='A' in failing tests
kappybar Oct 22, 2025
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2 changes: 1 addition & 1 deletion src/sage/combinat/finite_state_machine_generators.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1961,7 +1961,7 @@ def f(n):
"Missing initial values for %s." %
sorted(missing_initial_values))

for cycle in recursion_digraph.all_simple_cycles():
for cycle in recursion_digraph.all_simple_cycles(algorithm="A"):
assert cycle[0] is cycle[-1]
cycle_set = set(cycle)
intersection = cycle_set.intersection(initial_values_set)
Expand Down
2 changes: 1 addition & 1 deletion src/sage/dynamics/arithmetic_dynamics/projective_ds.py
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Original file line number Diff line number Diff line change
Expand Up @@ -4895,7 +4895,7 @@ def periodic_points(self, n, minimal=True, formal=False, R=None, algorithm='vari
if R in FiniteFields():
g = f.cyclegraph()
points = []
for cycle in g.all_simple_cycles():
for cycle in g.all_simple_cycles(algorithm="A"):
m = len(cycle)-1
if minimal:
if m == n:
Expand Down
148 changes: 80 additions & 68 deletions src/sage/graphs/cycle_enumeration.py
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Original file line number Diff line number Diff line change
Expand Up @@ -309,10 +309,10 @@ def _all_simple_cycles_iterator_edge(self, edge, max_length=None,
sage: g = graphs.Grid2dGraph(2, 5)
sage: it = g._all_simple_cycles_iterator_edge(((0, 0), (0, 1), None), report_weight=True)
sage: for i in range(4): print(next(it))
(4, [(0, 0), (0, 1), (1, 1), (1, 0), (0, 0)])
(6, [(0, 0), (0, 1), (0, 2), (1, 2), (1, 1), (1, 0), (0, 0)])
(8, [(0, 0), (0, 1), (0, 2), (0, 3), (1, 3), (1, 2), (1, 1), (1, 0), (0, 0)])
(10, [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 4), (1, 3), (1, 2), (1, 1), (1, 0), (0, 0)])
(4.0, [(0, 0), (0, 1), (1, 1), (1, 0), (0, 0)])
(6.0, [(0, 0), (0, 1), (0, 2), (1, 2), (1, 1), (1, 0), (0, 0)])
(8.0, [(0, 0), (0, 1), (0, 2), (0, 3), (1, 3), (1, 2), (1, 1), (1, 0), (0, 0)])
(10.0, [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 4), (1, 3), (1, 2), (1, 1), (1, 0), (0, 0)])

Each edge must have a positive weight::

Expand Down Expand Up @@ -379,7 +379,6 @@ def _all_simple_cycles_iterator_edge(self, edge, max_length=None,
weight_function=weight_function,
by_weight=by_weight,
check_weight=check_weight,
algorithm=('Feng' if h.is_directed() else 'Yen'),
report_edges=False,
report_weight=True)

Expand Down Expand Up @@ -461,7 +460,8 @@ def all_cycles_iterator(self, starting_vertices=None, simple=False,

- The algorithm ``'B'`` holds cycle iterators starting with each edge,
and output them in increasing length order. It depends on the k-shortest
simple paths algorithm. Thus, it is not available if ``simple=False``.
simple paths algorithm. Thus, it is not available if ``simple=False`` or
``rooted=True`` or ``starting_vertices`` is not ``None``.

OUTPUT: iterator

Expand Down Expand Up @@ -573,15 +573,24 @@ def all_cycles_iterator(self, starting_vertices=None, simple=False,
[0, 1, 2, 0]
[2, 3, 4, 5, 2]

The algorithm ``'B'`` is available only when ``simple=True``::
The algorithm ``'B'`` is unavailable when ``simple=False`` or ``rooted=True``
or ``starting_vertices is not None``::

sage: g = DiGraph()
sage: g.add_edges([('a', 'b', 1), ('b', 'a', 1)])
sage: next(g.all_cycles_iterator(algorithm='B', simple=False))
....:
Traceback (most recent call last):
...
ValueError: The algorithm 'B' is available only when simple=True.
ValueError: The algorithm 'B' is unavailable when simple=False.
sage: next(g.all_cycles_iterator(algorithm='B', simple=True, rooted=True))
Traceback (most recent call last):
...
ValueError: The algorithm 'B' is unavailable when rooted=True.
sage: next(g.all_cycles_iterator(algorithm='B', simple=True, starting_vertices=['a']))
Traceback (most recent call last):
...
ValueError: The algorithm 'B' is unavailable when starting_vertices is not None.

