# Combinations(range(100), 100).list() takes forever

As title suggests, Combinations( range(100), 100 ).list() takes forever.

On the other hand, Combinations( range(100), 0 ).list() is pretty fast.

Is there anything I can do to improve the performance?

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PS. I am using itertools.combinations as an alternative.

( 2020-08-31 04:57:17 +0200 )edit

Remove .list() and just iterate over the set.

( 2020-08-31 09:14:30 +0200 )edit

That also hangs until one does ctrl-C.

( 2020-08-31 18:44:34 +0200 )edit

On macOS 10.14.6 Mojave, with Sage 9.2.beta9 built from source:

sage: C = Combinations(range(100), 100)
sage: C.cardinality()
1
sage: for c in C:
....:     print(c)
....:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31,
32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46,
47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61,
62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76,
77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91,
92, 93, 94, 95, 96, 97, 98, 99]
^C
Traceback (most recent call last)
...
KeyboardInterrupt:
src/cysignals/signals.pyx in cysignals.signals.python_check_interrupt()

( 2020-08-31 18:44:44 +0200 )edit

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The current implementation of the __iter__ method for Combinations is recursive and slow. A faster alternative is itertools.combinations or IntegerListsLex :

sage: C = IntegerListsLex(max_part=100-1, min_part=0, length=100, min_slope=1)
sage: %time C.list()
CPU times: user 9.4 ms, sys: 43 µs, total: 9.45 ms
Wall time: 9.41 ms
[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]]

more

Thank you; that will work.

( 2020-08-31 18:22:41 +0200 )edit

Deprecating the Combinations iterator is now tracked at

( 2020-09-01 16:29:36 +0200 )edit