[(1, 2, 3), (1, 2, 4), (1, 3, 4), (2, 3, 4)]
>>> for i in range(0, 6): print(i, combo("help", i))
...
0 ['']
1 ['h', 'e', 'l', 'p']
2 ['he', 'hl', 'hp', 'el', 'ep', 'lp']
3 ['hel', 'hep', 'hlp', 'elp']
4 ['help']
5 []Finally, subset is just fixed-length permutations; order matters, so the result is larger
than for combo. In fact, calling subset with the length of the sequence is identical to
permute:
>>> subset([1, 2, 3], 3)
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
>>> subset('abc', 3)
['abc', 'acb', 'bac', 'bca', 'cab', 'cba']
>>> for i in range(0, 6): print(i, subset("help", i))
...
0 ['']
1 ['h', 'e', 'l', 'p']
2 ['he', 'hl', 'hp', 'eh', 'el', 'ep', 'lh', 'le', 'lp', 'ph', 'pe', 'pl']
3 ['hel', 'hep', 'hle', 'hlp', 'hpe', 'hpl', 'ehl', 'ehp', 'elh', 'elp', 'eph',
'epl', 'lhe', 'lhp', 'leh', 'lep', 'lph', 'lpe', 'phe', 'phl', 'peh', 'pel',
'plh', 'ple']
4 ['help', 'hepl', 'hlep', 'hlpe', 'hpel', 'hple', 'ehlp', 'ehpl', 'elhp',
'elph', 'ephl', 'eplh', 'lhep', 'lhpe', 'lehp', 'leph', 'lphe', 'lpeh',
'phel', 'phle', 'pehl', 'pelh', 'plhe', 'pleh']
5 ['help', 'hepl', 'hlep', 'hlpe', 'hpel', 'hple', 'ehlp', 'ehpl', 'elhp',
'elph', 'ephl', 'eplh', 'lhep', 'lhpe', 'lehp', 'leph', 'lphe', 'lpeh',
'phel', 'phle', 'pehl', 'pelh', 'plhe', 'pleh']These are some fairly dense algorithms (and frankly, may seem to require a Zen-like
“moment of clarity” to grasp completely), but they are not too obscure if you trace
through a few simple cases first. They’re also representative of the sort of operation
that requires custom data structure code—unlike the last stop on our data structures
tour in the next section.
Reversing and Sorting Sequences
The permutation utilities of the prior section are useful in a variety of applications, but
there are even more fundamental operations that might seem prime candidates for
automation. Reversing and sorting collections of values, for example, are core opera-
tions in a broad range of programs. To demonstrate coding techniques, and to provide
examples that yield closure for a recurring theme of this chapter, let’s take a quick look
at both of these in turn.
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