The algorithm ``'A'`` works for undirected graphs as well. Specifically, each cycle is
enumerated exactly once, meaning a cycle and its reverse are not listed separately::
Expand All @@ -591,12 +600,17 @@ def all_cycles_iterator(self, starting_vertices=None, simple=False,
....: print(cycle)
[0, 1, 2, 0]
"""
if algorithm == 'B':
if not simple:
raise ValueError("The algorithm 'B' is unavailable when simple=False.")
if starting_vertices:
raise ValueError("The algorithm 'B' is unavailable when starting_vertices is not None.")
if rooted:
raise ValueError("The algorithm 'B' is unavailable when rooted=True.")

if starting_vertices is None:
starting_vertices = self

if algorithm == 'B' and not simple:
raise ValueError("The algorithm 'B' is available only when simple=True.")

by_weight, weight_function = self._get_weight_function(by_weight=by_weight,
weight_function=weight_function,
check_weight=check_weight)
Expand Down Expand Up @@ -700,7 +714,7 @@ def all_simple_cycles(self, starting_vertices=None, rooted=False,
max_length=None, trivial=False,
weight_function=None, by_weight=False,
check_weight=True, report_weight=False,
algorithm='A'):
algorithm='B'):
r"""
Return a list of all simple cycles of ``self``. The cycles are
enumerated in increasing length order. Each edge must have a
Expand Down Expand Up @@ -741,7 +755,7 @@ def all_simple_cycles(self, starting_vertices=None, rooted=False,
a cycle is returned. Otherwise a tuple of cycle length and cycle is
returned.

- ``algorithm`` -- string (default: ``'A'``); the algorithm used to
- ``algorithm`` -- string (default: ``'B'``); the algorithm used to
enumerate the cycles.

- The algorithm ``'A'`` holds cycle iterators starting with each vertex,
Expand Down Expand Up @@ -773,20 +787,20 @@ def all_simple_cycles(self, starting_vertices=None, rooted=False,
sage: g.all_simple_cycles(max_length=6)
[[0, 1, 0], [0, 4, 0], [0, 5, 0], [1, 2, 1], [1, 6, 1], [2, 3, 2],
[2, 7, 2], [3, 4, 3], [3, 8, 3], [4, 9, 4], [5, 7, 5], [5, 8, 5],
[6, 8, 6], [6, 9, 6], [7, 9, 7], [0, 1, 2, 3, 4, 0],
[0, 1, 2, 7, 5, 0], [0, 1, 6, 8, 5, 0], [0, 1, 6, 9, 4, 0],
[0, 4, 3, 2, 1, 0], [0, 4, 3, 8, 5, 0], [0, 4, 9, 6, 1, 0],
[0, 4, 9, 7, 5, 0], [0, 5, 7, 2, 1, 0], [0, 5, 7, 9, 4, 0],
[0, 5, 8, 3, 4, 0], [0, 5, 8, 6, 1, 0], [1, 2, 3, 8, 6, 1],
[1, 2, 7, 9, 6, 1], [1, 6, 8, 3, 2, 1], [1, 6, 9, 7, 2, 1],
[2, 3, 4, 9, 7, 2], [2, 3, 8, 5, 7, 2], [2, 7, 5, 8, 3, 2],
[2, 7, 9, 4, 3, 2], [3, 4, 9, 6, 8, 3], [3, 8, 6, 9, 4, 3],
[6, 8, 6], [6, 9, 6], [7, 9, 7], [0, 1, 6, 8, 5, 0],
[0, 1, 6, 9, 4, 0], [0, 1, 2, 7, 5, 0], [0, 1, 2, 3, 4, 0],
[0, 4, 9, 7, 5, 0], [0, 4, 9, 6, 1, 0], [0, 4, 3, 8, 5, 0],
[0, 4, 3, 2, 1, 0], [0, 5, 8, 6, 1, 0], [0, 5, 8, 3, 4, 0],
[0, 5, 7, 2, 1, 0], [0, 5, 7, 9, 4, 0], [1, 2, 7, 9, 6, 1],
[1, 2, 3, 8, 6, 1], [1, 6, 9, 7, 2, 1], [1, 6, 8, 3, 2, 1],
[2, 3, 8, 5, 7, 2], [2, 3, 4, 9, 7, 2], [2, 7, 9, 4, 3, 2],
[2, 7, 5, 8, 3, 2], [3, 4, 9, 6, 8, 3], [3, 8, 6, 9, 4, 3],
[5, 7, 9, 6, 8, 5], [5, 8, 6, 9, 7, 5], [0, 1, 2, 3, 8, 5, 0],
[0, 1, 2, 7, 9, 4, 0], [0, 1, 6, 8, 3, 4, 0],
[0, 1, 6, 9, 7, 5, 0], [0, 4, 3, 2, 7, 5, 0],
[0, 1, 2, 7, 9, 4, 0], [0, 1, 6, 9, 7, 5, 0],
[0, 1, 6, 8, 3, 4, 0], [0, 4, 3, 2, 7, 5, 0],
[0, 4, 3, 8, 6, 1, 0], [0, 4, 9, 6, 8, 5, 0],
[0, 4, 9, 7, 2, 1, 0], [0, 5, 7, 2, 3, 4, 0],
[0, 5, 7, 9, 6, 1, 0], [0, 5, 8, 3, 2, 1, 0],
[0, 4, 9, 7, 2, 1, 0], [0, 5, 7, 9, 6, 1, 0],
[0, 5, 7, 2, 3, 4, 0], [0, 5, 8, 3, 2, 1, 0],
[0, 5, 8, 6, 9, 4, 0], [1, 2, 3, 4, 9, 6, 1],
[1, 2, 7, 5, 8, 6, 1], [1, 6, 8, 5, 7, 2, 1],
[1, 6, 9, 4, 3, 2, 1], [2, 3, 8, 6, 9, 7, 2],
Expand All @@ -798,8 +812,8 @@ def all_simple_cycles(self, starting_vertices=None, rooted=False,
sage: g = graphs.CompleteGraph(4).to_directed()
sage: g.all_simple_cycles()
[[0, 1, 0], [0, 2, 0], [0, 3, 0], [1, 2, 1], [1, 3, 1], [2, 3, 2],
[0, 1, 2, 0], [0, 1, 3, 0], [0, 2, 1, 0], [0, 2, 3, 0],
[0, 3, 1, 0], [0, 3, 2, 0], [1, 2, 3, 1], [1, 3, 2, 1],
[0, 1, 3, 0], [0, 1, 2, 0], [0, 2, 3, 0], [0, 2, 1, 0],
[0, 3, 2, 0], [0, 3, 1, 0], [1, 2, 3, 1], [1, 3, 2, 1],
[0, 1, 2, 3, 0], [0, 1, 3, 2, 0], [0, 2, 1, 3, 0],
[0, 2, 3, 1, 0], [0, 3, 1, 2, 0], [0, 3, 2, 1, 0]]

Expand All @@ -810,41 +824,39 @@ def all_simple_cycles(self, starting_vertices=None, rooted=False,
sage: g = graphs.CompleteGraph(20).to_directed()
sage: g.all_simple_cycles(max_length=2)
[[0, 1, 0], [0, 2, 0], [0, 3, 0], [0, 4, 0], [0, 5, 0], [0, 6, 0], [0, 7, 0],
[0, 8, 0], [0, 9, 0], [0, 10, 0], [0, 11, 0], [0, 12, 0], [0, 13, 0],
[0, 14, 0], [0, 15, 0], [0, 16, 0], [0, 17, 0], [0, 18, 0], [0, 19, 0],
[1, 2, 1], [1, 3, 1], [1, 4, 1], [1, 5, 1], [1, 6, 1], [1, 7, 1], [1, 8, 1],
[1, 9, 1], [1, 10, 1], [1, 11, 1], [1, 12, 1], [1, 13, 1], [1, 14, 1],
[1, 15, 1], [1, 16, 1], [1, 17, 1], [1, 18, 1], [1, 19, 1], [2, 3, 2],
[2, 4, 2], [2, 5, 2], [2, 6, 2], [2, 7, 2], [2, 8, 2], [2, 9, 2], [2, 10, 2],
[2, 11, 2], [2, 12, 2], [2, 13, 2], [2, 14, 2], [2, 15, 2], [2, 16, 2],
[2, 17, 2], [2, 18, 2], [2, 19, 2], [3, 4, 3], [3, 5, 3], [3, 6, 3],
[3, 7, 3], [3, 8, 3], [3, 9, 3], [3, 10, 3], [3, 11, 3], [3, 12, 3],
[3, 13, 3], [3, 14, 3], [3, 15, 3], [3, 16, 3], [3, 17, 3], [3, 18, 3],
[3, 19, 3], [4, 5, 4], [4, 6, 4], [4, 7, 4], [4, 8, 4], [4, 9, 4], [4, 10, 4],
[4, 11, 4], [4, 12, 4], [4, 13, 4], [4, 14, 4], [4, 15, 4], [4, 16, 4],
[4, 17, 4], [4, 18, 4], [4, 19, 4], [5, 6, 5], [5, 7, 5], [5, 8, 5],
[5, 9, 5], [5, 10, 5], [5, 11, 5], [5, 12, 5], [5, 13, 5], [5, 14, 5],
[5, 15, 5], [5, 16, 5], [5, 17, 5], [5, 18, 5], [5, 19, 5], [6, 7, 6],
[6, 8, 6], [6, 9, 6], [6, 10, 6], [6, 11, 6], [6, 12, 6], [6, 13, 6],
[6, 14, 6], [6, 15, 6], [6, 16, 6], [6, 17, 6], [6, 18, 6], [6, 19, 6],
[7, 8, 7], [7, 9, 7], [7, 10, 7], [7, 11, 7], [7, 12, 7], [7, 13, 7],
[7, 14, 7], [7, 15, 7], [7, 16, 7], [7, 17, 7], [7, 18, 7], [7, 19, 7],
[8, 9, 8], [8, 10, 8], [8, 11, 8], [8, 12, 8], [8, 13, 8], [8, 14, 8],
[8, 15, 8], [8, 16, 8], [8, 17, 8], [8, 18, 8], [8, 19, 8], [9, 10, 9],
[9, 11, 9], [9, 12, 9], [9, 13, 9], [9, 14, 9], [9, 15, 9], [9, 16, 9],
[9, 17, 9], [9, 18, 9], [9, 19, 9], [10, 11, 10], [10, 12, 10], [10, 13, 10],
[10, 14, 10], [10, 15, 10], [10, 16, 10], [10, 17, 10], [10, 18, 10],
[10, 19, 10], [11, 12, 11], [11, 13, 11], [11, 14, 11], [11, 15, 11],
[11, 16, 11], [11, 17, 11], [11, 18, 11], [11, 19, 11], [12, 13, 12],
[12, 14, 12], [12, 15, 12], [12, 16, 12], [12, 17, 12], [12, 18, 12],
[12, 19, 12], [13, 14, 13], [13, 15, 13], [13, 16, 13], [13, 17, 13],
[13, 18, 13], [13, 19, 13], [14, 15, 14], [14, 16, 14], [14, 17, 14],
[14, 18, 14], [14, 19, 14], [15, 16, 15], [15, 17, 15], [15, 18, 15],
[15, 19, 15], [16, 17, 16], [16, 18, 16], [16, 19, 16], [17, 18, 17],
[17, 19, 17], [18, 19, 18]]
[0, 8, 0], [0, 9, 0], [0, 10, 0], [0, 11, 0], [0, 12, 0], [0, 13, 0], [0, 14, 0],
[0, 15, 0], [0, 16, 0], [0, 17, 0], [0, 18, 0], [0, 19, 0], [1, 2, 1], [1, 3, 1],
[1, 4, 1], [1, 5, 1], [1, 6, 1], [1, 7, 1], [1, 8, 1], [1, 9, 1], [2, 3, 2],
[2, 4, 2], [2, 5, 2], [2, 6, 2], [2, 7, 2], [2, 8, 2], [2, 9, 2], [3, 4, 3],
[3, 5, 3], [3, 6, 3], [3, 7, 3], [3, 8, 3], [3, 9, 3], [4, 5, 4], [4, 6, 4],
[4, 7, 4], [4, 8, 4], [4, 9, 4], [5, 6, 5], [5, 7, 5], [5, 8, 5], [5, 9, 5],
[6, 7, 6], [6, 8, 6], [6, 9, 6], [7, 8, 7], [7, 9, 7], [8, 9, 8], [10, 1, 10],
[10, 2, 10], [10, 3, 10], [10, 4, 10], [10, 5, 10], [10, 6, 10], [10, 7, 10],
[10, 8, 10], [10, 9, 10], [11, 1, 11], [11, 2, 11], [11, 3, 11], [11, 4, 11],
[11, 5, 11], [11, 6, 11], [11, 7, 11], [11, 8, 11], [11, 9, 11], [11, 10, 11],
[12, 1, 12], [12, 2, 12], [12, 3, 12], [12, 4, 12], [12, 5, 12], [12, 6, 12],
[12, 7, 12], [12, 8, 12], [12, 9, 12], [12, 10, 12], [12, 11, 12], [13, 1, 13],
[13, 2, 13], [13, 3, 13], [13, 4, 13], [13, 5, 13], [13, 6, 13], [13, 7, 13],
[13, 8, 13], [13, 9, 13], [13, 10, 13], [13, 11, 13], [13, 12, 13], [14, 1, 14],
[14, 2, 14], [14, 3, 14], [14, 4, 14], [14, 5, 14], [14, 6, 14], [14, 7, 14],
[14, 8, 14], [14, 9, 14], [14, 10, 14], [14, 11, 14], [14, 12, 14], [14, 13, 14],
[15, 1, 15], [15, 2, 15], [15, 3, 15], [15, 4, 15], [15, 5, 15], [15, 6, 15],
[15, 7, 15], [15, 8, 15], [15, 9, 15], [15, 10, 15], [15, 11, 15], [15, 12, 15],
[15, 13, 15], [15, 14, 15], [16, 1, 16], [16, 2, 16], [16, 3, 16], [16, 4, 16],
[16, 5, 16], [16, 6, 16], [16, 7, 16], [16, 8, 16], [16, 9, 16], [16, 10, 16],
[16, 11, 16], [16, 12, 16], [16, 13, 16], [16, 14, 16], [16, 15, 16], [17, 1, 17],
[17, 2, 17], [17, 3, 17], [17, 4, 17], [17, 5, 17], [17, 6, 17], [17, 7, 17],
[17, 8, 17], [17, 9, 17], [17, 10, 17], [17, 11, 17], [17, 12, 17], [17, 13, 17],
[17, 14, 17], [17, 15, 17], [17, 16, 17], [18, 1, 18], [18, 2, 18], [18, 3, 18],
[18, 4, 18], [18, 5, 18], [18, 6, 18], [18, 7, 18], [18, 8, 18], [18, 9, 18],
[18, 10, 18], [18, 11, 18], [18, 12, 18], [18, 13, 18], [18, 14, 18], [18, 15, 18],
[18, 16, 18], [18, 17, 18], [19, 1, 19], [19, 2, 19], [19, 3, 19], [19, 4, 19],
[19, 5, 19], [19, 6, 19], [19, 7, 19], [19, 8, 19], [19, 9, 19], [19, 10, 19],
[19, 11, 19], [19, 12, 19], [19, 13, 19], [19, 14, 19], [19, 15, 19], [19, 16, 19],
[19, 17, 19], [19, 18, 19]]

sage: g = graphs.CompleteGraph(20).to_directed()
sage: g.all_simple_cycles(max_length=2, starting_vertices=[0])
sage: g.all_simple_cycles(max_length=2, starting_vertices=[0], algorithm='A')
[[0, 1, 0], [0, 2, 0], [0, 3, 0], [0, 4, 0], [0, 5, 0],
[0, 6, 0], [0, 7, 0], [0, 8, 0], [0, 9, 0], [0, 10, 0],
[0, 11, 0], [0, 12, 0], [0, 13, 0], [0, 14, 0], [0, 15, 0],
Expand All @@ -854,9 +866,9 @@ def all_simple_cycles(self, starting_vertices=None, rooted=False,
vertices (compare the following examples)::

sage: g = graphs.CompleteGraph(4).to_directed()
sage: g.all_simple_cycles(max_length=2, rooted=False)
sage: g.all_simple_cycles(max_length=2, rooted=False, algorithm='A')
[[0, 1, 0], [0, 2, 0], [0, 3, 0], [1, 2, 1], [1, 3, 1], [2, 3, 2]]
sage: g.all_simple_cycles(max_length=2, rooted=True)
sage: g.all_simple_cycles(max_length=2, rooted=True, algorithm='A')
[[0, 1, 0], [0, 2, 0], [0, 3, 0], [1, 0, 1], [1, 2, 1], [1, 3, 1],
[2, 0, 2], [2, 1, 2], [2, 3, 2], [3, 0, 3], [3, 1, 3], [3, 2, 3]]

Expand All @@ -865,12 +877,12 @@ def all_simple_cycles(self, starting_vertices=None, rooted=False,
sage: cycles = g.all_simple_cycles(weight_function=lambda e:e[0]+e[1],
....: by_weight=True, report_weight=True)
sage: cycles
[(2, [0, 1, 0]), (4, [0, 2, 0]), (6, [0, 1, 2, 0]), (6, [0, 2, 1, 0]),
(6, [0, 3, 0]), (6, [1, 2, 1]), (8, [0, 1, 3, 0]), (8, [0, 3, 1, 0]),
(8, [1, 3, 1]), (10, [0, 2, 3, 0]), (10, [0, 3, 2, 0]), (10, [2, 3, 2]),
(12, [0, 1, 2, 3, 0]), (12, [0, 1, 3, 2, 0]), (12, [0, 2, 1, 3, 0]),
(12, [0, 2, 3, 1, 0]), (12, [0, 3, 1, 2, 0]), (12, [0, 3, 2, 1, 0]),
(12, [1, 2, 3, 1]), (12, [1, 3, 2, 1])]
[(2.0, [0, 1, 0]), (4.0, [0, 2, 0]), (6.0, [0, 1, 2, 0]), (6.0, [0, 2, 1, 0]),
(6.0, [0, 3, 0]), (6.0, [1, 2, 1]), (8.0, [0, 1, 3, 0]), (8.0, [0, 3, 1, 0]),
(8.0, [1, 3, 1]), (10.0, [0, 2, 3, 0]), (10.0, [0, 3, 2, 0]), (10.0, [2, 3, 2]),
(12.0, [0, 1, 3, 2, 0]), (12.0, [0, 1, 2, 3, 0]), (12.0, [0, 2, 3, 1, 0]),
(12.0, [0, 2, 1, 3, 0]), (12.0, [0, 3, 2, 1, 0]), (12.0, [0, 3, 1, 2, 0]),
(12.0, [1, 2, 3, 1]), (12.0, [1, 3, 2, 1])]

The algorithm ``'B'`` can be used::

Expand Down
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